,,the ,,thought ,,is ,,in ,,the ,,question ,,the ,,information ,,is ,,in ,,the ,,answer ,illustration3 ,,hawkins ,,electrical ,,guide ,,number ,,five ,,questions ,,answers ,,illustrations ,a ,,progressive ,,course ,,of ,,study ,,for ,,engineers1 ,,electricians1 ,,students ,,and ,,those ,,desiring ,,to ,,acquire ,a ,,working ,,knowledge ,,of ,,electricity ,,and ,,its ,,applications ,a ,,practical ,,treatise by ,,hawkins ,,and ,,staff ,illustration3 ,,theo4 ,,audel ,,co4 #gb ,,fifth ,,ave4 ,,new ,,york4 ,,copyrighted1 #aiad1 ,,by ,,theo4 ,,audel ,,co41 ,,new ,,york4 ,printed in the ,united ,states4 ,,table ,,of ,,contents ,,guide ,,no4 #e4 ,,alternating ,,currents #iig to #a1jff ,the word alternating--advantages of alternating current--direct current apparatus2 alternating current apparatus--disadvantages of alternating current--alternating current principles--the sine--application and construction of the sine curve--illustrated definitions3 cycle1 alternation1 amplitude1 period1 periodicity1 frequency--commercial frequencies--advantages of low frequency--phase--phase difference--phase displacement--synchronism--in phase--curves illustrating in phase and out of phase--illustrated definitions3 in phase2 in quadrature1 current leading2 in quadrature1 current lagging2 in opposition--maximum volts and amperes--average volts and amperes--elementary alternator developing one average volt--virtual volts and amperes--effective volts and amperes--relation between shape of wave and form factor--wave form--oscillograph wave form records--what determines wave form--effect of one coil per phase per pole--single phase current2 hydraulic analogy--two phase current2 hydraulic analogy--two phase current distribution--three phase current2 hydraulic analogy2 distribution--inductance--the henry--inductive and non-inductive coils--hydraulic analogy of inductance--inductance coil calculations--ohmic value of inductance--capacity3 hydraulic analogy--the farad--specific inductive capacity--condenser connections--ohmic value of capacity--lag and lead--mechanical analogy of lag--lag measurement--steam engine analogy of current flow at zero pressure--reactance--examples--choking coil--impedance curve--resonance--critical frequency--skin effect4 ,,alternating ,,current ,,diagrams #a1jfg to #a1ajj ,definitions3 impressed pressure1 active pressure1 self-induction pressure1 reverse pressure of self-induction--rate of change in current strength--properties of right angle triangles--equations of the right triangle--representation of forces by wires--parallelogram of forces2 the resultant--circuits containing resistance and inductance--graphical method of obtaining the impressed pressure--equations for ohmic drop and reactance drop--examples--diagram for impedance1 angle of lag1 etc4--circuits containing resistance and capacity--capacity in series1 and in parallel--amount of lead--action of condenser--the condenser pressure--capacity pressure--equation for impedance--- examples and diagrams--circuits containing resistance1 inductance1 and capacity--impedance equation--examples and diagrams--equation for impressed pressure--examples and diagrams4 ,,the ,,power ,,factor #a1aja to #a1abd ,definition of power factor--true watts--- apparent watts--ferry boat analogy of power factor--limits of power factor--effect of lag or lead--how to obtain the power curve--nature of the power curve--synchronism of current and pressure2 power factor unity--case of synchronism of current and pressure with power factor less than unity--steam engine analogy of power factor--wattless current2 power factor zero--examples of phase difference nearly #ij degrees--mechanical analogy of wattless current--why the power factor is equal to cos --graphical method of obtaining the active component--examples and diagrams--effect of capacity--diagrams illustrating why the power factor is unity when there is no resultant reactance in the circuit--usual value of power factor--power factor test--how alternators are rated2 kva4--curves illustrating power factor--how to keep the power factor high--why power factor is important in station operation--wattmeter method of three phase power measurement4 ,,alternators #a1abe to #a1ahf ,uses of alternators--classes of alternator--single phase alternators2 essential features2 width of armature coils--elementary single phase alternator--polyphase alternators--uses for two and three phase current--elementary three phase alternator--starting difficulty with single phase motors--six and twelve phase windings--belt or chain driven alternators--sub-base and ratchet device for tightening the belt--horse power transmitted by belts--best speeds for belts--advantages of chain drive2 objections--direct connected alternator--direct connected and direct coupled units--revolving armature alternators2 their uses--revolving field alternators--marine view showing that motion is purely a relative matter--essential parts of revolving field alternator--the terms stator and rotor--inductor alternators3 classes1 use1 defects--hunting or surging in alternators--amortisseur windings--monocyclic alternators--diagram of connections--teaser coil--armature reaction--distortion of field--strengthening and weakening effects--superpositions of fields--three phase reactions--magnetic leakage--field excitation of alternators--self-excited alternator--direct connected exciter--gear driven exciters--slow speed alternators--fly wheel alternators--high speed alternators--water wheel alternators--construction of rotor--turbine driven alternators--construction--step bearing--alternators of exceptional character--asynchronous alternators--image current alternators--extra high frequency alternators--self-exciting image current alternators4 ,,construction ,,of ,,alternators #a1ahg to #a1bff ,essential parts of an alternator--field magnets--methods of excitation3 self-excited1 separately excited1 compositely excited--magneto--construction of stationary magnets--revolving field--slip rings--spider for large alternator--provision for shifting armature to give access to field--armatures--core construction--advantages of slotted core armatures--armature windings--classification3 revolving and stationary windings--half coil and whole coil windings--concentrated or uni-coil winding2 features2 waveform--distributed or multi-coil windings3 breadth of coil1 partial and fully distributed coils--the ,kapp coefficient--general equation for voltage--wire1 strap1 and bar windings--condition1 governing type of inductor--coil covering--single and double layer multi-wire inductors and methods of placing them on the core--insulation--core stamping--single and multi-slot windings--- arrangement in slot of two layer bar winding--table of relative effectiveness of windings--single phase windings--advantage of half coil winding--two phase windings--shape of coil ends--three phase windings--shape of coil ends--kind of coil used with three phase windings--grouping of phases--two phase star connection--two phase mesh connection--three phase star connection--winding diagrams with star and connections--three phase connection--three phase winding with short coils--three phase lap winding star connection--three phase wave winding star connection--output of star and delta connected alternators--gramme ring armatures showing three phase star and mesh connections with direction of currents in the coils--features of star connection--characteristics of delta connection--proper ends to connect to star point--determination of path and value of currents in delta connection--points to be noted with ,y connection--diagram of ,y connection with return wire--chain or basket winding--skew winding--fed-in winding--imbricated winding--spiral winding--mummified winding--shuttle winding--creeping winding--turbine alternator winding3 how the high voltage is obtained with so few poles2 table of frequency and revolutions--turbine alternator construction--form of armature generally used--two pole radial slot field--parallel slot field--difficulty experienced with revolving armatures--how the field design is modified to reduce centrifugal force--examples of revolving fields4 ,,chapter ,,xlvi ,,alternating ,,currents ,the word alternating is used with a large number of electrical and magnetic quantities to denote that their magnitudes vary continuously1 passing repeatedly through a definite cycle of values in a definite interval of time4 ,as applied to the flow of electricity1 an alternating current may be defined as3 ,a current which reverses its direction in a periodic manner1 rising from zero to maximum strength1 returning to zero1 and then going through similar variations in strength in the opposite direction2 these changes comprise the cycle which is repeated with great rapidity4 ,the properties of alternating currents are more complex than those of continuous currents1 and their behavior more difficult to predict4 ,this arises from the fact that the magnetic effects are of far more importance than those of steady currents4 ,with the latter the magnetic effect is constant1 and has no reactive influence on the current when the latter is once established4 ,the lines of force1 however1 produced by alternating currents are changing as rapidly as the current itself1 and they thus induce electric pressures in neighboring circuits1 and even in adjacent parts of the same circuit4 ,this inductive influence in alternating currents renders their action very different from that of continuous current4 ,ques4 ,what are the advantages of alternating current over direct current8 ,ans4 ,the reduced cost of transmission by use of high voltages and transformers1 greater simplicity of generators and motors1 facility of transforming from one voltage to another 7either higher or lower7 for different purposes4 ,illustration3 ,,figs4 #a1bjf to #a1bab4--;,apparatus which operates successfully on a direct current circuit4 ,the direct current will operate incandescent lamps1 arc lamps1 electric heating apparatus1 electro-plating and typing bath1 direct current motors2 charge storage batteries1 produce electro-chemical action4 ,it will flow through a straight wire or just as freely through the same wire when wound over an iron bar4 ,illustration3 ,,figs4 #a1bac to #a1bag4--;,apparatus which operates successfully on an alternating circuit4 ,the alternating current will operate incandescent lamps1 arc lamps1 electric heating apparatus1 alternating current motors4 ,it will flow through a straight wire with slightly increased retarding effect1 but if the wire be wound on an iron bar its strength is greatly reduced4 ,the size of wire needed to transmit a given amount of electrical energy 7watts7 with a given percentage of drop1 being inversely proportional to the square of the voltage employed1 the great saving in copper by the use of alternating current at high pressure must be apparent4 ,this advantage can be realized either by a saving in the weight of wire required1 or by transmitting the current to a greater distance with the same weight of copper4 ,in alternating current electric lighting1 the primary voltage is usually at least #a1jjj and often #b1jjj to #aj1jjj volts4 ,ques4 ,why is alternating current used instead of direct current on constant pressure lighting circuits8 ,ans4 ,it is due to the greater ease with which the current can be transformed from higher to lower pressures4 ,ques4 ,how is this accomplished8 ,ans4 ,by means of simple transformers1 consisting merely of two or more coils of wire wound upon an iron core4 ,since there are no moving parts1 the attention required and the likelihood of the apparatus getting out of order are small4 ,the apparatus necessary for direct current consists of a motor dynamo set which is considerably more costly than a transformer and not so efficient4 ,ques4 ,what are some of the disadvantages of alternating current8 ,ans4 ,the high pressure at which it is used renders it dangerous1 and requires more efficient insulation2 alternating current cannot be used for such purposes as electro-plating1 charging storage batteries1 etc4 ,illustration3 ,,fig4 #a1bah4--;,application and construction of the sine curve4 ,the sine curve is a wavelike curve used to represent the changes in strength and direction of an alternating current4 ,at the left of the figure is shown an elementary alternator1 consisting of a loop of wire ,,abcd1 whose ends are attached to the ring ,f1 and shaft ,g1 being arranged to revolve in a uniform magnetic field1 as indicated by the vertical arrows representing magnetic lines at equidistances4 ,the alternating current induced in the loop is carried to the external circuit through the brushes ,m and ,s4 ,the loop1 as shown1 is in its horizontal position at right angles to the magnetic field4 ,the dotted circle indicates the circular path described by ,,ab or ,,cd during the revolution of the loop4 ,now1 as the loop rotates1 the induced electric pressure will vary in such a manner that its intensity at any point of the rotation is proportional to the sine of the angle corresponding to that point4 ,hence1 on the horizontal line which passes through the center of the dotted circle1 take any length as #jh1 and divide into any number of equal parts representing fractions of a revolution1 as #j1 #ij1 #ahj1 etc4 ,erect perpendiculars at these points1 and from the corresponding points on the dotted circle project lines 7parallel to #jh7 to the perpendiculars2 these intersections give points1 on the sine curve1 for instance1 through #b at the #ij point of the revolution of the loop1 and projecting over to the corresponding perpendicular gives #b'b1 whose length is proportional to the electric pressure at that point4 ,in like manner other points are obtained1 and the curved line through them will represent the variation in the electric pressure for all points of the revolution4 ,at #ij the pressure is at a maximum1 hence by using a pressure scale such that the length of the perpendicular #b'b for #ij will measure the maximum pressure1 the length of the perpendicular at any other point will represent the actual pressure at that point4 ,the curve lies above the horizontal axis during the first half of the revolution and below it during the second half1 which indicates that the current flows in one direction for a half revolution1 and in the opposite direction during the remainder of the revolution4 ,alternating ,current ,principles4--,in the operation of a direct current generator or dynamo1 as explained in ,chapter ,,xiii1 alternating currents are generated in the armature winding and are changed into direct current by the action of the commutator4 ,it was therefore necessary in that chapter1 in presenting the basic principles of the dynamo1 to explain the generation of alternating currents at length1 and the graphic method of representing the alternating current cycle by the sine curve4 ,in order to avoid unnecessary repetition1 the reader should carefully review the above mentioned chapter before continuing further4 ,the diagram fig4 #afh1 showing the construction and application of the sine curve to the alternating current1 is however for convenience here shown enlarged 7fig4 #a1bah74 ,in the diagram the various alternating current terms are graphically defined4 ,illustration3 ,,fig4 #a1bai--;,diagram illustrating the sine of an angle4 ,in order to understand the sine curve1 it is necessary to know the meaning of the sine of an angle4 ,this is defined as the ratio of the perpendicular let fall from any point in one side of the angle to the other side divided by the hypotenuse of the triangle thus formed4 ,for instance1 in the diagram1 let ,,ad and ,,ae be the two sides of the angle 1 and ,,de a perpendicular let fall from any point ,d of the side ,,ad to the other side ,,ae4 ,then1 the sine of the angle 7written sin 7 ,,de ,,ad4 ,it is evident that if the perpendicular be let fall at a unit's distance from the apex ,a1 as at ,b1 ,,bc ,,bc ,sin -- -- ,,bc ,,ab #a ,this line ,,bc is called the natural sine of the angle1 and its values for different angles are given in the table on page #dea4 ,illustration3 ,,fig4 #a1bbj4--;,diagram illustrating the equation of the sine curve3 y sin 4 y is any ordinate1 and 1 the angle which the coil makes with the horizontal line1 corresponding to the particular value of y taken4 ,the alternating current1 as has been explained1 rises from zero to a maximum1 falls to zero1 reverses its direction1 attains a maximum in the new direction1 and again returns to zero2 this comprises the cycle4 ,this series of changes can best be represented by a curve1 whose absciss represent time1 or degrees of armature rotation1 and whose ordinates1 either current or pressure4 ,the curve usually chosen for this purpose is the sine curve1 as shown in fig4 #a1bah1 because it closely agrees with that given by most alternators4 ,the equation of the sine curve is y sin in which y is any ordinate1 and 1 the angle of the corresponding position of the coil in which the current is being generated as illustrated in fig4 #a1bbj4 ,ques4 ,what is an alternation8 ,ans4 ,the changes which the current undergoes in rising from zero to maximum pressure and returning back to zero2 that is1 a single positive or negative wave or half period1 as shown in fig4 #a1bba4 ,illustration3 ,,fig4 #a1bba4--;,diagram showing one alternation of the current in which the latter varies from zero to maximum and back to zero while the generating loop ,,abcd makes one half revolution4 ,ques4 ,what is the amplitude of the current8 ,ans4 ,the greatest value of the current strength attained during the cycle4 ,the foregoing definitions are also illustrated in fig4 #a1bah4 ,illustration3 ,,fig4 #a1bbb4--;,diagram illustrating amplitude of the current4 ,the current reaches its amplitude or maximum value in one quarter period from its point of zero value1 as1 for instance1 while the generating loop moves from position ,,abcd to ,a',b',c',d'4 ,at three-quarter revolution1 the current reaches its maximum value in the opposite direction4 ,ques4 ,define the term period4 ,ans4 ,this is the time of one cycle of the alternating current4 ,ques4 ,what is periodicity8 ,ans4 ,a term sometimes used for frequency4 ,frequency4--,if a slowly varying alternating current be passed through an incandescent lamp1 the filament will be seen to vary in brightness1 following the change of current strength4 ,if1 however1 the alternations take place more rapidly than about #ej to #fj per second1 the eye cannot follow the variations and the lamp appears to burn steadily4 ,hence it is important to consider the rate at which the alternations take place1 or as it is called1 the frequency1 which is defined as3 the number of cycles per second4 ,illustration3 ,,fig4 #a1bbc4--;,diagram of alternator and engine1 illustrating frequency4 ,the frequency or cycles per second is equal to the revolution of armature per second multiplied by one-half the number of poles per phase4 ,in the figure the armature makes #f revolutions to one of the engine2 one-half the number of poles #h #b #d1 hence frequency 7#aej #d #f7 #fj #fj4 ,the expression in the parenthesis gives the cycles per minute1 and dividing by #fj1 the cycles per second4 ,in a two pole machine1 the frequency is the same as the number of revolutions per second1 but in multipolar machines1 it is greater in proportion to the number of pairs of poles per phase4 ,thus1 in an #h pole machine1 there will be four cycles per revolution4 ,if the speed be #ijj revolutions per minute1 the frequency is #h #ijj - --- #fj #b #fj ,the symbol is read cycles per second4 ,ques4 ,what frequencies are used in commercial machines8 ,ans4 ,the two standard frequencies are #be and #fj cycles4 ,illustration3 ,,fig4 #a1bbd--;,diagram answering the question3 ,why are alternators always built multipolar8 ,they are made multipolar because it is desirable that the frequency be high4 ,it is evident from the figure that to obtain high frequency would require too many revolutions of the armature of a bipolar machine for mechanical safety--especially in large alternators4 ,moreover a double reduction gear in most cases would be necessary1 adding complication to the drive4 ,comparing the above illustration with fig4 #a1bbc1 shows plainly the reason for multipolar construction4 ,ques4 ,for what service are these frequencies adapted8 ,ans4 ,the #be cycle frequency is used for conversion to direct current1 for alternating current railways1 and for machines of large size2 the #fj cycle frequency is used for general distribution for lighting and power4 ,the frequency of #dj cycles1 which once was introduced as a compromise between #be and #fj has been found not desirable1 as it is somewhat low for general distribution1 and higher than desirable for conversion to direct current4 ,illustration3 ,,fig4 #a1bbe4--;,diagram illustrating phase4 ,in wave1 vibratory1 and simple harmonic motion1 phase may be defined as3 the portion of one complete vibration1 measured either in angle or in time1 that any moving point has executed4 ,ques4 ,what are the advantages of low frequency8 ,ans4 ,the number of revolutions of the rotor is correspondingly low2 arc lamps can be more readily operated2 better pressure regulation2 small motors such as fan motors can be operated more easily from the circuit4 ,phase4--,as applied to an alternating current1 phase denotes the angle turned through by the generating element reckoned from a given instant4 ,phase is usually measured in degrees from the initial position of zero generation4 ,if in the diagram fig4 #a1bbe1 the elementary armature or loop be the generating element1 and the curve at the right be the sine curve representing the current1 then the phase of any point p will be the angle or angle moved through from the horizontal line1 the starting point4 ,ques4 ,what is phase difference8 ,ans4 ,the angle between the phases of two or more alternating current quantities as measured in degrees4 ,ques4 ,what is phase displacement8 ,ans4 ,a change of phase of an alternating pressure or current4 ,illustration3 ,,figs4 #a1bbf and #a1bbg4--;,diagram and sine curves illustrating synchronism4 ,if two alternators1 with coils in parallel planes1 be made to rotate at the same speed by connecting them with chain drive or equivalent means1 they will then be in synchronism that is1 the alternating pressure or current in one will vary in step with that in the other4 ,in other words1 the cycles of one take place with the same frequency and at the same time as the cycles of the other as indicated by the curves1 fig4 #a1bbf4 ,it should be noted that the maximum values are not necessarily the same but the maximum and zero values must occur at the same time in both machines1 and the maximum value must be of the same sign4 ,if the waves be distorted the maximum values may not occur simultaneously4 ,see fig4 #a1cdh4 ,synchronism4--,this term may be defined as3 the simultaneous occurrence of any two events4 ,thus two alternating currents or pressures are said to be in synchronism when they have the same frequency and are in phase4 ,ques4 ,what does the expression in phase mean8 ,ans4 ,two alternating quantities are said to be in phase1 when there is no phase difference between2 that is when the angle of phase difference equals zero4 ,thus the current is said to be in phase with the pressure when it neither lags nor leads1 as in fig4 #a1bbh4 ,a rotating cylinder1 or the movement of an index or trailing arm is brought into synchronism with another rotating cylinder or another index or trailing arm1 not only when the two are moving with exactly the same speed1 but when in addition they are simultaneously moving over similar portions of their respective paths4 ,illustration3 ,,fig4 #a1bbh--,pressure and current curves illustrating the term in phase4 ,the current is said to be in phase with the pressure when it neither lags nor leads4 ,when there is phase difference1 as between current and pressure1 they are said to be out of phase the phase difference being measured as in fig4 #a1bbi by the angle 4 ,illustration3 ,,fig4 #a1bbi--,pressure and current curves illustrating the term out of phase4 ,the current is said to be out of phase with the pressure when it either lags or leads1 that is when the current is not in synchronism with the pressure4 ,in practice the current and pressure are nearly always out of phase4 ,when the phase difference is #ij as in fig4 #a1bca or #a1bcb1 the two alternating quantities are said to be in quadrature2 when it is #ahj1 as in fig4 #a1bcc1 they are said to be in opposition4 ,when they are in quadrature1 one is at a maximum when the other is at zero2 when they are in opposition1 one reaches a positive maximum when the other reaches a negative minimum1 being at each instant opposite in sign4 ,ques4 ,what is a departure from synchronism called8 ,ans4 ,loss of synchronism4 ,illustration3 ,,figs4 #a1bcj to #a1bcc4--;,curves showing some phase relations between current and pressure4 ,fig4 #a1bcj1 synchronism of current and pressure1 expressed by the term in phase1 meaning simultaneous zero values1 and simultaneous maximum values of the same sign2 fig4 #a1bca1 in quadrature1 current leading #ij2 fig4 #a1bcb in quadrature1 current lagging #ij2 fig4 #a1bcc1 in opposition1 meaning that the phase different between current and pressure is #ahj4 ,maximum ,volts and ,amperes4--,in the operation of an alternator1 the pressure and strength of the current are continually rising1 falling and reversing4 ,during each cycle there are two points at which the pressure or current reaches its greatest value1 being known as the maximum value4 ,this maximum value is not used to any great extent1 but it shows the maximum to which the pressure rises1 and hence1 the greatest strain to which the insulation of the alternator is subjected4 ,illustration3 ,,fig4 #a1bcd4--;,elementary alternator developing one average volt4 ,if the loop make one revolution per second1 and the maximum number of lines of force embraced by the loop in the position shown 7the zero position7 be denoted by ,n1 then each limb will cut #b,n lines per second1 because it cuts every line during the right sweep and again during the left sweep4 ,hence each limb develops an average pressure of #b,n units 7,c4,g4,s4 units71 and as both limbs are connected in series1 the total pressure is #d,n units per revolution4 ,now1 if the loop make f revolutions per second instead of only one1 then f times as many lines will be cut per second1 and the average pressure will be #d,n f units4 ,since the ,c4,g4,s4 unit of pressure is so extremely small1 a much greater practical unit called the volt is used1 which is equal to #ajj1jjj1jjj1 or #aj ,c4,g4,s4 units is employed4 ,hence average voltage #d,nf #aj4 ,the value of ,n in actual machines is very high1 being several million lines of force4 ,the illustration shows one set of conditions necessary to generate one average volt4 ,the maximum pressure developed is #a 4#fcg #a4eg volts2 virtual pressure #a4eg 4#gjg #a4aa volts4 ,average ,volts and ,amperes4--,since the sine curve is used to represent the alternating current1 the average value may be defined as3 the average of all the ordinates of the curve for one-half of a cycle4 ,ques4 ,of what use is the average value8 ,ans4 ,it is used in some calculations but1 like the maximum value1 not very often4 ,the relation between the average and virtual value is of importance as it gives the form factor4 ,virtual ,volts and ,amperes4--,the virtual#a value of an alternating pressure or current is equivalent to that of a direct pressure or current which would produce the same effect2 those effects of the pressure and current are taken which are not affected by rapid changes in direction and strength1--in the case of pressure1 the reading of an electrostatic voltmeter1 and in the case of current1 the heating effect4 #a ,,note4--,i adhere to the term virtual1 as it was in use before the term efficace which was recommended in #ahhi by the ,paris ,congress to denote the square root of mean square value4 ,the corresponding ,english adjective is efficacious2 but some engineers mistranslate it with the word effective4 ,i adhere to the term virtual mainly because the adjective effective is required in its usual meaning in kinematics to represent the resolved part of a force which acts obliquely to the line of motion1 the effective force being the whole force multiplied by the cosine of the angle at which it acts with respect to the direction of motion4 ,some authors use the expression ',r4,m4,s4 value' 7meaning 'root mean square'7 to denote the virtual or quadratic mean value4--,s4 ,p4 ,thompson4 ,illustration3 ,,fig4 #a1bce4--,maximum and average values of the sine curve4 ,the average value of the sine curve is represented by an ordinate ,,ms of such length that when multiplied by the base line ,,fg1 will give a rectangle ,,mfsg whose area is equal to that included between the curve and base line ,,fdgs4 ,illustration3 ,,fig4 #a1bcf4--;,diagram illustrating virtual volts and amperes4 ,the word virtual is defined as3 ,being in essence or effect1 not in fact2 not actual1 but equivalent1 so far as effect is concerned4 ,as applied to the alternating current1 it denotes an imaginary direct current of such value as will produce an effect equivalent to that of the alternating current4 ,thus1 a virtual pressure of #a1jjj volts is one that would produce the same deflection in an electrostatic voltmeter as a direct pressure of #a1jjj volts3 a virtual current of #aj amperes is that current which would produce the same heating effect as a direct current of #aj amperes4 ,both pressure and current vary continually above and below the virtual values in alternating current circuits4 ,distinction should be made between the virtual and effective values of an alternating current4 ,see fig4 #a1bcg4 ,the word effective is commonly used erroneously for virtual4 ,see note page #a1jaa4 ,the attraction 7or repulsion7 in electrostatic voltmeters is proportional to the square of the volts4 ,the readings which these instruments give1 if first calibrated by using steady currents1 are not true means1 but are the square roots of the means of the squares4 ,now the mean of the squares of the sine 7taken over either one quadrant or a whole circle7 is 2 hence the square root of mean square value of the sine functions is obtained by multiplying their maximum value by #a #b1 or by #j4gjg4 ,the arithmetical mean of the values of the sine1 however1 is #j4fcg4 ,hence an alternating current1 if it obey the sine law1 will produce a heating effect greater than that of a steady current of the same average strength1 by the ratio of #j4gjg to #j4fcg2 that is1 about #a4aa times greater4 ,if a ,cardew voltmeter be placed on an alternating circuit in which the volts are oscillating between maxima of #ajj and -#ajj volts1 it will read #gj4g volts1 though the arithmetical mean is really only #fc4g2 and #gj4g steady volts would be required to produce an equal reading4 ,illustration3 ,,fig4 #a1bcg4--;,diagram illustrating virtual and effective pressure4 ,if the coil be short circuited by the switch and a constant virtual pressure be impressed on the circuit1 the whole of the impressed pressure will be effective in causing current to flow around the circuit4 ,in this case the virtual and effective pressures will be equal4 ,if the coil be switched into circuit1 the reverse pressure due to self induction will oppose the virtual pressure2 hence1 the effective pressure 7which is the difference between the virtual and reverse pressures7 will be reduced1 the virtual or impressed pressure remaining constant all the time4 ,a virtual current is that indicated by an ammeter regardless of the phase relation between current and pressure4 ,an effective current is that indicated by an ammeter when the current is in phase with the pressure4 ,in practice1 the current is hardly ever in phase with the pressure1 usually lagging1 though sometimes leading in phase4 ,now the greater this phase difference1 either way1 the less is the power of a given virtual current to do work4 ,with respect to this feature1 effective current may be defined as3 that proportion of a given virtual current which can do useful work4 ,if there be no phase difference1 then effective current is equal to virtual current4 ,the matter may be looked at in a different way4 ,if an alternating current is to produce in a given wire the same amount of effect as a continuous current of #ajj amperes1 since the alternating current goes down to zero twice in each period1 it is clear that it must at some point in the period rise to a maximum greater than #ajj amperes4 ,how much greater must the maximum be8 ,the answer is that1 if it undulate up and down with a pure wave form1 its maximum must be #b times as great as the virtual mean2 or conversely the virtual amperes will be equal to the maximum divided by #b4 ,in fact1 to produce equal effect1 the equivalent direct current will be a kind of mean between the maximum and the zero value of the alternating current2 but it must not be the arithmetical mean1 nor the geometrical mean1 nor the harmonic mean1 but the quadratic mean2 that is1 it will be the square root of the mean of the squares of all the instantaneous values between zero and maximum4 ,effective ,volts and ,amperes4--,virtual pressure1 although already explained1 may be further defined as the pressure impressed on a circuit4 ,now1 in nearly all circuits the impressed or virtual pressure meets with an opposing pressure due to inductance and hence the effective pressure is something less than the virtual1 being defined as that pressure which is available for driving electricity around the circuit1 or for doing work4 ,the difference between virtual and effective pressure is illustrated in fig4 #a1bcg4 ,ques4 ,does a given alternating voltage affect the insulation of the circuit differently than a direct pressure of the same value8 ,ans4 ,it puts more strain on the insulation in the same proportion as the maximum pressure exceeds the virtual pressure4 ,illustration3 ,,fig4 #a1bch4--;,current or pressure curve illustrating form factor4 ,it is simply the virtual value divided by the average value4 ,for a sine wave the virtual value is #a _/ #b times the maximum1 and the average is #b _/ times the maximum1 so that the form factor is _/ #bb or #a4aa4 ,the induction wave which generates an alternating pressure wave has a maximum value proportional to the area1 that is1 to the average value of the pressure wave4 ,hence the induction values corresponding to two pressure waves whose virtual values are equal1 will be inversely proportional to their form factors4 ,this is illustrated by the fact that a peaked wave causes less hysteresis loss in a transformer core than a flat topped wave1 owing to the higher form factor of the peaked wave4 ,see wave forms1 figs4 #a1bde to #a1bdh4 ,form ,factor4--,this term was introduced by ,fleming1 and denotes the ratio of the virtual value of an alternating wave to the average value4 ,that is virtual value 4#gjg form factor ------------- ---- #a4aa average value 4#fcg ,ques4 ,what does this indicate8 ,ans4 ,it gives the relative heating effects of alternating and direct currents1 as illustrated in figs4 #a1bci and #a1bdj4 ,that is1 the alternating current will have about #aa per cent4 more heating power than the direct current which is of the same average strength4 ,if an alternating current voltmeter be placed upon a circuit in which the volts range from #ajj to -#ajj1 it will read #gj4g volts1 although the arithmetical average1 irrespective of or-sign1 is only #fc4g volts4 ,if the voltmeter be connected to a direct current circuit1 the pressure necessary to give the same reading would be #gj4g volts4 ,illustration3 ,,figs4 #a1bci and #a1bdj4--,relative heating effects of alternating and direct currents4 ,if it takes say five minutes to produce a certain heating effect with alternating current at say #fc4g average volts1 it will take #cc seconds longer with direct current at the same pressure1 that is1 the alternating current has about #aa per cent4 more heating power than the direct current of the same average pressure4 ,the reader should be careful not to get a wrong conception of the above2 it does not mean that there is a saving by using alternating current4 ,when both voltmeters read the same1 that is1 when the virtual pressure of the alternating current is the same as the direct current pressure1 the heating effect is of course the same4 ,ques4 ,what is the relation between the shape of the wave curve and the form factor8 ,ans4 ,the more peaked the wave1 the greater the value of its form factor4 ,a form factor of units would correspond to a rectangular wave2 this is the least possible value of the form factor1 and one which is not realized in commercial machines4 ,illustration3 ,,figs4 #a1bda to #a1bdd4--,various forms of pressure or current waves4 ,figs4 #a1bda to #a1bdc show the general shape of the waves produced by some alternators used largely for lighting work and having toothed armatures4 ,the effect of the slots and shape of pole pieces is here very marked4 ,fig4 #a1bdd shows a wave characteristic of large alternators designed for power transmission and having multi-slot or distributed windings4 ,wave ,form4--,there is always more or less irregularity in the shape of the current waves as met in practice1 depending upon the construction of the alternator4 ,the ideal wave curve is the so called true sine wave1 and is obtained with a rate of cutting of lines of force1 by the armature coils1 equivalent to the swing of a pendulum1 which increases in speed from the end to the middle of the swing1 decreasing at the same rate after passing the center4 ,this swing is expressed in physics1 as simple harmonic motion4 ,illustration3 ,,figs4 #a1bde and #a1bdf4--,resolution of complex curves into sine curves4 ,the heavy curve can be resolved into the simpler curves ,a and ,b shown in ,no4 #a1 the component curves ,a and ,b have in the ratio of three to one2 that is1 curve ,b has three times as many periods per second as curve ,a4 ,all the curves1 however1 cross the zero line at the same time1 and the resultant curve1 though curiously unlike either of them1 has a certain symmetry4 ,in ,no4 #b the component curves1 besides having periods in the ratio of three to one1 cross the zero line at different points4 ,the resultant curve produced is still less similar to its components1 and is curiously and unsymmetrically humped4 ,at first sight it is difficult to believe that such a curious curve could be resolved into two such simple and symmetrical ones4 ,in both figures the component curves are sine curves1 and as the curves for sine and cosine functions are exactly similar in form1 the simplest supposition that can be made for the variation of pressure or of current is that both follow a sine law4 ,illustration3 ,,fig4 #a1bdg4--,reproduction of oscillograph record of wave form of alternator with one coil per phase per pole4 ,here the so-called super-imposed harmonic is clearly indicated4 ,illustration3 ,,fig4 #a1bdh4--,reproduction of oscillograph record of ,wagner alternator having three coils per phase per pole4 ,the losses in all secondary apparatus are slightly lower with the so called peaked form of wave4 ,for the same virtual voltage1 however1 the top of the peak will be much higher1 thereby submitting the insulation to that much greater strain4 ,by reason of the fact that the losses are less under such wave forms1 many manufacturers in submitting performance data on transformers recite that the figures are for sine wave conditions1 stating further that if the transformers are to be operated in a circuit more peaked than the sine wave1 the losses will be less than shown4 ,the slight saving in the losses of secondary apparatus1 obtained with a peaked wave1 by no means compensates for the increased insulation strains and an alternator having a true sine wave is preferred4 ,ques4 ,what determines the form of the wave8 ,ans4 #a4 ,the number of coils per phase per pole1 #b1 shape of pole faces1 #c1 eddy currents in the pole pieces1 and #d1 the air gap4 ,ques4 ,what are the requirements for proper rate of cutting of the lines of force8 ,ans4 ,it is necessary to have1 as a minimum1 two coils per phase per pole in three phase work4 ,ques4 ,what is the effect of only one coil per phase per pole8 ,ans4 ,the wave form will be distorted as shown in fig4 #a1bdg4 ,ques4 ,what is the least number of coils per phase per pole that should be used for two and three phase alternators8 ,ans4 ,for three phase1 two coils1 and for two phase1 three coils1 per phase per pole4 ,single or ,monophase ,current4--,this kind of alternating current is generated by an alternator having a single winding on its armature4 ,two wires1 a lead and return1 are used as in direct current4 ,an elementary diagram showing the working principles is illustrated in fig4 #a1bdi1 a similar hydraulic cycle being shown in figs4 #a1bej to #a1beb4 ,illustration3 ,,fig4 #a1bdi4--;,elementary one loop alternator and sine curve illustrating single phase alternating current4 ,there are three points during the revolution at which there is no current3 at #j the position shown1 #ahj1 and #cfj2 in other words1 at the beginning1 middle point and end of the cycle4 ,the current reaches a maximum at #ij1 reverses at #ahj1 and reaches a maximum in the reverse direction at #bgj4 ,two ,phase ,current4--,in most cases two phase current actually consists of two distinct single phase currents flowing in separate circuits4 ,there is often no electrical connection between them2 they are of equal period and equal amplitude1 but differ in phase by one quarter of a period4 ,with this phase relation one of them will be at a maximum when the other is at zero4 ,two phase current is illustrated by sine curves in fig4 #a1bec1 and by hydraulic analogy in figs4 #a1bed and #a1bee4 ,illustration3 ,,figs4 #a1bej to #a1beb4--;,hydraulic analogy illustrating the difference between direct 7continuous7 and alternating current4 ,in fig4 #a1bej a centrifugal pump ,c forces water to the upper pipe1 from which it falls by gravity to the lower pipe ,b and re-enters the pump4 ,the current is continuous1 always flowing in one direction1 that is1 it does not reverse its direction4 ,similarly a direct electric current is constant in direction 7does not reverse72 though not necessarily constant in value4 ,a direct current1 constant in both value and direction as a result of constant pressure1 is called continuous current4 ,similarly in the figure the flow is constant1 and a gauge ,d placed at any point will register a constant pressure1 hence the current may be called1 in the electrical sense1 continuous4 ,the conditions in fig4 #a1bea are quite different4 ,the illustration represents a double acting cylinder with the ends connected by a pipe ,a1 and the piston driven by crank and ,scotch yoke as shown4 ,in operation1 if the cylinder and pipe be full of water1 a current of water will begin to flow through the pipe in the direction indicated as the piston begins its stroke1 increasing to maximum velocity at one-quarter revolution of the crank1 decreasing and coming to rest at one-half revolution1 then reversing and reaching maximum velocity in the reverse direction at three-quarter revolution1 and coming to rest again at the end of the return stroke4 ,a pressure gauge at ,g will register a pressure which varies with the current4 ,since the alternating electric current undergoes similar changes1 the sine curve will apply equally as well to the pump cycle as to the alternating current cycle4 ,illustration3 ,,fig4 #a1bec4--;,elementary two loop alternator and sine curves1 illustrating two phase alternating current4 ,if the loops be placed on the alternator armature at #ij magnetic degrees1 a single phase current will be generated in each of the windings1 the current in one winding being at its maximum value when the other is at zero4 ,in this case four transmission conductors are generally used1 two for each separate circuit1 and the motors to which the current is led have a double winding corresponding to that on the alternator armature4 ,if two identical simple alternators have their armature shafts coupled in such a manner1 that when a given armature coil on one is directly under a field pole1 the corresponding coil on the other is midway between two poles of its field1 the two currents generated will differ in phase by a half alternation1 and will be two phase current4 ,ques4 ,how must an alternator be constructed to generate two phase current8 ,ans4 ,it must have two independent windings1 and these must be so spaced out that when the volts generated in one of the two phases are at a maximum1 those generated in the other are at zero4 ,in other words1 the windings1 which must be alike1 of an equal number of turns1 must be displaced along the armature by an angle corresponding to one-quarter of a period1 that is1 to half the pole pitch4 ,illustration3 ,,figs4 #a1bed and #a1bee4--;,hydraulic analogy illustrating two phase alternating current4 ,in the figure two cylinders1 similar to the one in fig4 #a1bea1 are shown1 operated from one shaft by crank and ,scotch yoke drive4 ,the cranks are at #ij as shown1 and the cylinders and connecting pipes full of water4 ,in operation1 the same cycle of water flow takes place as in fig4 #a1bea4 ,since the cranks are at #ij1 the second piston is one-half stroke behind the first2 the flow of water in ,no4 #a 7phase ,a7 is at a maximum when the flow in ,no4 #b 7phase ,b7 comes to rest1 the current conditions in both pipes for the entire cycle being represented by the two sine curves whose phase difference is #ij4 ,comparing these curves with fig4 #a1bec1 it will be seen that the water and electric current act in a similar manner4 ,the windings of the two phases must1 of course1 be kept separate1 hence the armature will have four terminals1 or if it be a revolving armature it will have four collector rings4 ,as must be evident the phase difference may be of any value between #j and #cfj1 but in practice it is almost always made #ij4 ,ques4 ,in what other way may two phase current be generated8 ,ans4 ,by two single phase alternators coupled to one shaft4 ,ques4 ,how many wires are required for two phase distribution8 ,ans4 ,a two phase system requires four lines for its distribution2 two lines for each phase as in fig4 #a1bec4 ,it is possible1 but not advisable1 to reduce the number to #c1 by employing one rather thicker line as a common return for each of the phases as in fig4 #a1bef4 ,illustration3 ,,fig4 #a1bef4--;,diagram of three wire two phase current distribution4 ,in order to save one wire it is possible to use a common return conductor for both circuits1 as shown1 the dotted portion of one wire #d being eliminated by connecting across to #a at ,m and ,s4 ,for long lines this is economical1 but the interconnection of the circuits increases the chance of trouble from grounds or short circuits4 ,the current in the conductor will be the resultant of the two currents1 differing by #ij in phase4 ,if this be done1 the voltage between the ,a line and the ,b line will be equal to #b times the voltage in either phase1 and the current in the line used as common return will be #b times as great as the current in either line1 assuming the two currents in the two phases to be equal4 ,ques4 ,in what other way may two phase current be distributed8 ,ans4 ,the mid point of the windings of the two phases may be united in the alternator at a common junction4 ,illustration3 ,,figs4 #a1beg to #a1bei4--,various two phase armature connections4 ,fig4 #a1beg1 two separate circuit four collector ring arrangement2 fig4 #a1beh1 common middle connection1 four collector rings2 fig4 #a1bei1 circuit connected in armature for three collector rings4 ,in the figures the black winding represents phase ,a1 and the light winding1 phase ,b4 ,this is equivalent to making the machine into a four phase alternator with half the voltage in each of the four phases1 which will then be in successive quadrature with each other4 ,ques4 ,how are two phase alternator armatures wound8 ,ans4 ,the two circuits may be separate1 each having two collector rings1 as shown in fig4 #a1beg1 or the two circuits may be coupled at a common middle as in fig4 #a1beh1 or the two circuits may be coupled in the armature so that only three collector rings are required as shown in fig4 #a1bei4 ,illustration3 ,,fig4 #a1bfj4--;,elementary three loop alternator and sine curves1 illustrating three phase alternating current4 ,if the loops be placed on the alternator armature at #abj magnetic degrees from one another1 the current in each will attain its maximum at a point one-third of a cycle distant from the other two4 ,the arrangement here shown gives three independent single phase currents and requires six wires for their transmission4 ,a better arrangement and the one generally used is shown in fig4 #a1bfa4 ,illustration3 ,,fig4 #a1bfa4--;,elementary three wire three phase alternator4 ,for the transmission of three phase current1 it is not customary to use six wires1 as in fig4 #a1bfj1 instead1 three ends 7one end of each of the loops7 are brought together to a common connection as shown1 and the other ends1 connected to the collector rings1 giving only three wires for the transmission of the current4 ,three ,phase ,current4--,a three phase current consists of three alternating currents of equal frequency and amplitude1 but differing in phase from each other by one-third of a period4 ,three phase current as represented by sine curves is shown in fig4 #a1bfj1 and by hydraulic analogy in fig4 #a1bfb4 ,inspection of the figures will show that when any one of the currents is at its maximum1 the other two are of half their maximum value1 and are flowing in the opposite direction4 ,illustration3 ,,figs4 #a1bfb and #a1bfc4--;,hydraulic analogy illustrating three phase alternating current4 ,three cylinders are here shown with pistons connected through ,scotch yokes to cranks placed #abj apart4 ,the same action takes place in each cylinder as in the preceding cases1 the only difference being the additional cylinder1 and difference in phase relation4 ,ques4 ,how is three phase current generated8 ,ans4 ,it requires three equal windings on the alternator armature1 and they must be spaced out over its surface so as to be successively and of the period 7that is1 of the double pole pitch7 apart from one another4 ,ques4 ,how many wires are used for three phase distribution8 ,ans4 ,either six wires or three wires4 ,six wires1 as in fig4 #a1bfj1 might be used where it is desired to supply entirely independent circuits1 or as is more usual only three wires are used as shown in fig4 #a1bfa4 ,in this case it should be observed that if the voltage generated in each one of the three phases separately ,e 7virtual7 volts1 the voltage generated between any two of the terminals will be equal to #c ,e4 ,thus1 if each of the three phases generate #ajj volts1 the voltage from the terminal of the ,a phase to that of the ,b phase will be #agc volts4 ,illustration3 ,,fig4 #a1bfd4--;,experiment illustrating self-induction in an alternating current circuit4 ,if an incandescent lamp be connected in series with a coil made of one pound of ,no4 #bj magnet wire1 and connected to the circuit1 the current through the lamp will be decreased due to the self-induction of the coil4 ,if now an iron core be gradually pushed into the coil1 the self-induction will be greatly increased and the lamp will go out1 thus showing the great importance which self-induction plays in alternating current work4 ,inductance4--,each time a direct current is started1 stopped or varied in strength1 the magnetism changes1 and induces or tends to induce a pressure in the wire which always has a direction opposing the pressure which originally produced the current4 ,this self-induced pressure tends to weaken the main current at the start and prolong it when the circuit is opened4 ,the expression inductance is frequently used in the same sense as coefficient of self-induction1 which is a quantity pertaining to an electric circuit depending on its geometrical form and the nature of the surrounding medium4 ,if the direct current maintains the same strength and flow steadily1 there will be no variations in the magnetic field surrounding the wire and no self-induction1 consequently the only retarding effect of the current will be the ohmic resistance of the wire4 ,if an alternating current be sent through a circuit1 there will be two retarding effects3 #a4 ,the ohmic resistance2 #b4 ,the spurious resistance4 ,illustration3 ,,fig4 #a1bfe4--,non-inductive and inductive resistances4 ,two currents are shown joined in parallel1 one containing a lamp and non-inductive resistance1 and the other a lamp and inductive resistance4 ,the two resistances being the same1 a sufficient direct pressure applied at ,t1 ,t' will cause the lamps to light up equally4 ,if1 however1 an alternating pressure be applied1 ,m will burn brightly1 while ,s will give very little or no light because of the effect of the inductance of the inductive resistance4 ,ques4 ,upon what does the ohmic resistance depend8 ,ans4 ,upon the length1 cross sectional area and material of the wire4 ,ques4 ,upon what does the spurious resistance depend8 ,ans4 ,upon the frequency of the alternating current1 the shape of the conductor1 and nature of the surrounding medium4 ,illustration3 ,,fig4 #a1bff4--;,inductance test1 illustrating the self-induction of a coil which is gradually increased by moving an iron wire core inch by inch into the coil4 ,the current is kept constant with the adjustable resistance throughout the test and readings taken1 first without the iron core1 and again when the core is put in the coil and moved to the #a1 #b1 #c1 #d1 etc41 inch marks4 ,by plotting the voltmeter readings and the position of the iron core on section paper1 a curve is obtained showing graphically the effect of the self-induction4 ,a curve of this kind is shown in fig4 #a1cjb4 ,ques4 ,define inductance4 ,ans4 ,it is the total magnetic flux threading the circuit per unit current which flows in the circuit1 and which produces the flux4 ,in this it must be understood that if any portion of the flux thread the circuit more than once1 this portion must be added in as many times as it makes linkage4 ,inductance1 or the coefficient of self-induction is the capacity which an electric circuit has of producing induction within itself4 ,inductance is considered as the ratio between the total induction through a circuit to the current producing it4 ,ques4 ,what is the unit of inductance8 ,ans4 ,the henry4 ,ques4 ,define the henry4 ,ans4 ,a coil has an inductance of one henry when the product of the number of lines enclosed by the coil multiplied by the number of turns in the coil1 when a current of one ampere is flowing in the coil1 is equal to #ajj1jjj1jjj or #aj4 ,an inductance of one henry exists in a circuit when a current changing at the rate of one ampere per second induces a pressure of one volt in the circuit4 ,ques4 ,what is the henry called8 ,ans4 ,the coefficient of self-induction4 ,illustration3 ,,fig4 #a1bfg4--;,diagram illustrating the henry4 ,by definition3 ,a circuit has an inductance of one henry when a rate of change of current of one ampere per second induces a pressure of one volt4 ,in the diagram it is assumed that the internal resistance of the cell and resistance of the connecting wires are zero4 ,the henry is the coefficient by which the time rate of change of the current in the circuit must be multiplied1 in order to give the pressure of self-induction in the circuit4 ,the formula for the henry is as follows3 magnetic flux turns henrys --------------------- current #ajj1jjj1jjj or ,n ,t ,l ----- 7#a7 #aj where ,l coefficient of self induction in henrys2 ,n total number of lines of force threading a coil when the current is one ampere2 ,t number of turns of coil4 ,if a coil had a coefficient of self-induction of one henry1 it would mean that if the coil had one turn1 one ampere would set up #ajj1jjj1jjj1 or #aj1 lines through it4 ,illustration3 ,,figs4 #a1bfh to #a1bgj4--,various coils4 ,the inductance effect1 though perceptible in an air core coil1 fig4 #a1bfh1 may be greatly intensified by inserting a core made of numerous pieces of iron wire1 as in fig4 #a1bfi4 ,fig4 #a1bgj shows a non-inductive coil4 ,when wound in this manner1 a coil will have little or no inductance because each half of the coil neutralizes the magnetic effect of the other4 ,this coil1 though non-inductive1 will have capacity4 ,it would be useless for solenoids or electromagnets1 as it would have no magnetic field4 ,the henry#b is too large a unit for use in practical computations1 which involves that the millihenry1 or _/th henry1 is the accepted unit4 ,in pole suspended lines the inductance varies as the metallic resistance1 the distance between the wires on the cross arm and the number of cycles per second1 as indicated by accepted tables4 ,thus1 for one mile of ,no4 #h ,b4 ,s4 copper wire1 with a resistance of #c1djf ohms1 the coefficient of self-induction with #f inches between centers is 4#jjaec1 and1 with #ab inches1 4#jjage4 #b ,,note4--,the ,american physicist1 ,joseph ,henry1 was born in #agih and died #ahgh4 ,he was noted for his researches in electromagnetism4 ,he developed the electromagnet1 which had been invented by ,sturgeon in ,england1 so that it became an instrument of far greater power than before4 ,in #ahca1 he employed a mile of fine copper wire with an electromagnet1 causing the current to attract the armature and strike a bell1 thereby establishing the principle employed in modern telegraph practice4 ,he was made a professor at ,princeton in #ahcb1 and while experimenting at that time1 he devised an arrangement of batteries and electromagnets embodying the principle of the telegraph relay which made possible long distance transmission4 ,he was the first to observe magnetic self-induction1 and performed important investigations in oscillating electric discharges 7#ahdb71 and other electrical phenomena4 ,in #ahdf he was chosen secretary of the ,smithsonian ,institution at ,washington1 an office which he held until his death4 ,as chairman of the ,u4 ,s4 ,lighthouse ,board1 he made important tests in marine signals and lights4 ,in meteorology1 terrestrial magnetism1 and acoustics1 he carried on important researches4 ,henry enjoyed an international reputation1 and is acknowledged to be one of ,america's greatest scientists4 ,illustration3 ,,fig4 #a1bga4--;,hydraulic-mechanical analogy illustrating inductance in an alternating current circuit4 ,the two cylinders are connected at their ends by the vertical pipes1 each being provided with a piston and the system filled with water4 ,reciprocating motion is imparted to the lower pulley by ,scotch yoke connection with the drive pulley4 ,the upper piston is connected by rack and pinion gear with a fly wheel4 ,in operation1 the to and fro movement of the lower piston produces an alternating flow of water in the upper cylinder which causes the upper piston to move back and forth4 ,the rack and pinion connection with the fly wheel causes the latter to revolve first in one direction1 then in the other1 in step with the upper piston4 ,the inertia of the fly wheel causes it to resist any change in its state1 whether it be at rest or in motion1 which is transmitted to the upper piston1 causing it to offer resistance to any change in its rate or direction of motion4 ,inductance in the alternating current circuit has precisely the same effect1 that is1 it opposes any change in the strength or direction of the current4 ,ques4 ,how does the inductance of a coil vary with respect to the core8 ,ans4 ,it is least with an air core2 with an iron core1 it is greater in proportion to the permeability#c of the iron4 #c ,,note4--,the permeability of iron varies from #ejj to #a1jjj or more4 ,the permeability of a given sample of iron is not constant1 but decreases in value as the magnetizing force increases4 ,therefore the inductance of a coil having an iron core is not a constant quantity as is the inductance of an air core coil4 ,the coefficient ,l for a given coil is a constant quantity so long as the magnetic permeability of the material surrounding the coil does not change4 ,this is the case where the coil is surrounded by air4 ,when iron is present1 the coefficient ,l is practically constant1 provided the magnetism is not forced too high4 ,in most cases arising in practice1 the coefficient ,l may be considered to be a constant quantity1 just as the resistance ,r is usually considered constant4 ,the coefficient ,l of a coil or circuit is often spoken of as its inductance4 ,illustration3 ,,fig4 #a1bgb4--;,experiment showing effect of inductive and non-inductive coils in alternating current circuit4 ,the apparatus is connected up as shown2 by means of the switch1 the lamp may be placed in parallel with either the inductive or non-inductive coil4 ,these coils should have the same resistance4 ,pass an alternating current through the lamp and non-inductive coil1 of such strength that the lamp will be dimly lighted4 ,now turn the switch so as to put the lamp and inductive coil in parallel and the lamp will burn with increased brilliancy4 ,the reason for this is because of the opposition offered by the inductive coil to the current1 less current is shunted from the lamp when the inductive coil is in the circuit than when the non-inductive coil is in the circuit4 ,that is1 each coil has the same ohmic resistance1 but the inductive coil has in addition the spurious resistance due to inductance1 hence it shunts less current from the lamp than does the non-inductive coil4 ,ques4 ,why is the iron core of an inductive coil made with a number of small wires instead of one large rod8 ,ans4 ,it is laminated in order to reduce eddy currents and consequent loss of energy1 and to prevent excessive heating of the core4 ,ques4 ,how does the number of turns of a coil affect the inductance8 ,ans4 ,the inductance varies as the square of the turns4 ,that is1 if the turns be doubled1 the inductance becomes four times as great4 ,the inductance of a coil is easily calculated from the following formul3 ,l #drn 7l #aj7 7#a7 for a thin coil with air core1 and ,l #drn 7l #aj7 7#b7 for a coil having an iron core4 ,in the above formul3 ,l inductance in henrys2 #c4adaf2 r average radius of coil in centimeters2 n number of turns of wire in coil2 permeability of iron core2 l length of coil in centimeters4 ,,example4--,an air core coil has an average radius of #aj centimeters and is #bj centimeters long1 there being #ejj turns1 what is the inductance8 ,substituting these values in formula 7#a7 ,l #d 7#c4adaf7 #aj #ejj 7#bj #aj7 4#jjdid henry ,ques4 ,is the answer in the above example in the customary form8 ,ans4 ,no2 the henry being a very large unit1 it is usual to express inductance in thousandths of a henry1 that is1 in milli-henrys4 ,the answer then would be 4#jdice #a1jjj #di4ce milli-henrys4 ,illustration3 ,,figs4 #a1bgc to #a1bge4--;,general ,electric choke coils4 ,fig4 #a1bgc1 hour glass coil1 #ce1jjj volts2 fig4 #a1bgd1 #d1fjj volt coil2 fig4 #a1bge1 #f1fjj volt coil4 ,a choke coil is a coil with large inductance and small resistance1 used to impede alternating currents4 ,the choke coil is used extensively as an auxiliary to the lightning arrester4 ,in this connection the primary objects of the choke coil should be3 #a1 to hold back the lightning disturbance from the transformer or generator until the lightning arrester discharges to earth4 ,if there be no lightning arrester the choke coil evidently cannot perform this function4 #b1 to lower the frequency of the oscillation so that whatever charge gets through the choke coil will be of a frequency too low to cause a serious drop of pressure around the first turns of the end coil in either generator or transformer4 ,another way of expressing this is from the standpoint of wave front3 a steep wave front piles up the pressure when it meets an inductance4 ,the second function of the choke coil is1 then1 to smooth out the wave front of the surge4 ,the principal electrical condition to be avoided is that of resonance4 ,the coil should be so arranged that if continual surges be set up in the circuit1 a resonant voltage due to the presence of the choke coil cannot build up at the transformer or generator terminals4 ,in the types shown above1 the hour glass coil has the following advantages on high voltages3 #a1 should there be any arcing between adjacent turns the coils will re-insulate themselves1 #b1 they are mechanically strong1 and sagging is prevented by tapering the coils toward the center turns1 #c1 the insulating supports can be best designed for the strains which they have to withstand4 ,choke coils should not be used in connection with cable systems4 ,,example4--,an air core coil has an inductance of #ej milli-henrys2 if an iron core1 having a permeability of #fjj be inserted1 what is the inductance8 ,the inductance of the air core coil will be multiplied by the permeability of the iron2 the inductance then is increased to #ej #fjj #cj1jjj milli-henrys1 or #cj henrys4 ,ohmic ,value of ,inductance4--,the rate of change of an alternating current at any point expressed in degrees is equal to the product of #b multiplied by the frequency1 the maximum current1 and the cosine of the angle of position 2 that is 7using symbols7 rate of change #b;f,icos 4 ,the numerical value of the rate of change is independent of its positive or negative sign1 so that the sign of the cos is disregarded4 ,illustration3 ,,fig4 #a1bgf4--;,inductance experiment with intermittent direct current4 ,a lamp ,s is connected in parallel with a coil of fairly fine wire having a removable iron core1 and the terminals ,t1 ,t' connected to a source of direct current1 a switch ,m being provided to interrupt the current4 ,the voltage of the current and resistance of the coil are of such values that when a steady current is flowing1 the lamp filament is just perceptibly red4 ,at the instant of making the circuit1 the lamp will momentarily glow more brightly than when the current is steady2 on breaking the circuit the lamp will momentarily flash with great brightness4 ,in the first case1 the reverse pressure1 due to inductance1 as indicated by arrow b1 will momentarily oppose the normal pressure in the coil1 so that the voltage at the lamp will be momentarily increased1 and will consequently send a momentarily stronger current through the lamp4 ,on breaking the main circuit at ,m1 the field of the coil will collapse1 generating a momentary much greater voltage than in the first instance1 in the direction of arrow a1 the lamp will flash up brightly in consequence4 ,the period of greatest rate of change is that at which cos has the greatest value1 and the maximum value of a cosine is when the arc has a value of zero degrees or of #ahj degrees1 its value corresponding1 being #a4 7,see fig4 #a1jcg1 page #a1jfh47 ,the pressure due to inductance is equal to the product of the rate of change by the inductance2 that is1 calling the inductance ,l1 the pressure due to it at the point of maximum value or ,e #b;f,i ,l 7#a7 ,now by ,ohm's law ,e ,,ri 7#b7 for a current ,i1 hence substituting equation 7#b7 in equation 7#a7 ,,ri #b;f,i ,l from which1 dividing both sides by ,i1 and using ,x for ,r ,x #b;f,l 7#c7 which is the ohmic equivalent of inductance4 ,illustration3 ,,fig4 #a1bgg4--;,diagram showing alternating circuit containing inductance4 ,formula for calculating the ohmic value of inductance or inductance reactance1 is ,x #b;f,l in which ,x inductance reactance2 #c4adaf2 f frequency2 ,l inductance in henrys 7not milli-henrys74 ,l #ae milli-henrys #ae #ajjj 4#jae henrys4 ,substituting1 ,x #b #c4adaf #ajj 4#jae #i4db ohms4 ,the frequency of a current being the number of periods or waves per second1 then1 if ,t the time of a period1 the frequency of a current may be obtained by dividing #a second by the time of a period2 that is one second #a frequency ------------------ --- 7#d7 time of one period ,t substituting #a _/ ,t for f in equation 7#c7 ,l ,x #b - ,t ,illustration3 ,,fig4 #a1bgh4--- ,diagram illustrating effect of capacity in an alternating circuit4 ,considering its action during one cycle of the current1 the alternator first pumps1 say from ,m to ,s2 electricity will be heaped up1 so to speak1 on ,s1 and a deficit left on ,m1 that is1 ,s will be and ,m-4 ,if the alternator be now suddenly stopped1 there would be a momentary return flow of electricity from ,s to ,m through the alternator4 ,if the alternator go on working1 however1 it is obvious that the electricity heaped up on ,s helps or increases the flow when the alternator begins to pump from ,s to ,m in the second half of the cycle1 and when the alternator again reverses its pressure1 the charge on ,m flows round to ,s1 and helps the ordinary current4 ,the above circuit is not strictly analogous to the insulated plates of a condenser1 but1 as is verified in practice1 that with a rapidly alternating pressure1 the condenser action is not perceptibly affected if the cables be connected across by some non-inductive resistance as for instance incandescent lamps4 ,capacity4--,when an electric pressure is applied to a condenser1 the current plays in and out1 charging the condenser in alternate directions4 ,as the current runs in at one side and out at the other1 the dielectric becomes charged1 and tries to discharge itself by setting up an opposing electric pressure4 ,this opposing pressure rises just as the charge increases4 ,a mechanical analogue is afforded by the bending of a spring1 as in fig4 #a1bgi1 which1 as it is being bent1 exerts an opposing force equal to that applied1 provided the latter do not exceed the capacity of the spring4 ,ques4 ,what is the effect of capacity in an alternating circuit8 ,ans4 ,it is exactly opposite to that of inductance1 that is1 it assists the current to rise to its maximum value sooner than it would otherwise4 ,illustration3 ,,fig4 #a1bgi4--,mechanical analogy illustrating effect of capacity in an alternating circuit4 ,if an alternating twisting force be applied to the top ,r of the spring ,s1 the action of the latter may be taken to represent capacity1 and the rotation of the wheel ,w1 alternating current4 ,the twisting force 7impressed pressure7 must first be applied before the rotation of ,w 7current7 will begin4 ,the resiliency or rebounding effect of the spring will1 in time1 cause the wheel ,w to move 7amperes7 in advance of the twisting force 7voltage7 thus representing the current leading in phase4 ,ques4 ,is it necessary to have a continuous metallic circuit for an alternating current8 ,ans4 ,no1 it is possible for an alternating current to flow through a circuit which is divided at some point by insulating material4 ,ques4 ,how can the current flow under such condition8 ,ans4 ,its flow depends on the capacity of the circuit and accordingly a condenser may be inserted in the circuit as in fig4 #a1bhf1 thus interposing an insulated gap1 yet permitting an alternating flow in the metallic portion of the circuit4 ,illustration3 ,,fig4 #a1bhj4--;,hydraulic analogy illustrating capacity in an alternating current circuit4 ,a chamber containing a rubber diaphragm is connected to a double acting cylinder and the system filled with water4 ,in operation1 as the piston moves1 say to the left from the center1 the diaphragm is displaced from its neutral position ,n1 and stretched to some position ,m1 in so doing offering increasing resistance to the flow of water4 ,on the return stroke the flow is reversed and is assisted by the diaphragm during the first half of the stroke1 and opposed during the second half4 ,the diaphragm thus acts with the flow of water one-half of the time and in opposition to it one-half of the time4 ,this corresponds to the electrical pressure at the terminals of a condenser connected in an alternating current circuit1 and it has a maximum value when the current is zero and a zero value when the current is a maximum4 ,ques4 ,name the unit of capacity and define it4 ,ans4 ,the unit of capacity is called the farad and its symbol is ,c4 ,a condenser is said to have a capacity of one farad if one coulomb 7that is1 one ampere flowing one second71 when stored on the plates of the condenser will cause a pressure of one volt across its terminals4 ,the farad being a very large unit1 the capacities ordinarily encountered in practice are expressed in millionths of a farad1 that is1 in microfarads--a capacity equal to about three miles of an ,atlantic cable4 ,it should be noted that the microfarad is used only for convenience1 and that in working out problems1 capacity should always be expressed in farads before substituting in formul1 because the farad is chosen with respect to the volt and ampere1 as above defined1 and hence must be used in formul along with these units4 ,illustration3 ,,fig4 #a1bha--;,diagram illustrating a farad4 ,a condenser is said to have a capacity of one farad if it will absorb one coulomb of electricity when subjected to a pressure of one volt4 ,the farad is a very large unit1 and accordingly the microfarad or one millionth of a farad is often used1 though this must be reduced to farads before substituting in formul4 ,for instance1 a capacity of #h microfarads as given in a problem would be substituted in a formula as 4#jjjjjh of a farad4 ,the charge ,q forced into a condenser by a steady electric pressure ,e is ,q ,,ec in which ,q charge in coulombs2 ,e electric pressure in volts2 ,c capacity of condenser in farads4 ,ques4 ,what is the material between the plates of a condenser called8 ,ans4 ,the dielectric4 ,ques4 ,upon what does the capacity of a condenser depend8 ,ans4 ,it is proportional to the area of the plates1 and inversely proportional to the thickness of the dielectric between the plates1 a correction being required unless the thickness of dielectric be very small as compared with the dimensions of the plates4 ,the capacity of a condenser is also proportional to the specific inductive capacity of the dielectric between the plates of the condenser4 ,illustration3 ,,fig4 #a1bhb4--;,condenser of one microfarad capacity4 ,it is subdivided into five sections of 4#e1 4#b1 4#b1 4#je and 4#je microfarad4 ,the plates are mounted between and carried by lateral brass bars which are fastened to a hard rubber top4 ,each pair of condenser terminals is fastened to small binding posts mounted on hard rubber insulated posts4 ,specific ,inductive ,capacity4--,faraday discovered that different substances have different powers of carrying lines of electric force4 ,thus the charge of two conductors having a given difference of pressure between them depends on the medium between them as well as on their size and shape4 ,the number indicating the magnitude of this property of the medium is called its specific inductive capacity1 or dielectric constant4 ,the specific inductive capacity of air1 which is nearly the same as that of a vacuum1 is taken as unity4 ,in terms of this unit the following are some typical values of the dielectric constant3 water #hj1 glass #f to #aj1 mica #f4g1 gutta-percha #c1 ,india rubber #b4e1 paraffin wax #b1 ebonite #b4e1 castor oil #d4h4 ,in underground cables for very high pressures1 the insulation1 if homogeneous throughout1 would have to be of very great thickness in order to have sufficient dielectric strength4 ,by employing material of high specific inductive capacity close to the conductor1 and material of lower specific inductive capacity toward the outside1 that is1 by grading the insulation1 a considerably less total thickness affords equally high dielectric strength4 ,illustration3 ,,fig4 #a1bhc4--,parallel connection of condensers4 ,like terminals are joined together4 ,the joint capacity of such arrangement is equal to the sum of the respective capacities1 that is ,c c c' c4 ,ques4 ,how are capacity tests usually made8 ,ans4 ,by the aid of standard condensers4 ,ques4 ,how are condensers connected8 ,ans4 ,they may be connected in parallel as in fig4 #a1bhc1 or in series 7cascade7 as in fig4 #a1bhd4 ,condensers are now constructed so that the two methods of arranging the plates may conveniently be combined in one condenser1 thereby obtaining a wider range of capacity4 ,ques4 ,how may the capacity of a condenser1 wire1 or cable be tested8 ,ans4 ,this may be done by the aid of a standard condenser1 trigger key1 and an astatic or ballistic galvanometer4 ,in making the test1 first obtain a constant by noting the deflection d1 due to the discharge of the standard condenser after a charge of1 say1 #aj seconds from a given voltage4 ,then discharge the other condenser1 wire1 or cable through the galvanometer after #aj seconds charge1 and note the deflection d'4 ,the capacity ,c' of the latter is then d' ,c' ,c ---- d in which ,c is the capacity of the standard condenser4 ,illustration3 ,,fig4 #a1bhd4--,series or cascade connection of condensers4 ,unlike terminals are joined together as shown4 ,the total capacity of such connection is equal to the reciprocal of the sum of the reciprocals of the several capacities1 that is1 ,c #a 7#a _/ c #a _/ c' #a _/ c7 ,ohmic ,value of ,capacity4--,the capacity of an alternating current circuit is the measure of the amount of electricity held by it when its terminals are at unit difference of pressure4 ,every such circuit acts as a condenser4 ,if an alternating circuit1 having no capacity1 be opened1 no current can be produced in it1 but if there be capacity at the break1 current may be produced as in fig4 #a1bhf4 ,the action of capacity referred to the current wave is as follows3 ,as the wave starts from zero value and rises to its maximum value1 the current is due to the discharge of the capacity1 which would be represented by a condenser4 ,in the case of a sine current1 the period required for the current to pass from zero value to maximum is one-quarter of a cycle4 ,illustration3 ,,figs4 #a1bhe and #a1bhf4--;,diagrams showing effect of condenser in direct and alternating current circuits4 ,each circuit contains an incandescent lamp and a condenser1 one circuit connected to a dynamo and the other to an alternator4 ,since the condenser interposes a gap in the circuit1 evidently in fig4 #a1bhe no current will flow4 ,in the case of alternating current1 fig4 #a1bhf1 the condenser gap does not hinder the flow of current in the metallic portion of the circuit4 ,in fact the alternator produces a continual surging of electricity backwards and forwards from the plates of the condenser around the metallic portion of the circuit1 similar to the surging of waves against a bulkhead which projects into the ocean4 ,it should be understood that the electric current ceases at the condenser1 there being no flow between the plates4 ,at the beginning of the cycle1 the condenser is charged to the maximum amount it receives in the operation of the circuit4 ,at the end of the quarter cycle when the current is of maximum value1 the condenser is completely discharged4 ,the condenser now begins to receive a charge1 and continues to receive it during the next quarter of a cycle1 the charge attaining its maximum value when the current is of zero intensity4 ,hence1 the maximum charge of a condenser in an alternating circuit is equal to the average value of the current multiplied by the time of charge1 which is one-quarter of a period1 that is maximum charge average current period 7#a7 ,illustration3 ,,fig4 #a1bhg4--;,diagram showing alternating circuit containing capacity4 ,formula for calculating the ohmic value of capacity or capacity reactance is ,xc #a #b;f,c1 in which ,xc capacity reactance2 #c4adaf2 f frequency2 ,c capacity in farads 7not microfarads74 #bb microfarads #bb #a1jjj1jjj 4#jjjjbb farad4 ,substituting1 ,xc #a 7#b #c4adaf #ajj 4#jjjjbb7 #gb4d ohms4 ,since the time of a period #a frequency1 the time of one-quarter of a period is 7#a frequency71 or period f 7#b7 f1 being the symbol for frequency4 ,substituting 7#b7 in 7#a7 maximum charge ,i f 7#c7 ,the pressure of a condenser is equal to the quotient of the charge divided by the capacity1 that is charge condenser pressure -------- 7#d7 capacity ,substituting 7#c7 in 7#d7 #a ,i condenser pressure 7,i ----7 ,c ----- 7#e7 #d;f #d;f,c ,but1 ,i ,i #b _/ 1 and substituting this value of ,i in equation 7#e7 gives ,i #b _/ ,i condenser pressure ----------- ------ 7#f7 #d;f,c #b;f,c ,this last equation 7#f7 represents the condenser pressure due to capacity at the point of maximum value1 which pressure is opposed to the impressed pressure1 that is1 it is the maximum reverse pressure due to capacity4 ,now1 since by ,ohm's law ,e ,i ---1 or ,e ,i ,r ,r and as ,i #a ------ ,i ------ #b;f,c #b;f,c it follows that #a _/ 7#b;f,c7 is the ohmic value of capacity1 that is it expresses the resistance equivalent of capacity2 using the symbol ,xc for capacity reactance #a ,xc ------- 7#g7 #b;f,c ,,example4--,what is the resistance equivalent of a #ej microfarad condenser to an alternating current having a frequency of #ajj8 ,substituting the given values in the expression for ohmic value #a #a #a ,xc ------ -------------------------- ------- #ca4h ohms4 #b;f,c #b #c4adaf #ajj 4#jjjjej 4#jcadaf ,if the pressure of the supply be1 say #ajj volts1 the current would be #ajj #ca4h #c4ad amperes4 ,illustration3 ,,fig4 #a1bhh4--,pressure and current curves1 illustrating lag4 ,the effect of inductance in a circuit is to retard the current cycle1 that is to say1 if the current and pressure be in phase1 the introduction of inductance will cause a phase difference1 the current wave lagging behind the pressure wave as shown4 ,in other words1 inductance causes the current wave1 indicated in the diagram by the solid curve1 to lag behind the pressure wave1 indicated by the dotted curve4 ,following the curves starting from the left end of the horizontal line1 it will be noted that the current starts after the pressure starts and reverses after the pressure reverses2 that is1 the current lags in phase behind the pressure1 although the frequency of both is the same4 ,lag and ,lead4--,alternating currents do not always keep in step with the alternating volts impressed upon the circuit4 ,if there be inductance in the circuit1 the current will lag2 if there be capacity1 the current will lead in phase4 ,for example1 fig4 #a1bhh1 illustrates the lag due to inductance and fig4 #a1bhi1 the lead due to capacity4 ,ques4 ,what is lag8 ,ans4 ,lag denotes the condition where the phase of one alternating current quantity lags behind that of another4 ,the term is generally used in connection with the effect of inductance in causing the current to lag behind the impressed pressure4 ,illustration3 ,,fig4 #a1bhi4--,pressure and current curves illustrating lead4 ,the effect of capacity in a circuit is to cause the current to rise to its maximum value sooner than it would otherwise do2 capacity produces an effect exactly the opposite of inductance4 ,the phase relation between current and pressure with current leading is shown graphically by the two armature positions in full and dotted lines1 corresponding respectively to current and pressure at the beginning of the cycle4 ,ques4 ,how does inductance cause the current to lag behind the pressure8 ,ans4 ,it tends to prevent changes in the strength of the current4 ,when two parts of a circuit are near each other1 so that one is in the magnetic field of the other1 any change in the strength of the current causes a corresponding change in the magnetic field and sets up a reverse pressure in the other wire4 ,this induced pressure causes the current to reach its maximum value a little later than the pressure1 and also tends to prevent the current diminishing in step with the pressure4 ,ques4 ,what governs the amount of lag in an alternating current8 ,ans4 ,it depends on the relative values of the various pressures in the circuit1 that is1 upon the amount of resistance and inductance which tends to cause lag1 and the amount of capacity in the circuit which tends to reduce lag and cause lead4 ,ques4 ,how is lag measured8 ,ans4 ,in degrees4 ,illustration3 ,,fig4 #a1bij4--,mechanical analogy of lag4 ,if at one end force be applied to turn a very long shaft1 having a loaded pulley at the other1 the torsion thus produced in the shaft will cause it to twist an appreciable amount which will cause the movement of the pulley to lag behind that of the crank4 ,this may be indicated by a rod attached to the pulley and terminating in a pointer at the crank end1 the rod being so placed that the pointer registers with the crank when there is no torsion in the shaft4 ,the angle made by the pointer and crank when the load is thrown on1 indicates the amount of lag which is measured in degrees4 ,thus1 in fig4 #a1bhh1 the lag is indicated by the distance between the beginning of the pressure curve and the beginning of the current curve1 and is in this case #de4 ,ques4 ,what is the physical meaning of this8 ,ans4 ,in an actual alternator1 of which fig4 #a1bhh is an elementary diagram showing one coil1 if the current lag1 say #de behind the pressure1 it means that the coil rotates #de from its position of zero induction before the current starts1 as in fig4 #a1bhh4 ,,example ,i4--,a circuit through which an alternating current is passing has an inductance of #f ohms and a resistance of #b4e ohms4 ,what is the angle of lag8 ,illustration3 ,,fig4 #a1bia4--;,diagram of circuit for example ,i4 ,substituting these values in equation 7#a71 page #a1jec1 #f tan --- #b4d #b4e ,referring to the table of natural sines and tangents on page #dea the corresponding angle is approximately #fg4 ,,example ,,ii4--,a circuit has a resistance of #b4c ohms and an inductance of 4#jjcd henry4 ,if an alternating current having a frequency of #abe pass through it1 what is the angle of lag8 ,illustration3 ,,fig4 #a1bib4--;,diagram of circuit for example ,,ii4 ,here the inductance is given as a fraction of a henry2 this must be reduced to ohms by substituting in equation 7#c71 page #a1jch1 which gives the ohmic value of the inductance2 accordingly1 substituting the above given value in this equation inductance in ohms or ,x #b #abe 4#jjcd #b4fg ,substituting this result and the given resistance in equation 7#a71 page #a1jec1 #b4fg tan ---- #a4af #b4c the nearest angle from table 7page #dea7 is #di4 ,ques4 ,how great may the angle of lag be8 ,ans4 ,anything up to #ij4 ,the angle of lag1 indicated by the ,greek letter 7phi71 is the angle whose tangent is equal to the quotient of the inductance expressed in ohms or spurious resistance divided by the ohmic resistance1 that is reactance #b;f,l tan ---------- ------ 7#a7 resistance ,r ,illustration3 ,,fig4 #a1bic4--,steam engine analogy of current flow at zero pressure 7see questions below74 ,when the engine has reached the dead center point the full steam pressure is acting on the piston1 the valve having opened an amount equal to its lead4 ,the force applied at this instant1 indicated by the arrow is perpendicular to the crank pin circle1 that is1 the tangential or turning component is equal to zero1 hence there is no pressure tending to turn the crank4 ,the latter continues in motion past the dead center because of the momentum previously acquired4 ,similarly1 the electric current1 which is here analogous to the moving crank1 continues in motion1 though the pressure at some instants be zero1 because it acts as though it had weight1 that is1 it cannot be stopped or started instantly4 ,ques4 ,when an alternating current lags behind the pressure1 is there not a considerable current at times when the pressure is zero8 ,ans4 ,yes2 such effect is illustrated by analogy in fig4 #a1bic4 ,ques4 ,what is the significance of this8 ,ans4 ,it does not mean that current could be obtained from a circuit that showed no pressure when tested with a suitable voltmeter1 for no current would flow under such conditions4 ,however1 in the flow of an alternating current1 the pressure varies from zero to maximum values many times each second1 and the instants of no pressure may be compared to the dead centers of an engine at which points there is no pressure to cause rotation of the crank1 the crank being carried past these points by the momentum of the fly wheel4 ,similarly the electric current does not stop at the instant of no pressure because of the momentum acquired at other parts of the cycle4 ,ques4 ,on long lines having considerable inductance1 how may the lag be reduced8 ,ans4 ,by introducing capacity into the circuit4 ,in fact1 the current may be advanced so it will be in phase with the pressure or even lead the latter1 depending on the amount of capacity introduced4 ,there has been some objection to the term lead as used in describing the effect of capacity in an alternating circuit1 principally on the ground that such expressions as lead of current1 lead in phase1 etc41 tend to convey the idea that the effect precedes the cause1 that is1 the current is in advance of the pressure producing it4 ,there can1 of course1 be no current until pressure has been applied1 but if the circuit has capacity1 it will lead the pressure1 and this peculiar behavior is best illustrated by a mechanical analogy as has already been given4 ,ques4 ,what effect has lag or lead on the value of the effective current8 ,ans4 ,as the angle of lag or lead increases1 the value of the effective as compared with the virtual current diminishes4 ,reactance4--,the term reactance means simply reaction4 ,it is used to express certain effects of the alternating current other than that due to the ohmic resistance of the circuit4 ,thus1 inductance reactance means the reaction due to the spurious resistance of inductance expressed in ohms2 similarly1 capacity reactance1 means the reaction due to capacity1 expressed in ohms4 ,it should be noted that the term reactance1 alone1 that is1 unqualified1 is generally understood to mean inductance reactance1 though ill advisedly so4 ,the resistance offered by a wire to the flow of a direct current is expressed in ohms2 this resistance remains constant whether the wire be straight or coiled4 ,if an alternating current flow through the wire1 there is in addition to the ordinary or ohmic resistance of the wire1 a spurious resistance arising from the development of a reverse pressure due to induction1 which is more or less in value according as the wire be coiled or straight4 ,this spurious resistance as distinguished from the ohmic resistance is called the reactance1 and is expressed in ohms4 ,reactance1 may then be defined with respect to its usual significance1 that is1 inductance reactance1 as the component of the impedance which when multiplied into the current1 gives the wattless component of the pressure4 ,reactance is simply inductance measured in ohms4 ,illustration3 ,,fig4 #a1bid4--;,diagram of the circuit for example ,i4 ,here the resistance is taken at zero1 but this would not be possible in practice1 as all circuits contain more or less resistance though it may be1 in some cases1 negligibly small4 ,,example ,i4--,an alternating current having a frequency of #fj is passed through a coil whose inductance is 4#e henry4 ,what is the reactance8 ,here f #fj and ,l 4#e2 substituting these in formula for inductive reactance1 ,x #b;f,l #b #c4adaf #fj 4#e #ahh4e ohms ,the quantity #b;f,l or reactance being of the same nature as a resistance is used in the same way as a resistance4 ,accordingly1 since1 by ,ohm's law ,e ,,ri 7#a7 an expression may be obtained for the volts necessary to overcome reactance by substituting in equation 7#a7 the value of reactance given above1 thus ,e #b;f,,li 7#b7 ,illustration3 ,,fig4 #a1bie4--;,diagram of circuit for example ,,ii4 ,as in example ,i1 resistance is disregarded4 ,,example ,,ii4--,how many volts are necessary to force a current of #c amperes with frequency #fj through a coil whose inductance is 4#e henry8 ,substituting in equation 7#b7 the values here given ,e #b;f,,li #b #fj 4#e #c #efe volts4 ,the foregoing example may serve to illustrate the difference in behaviour of direct and alternating currents4 ,as calculated1 it requires #efe volts to pass only #c amperes of alternating current through the coil on account of the considerable spurious resistance4 ,the ohmic resistance of a coil is very small1 as compared with the spurious resistance1 say #b ohms4 ,then by ,ohm's law ,i ,e ,r #efe #b #bhb4e amperes4 ,instances of this effect are commonly met with in connection with transformers4 ,since the primary coil of a transformer has a high reactance1 very little current will flow when an alternating pressure is applied4 ,if the same transformer were placed in a direct current circuit and the current turned on it would at once burn out1 as very little resistance would be offered and a large current would pass through the winding4 ,illustration3 ,,fig4 #a1bif4--;,diagram of circuit for example ,,iii4 ,,example ,,iii4--,in a circuit containing only capacity1 what is the reactance when current is supplied at a frequency of #ajj1 and the capacity is #ej microfarads8 #a #ej microfarads #ej --------- 4#jjjje farad #a1jjj1jjj capacity reactance1 or #a #a ,xc ------ ------------------------- #ca4hd ohms #b;f,c #b #c4adaf #ajj 4#jjjje ,impedance4--,this term1 strictly speaking1 means the ratio of any impressed pressure to the current which it produces in a conductor4 ,it may be further defined as the total opposition in an electric circuit to the flow of an alternating current4 ,all power circuits for alternating current are calculated with reference to impedance4 ,the impedance may be called the combination of3 #a4 ,ohmic resistance2 #b4 ,inductance reactance2 #c4 ,capacity reactance4 ,the impedance of an inductive circuit which does not contain capacity is equal to the square root of the sum of the squares of the resistance and reactance1 that is impedance 7resistance reactance7 7#a7 ,illustration3 ,,fig4 #a1big4--;,diagram showing alternating circuit containing resistance1 inductance1 and capacity4 ,formula for calculating the impedance of this circuit is ,z 7,r 7,x - ,xc77 in which1 ,z impedance2 ,r resistance2 ,x inductance reactance2 ,xc capacity reactance4 ,example3 ,what is the impedance when ,r #d1 ,x #id4b1 and ,xc #gb4d8 ,substituting ,z 7#d 7#id4b - #gb4d77 #bb4b ohms4 ,where the ohmic values of inductance and capacity are given as in this example1 the calculation of impedance is very simple1 but when inductance and capacity are given in milli-henrys and microfarads respectively1 it is necessary to first calculate their ohmic values as in figs4 #a1bie and #a1bif4 ,,example ,i4--,if an alternating pressure of #ajj volts be impressed on a coil of wire having a resistance of #f ohms and inductance of #h ohms1 what is the impedance of the circuit and how many amperes will flow through the coil8 ,in the example here given1 #f ohms is the resistance and #h ohms the reactance4 ,substituting these in equation 7#a7 ,impedance 7#f #h7 7#ajj7 #aj ohms4 ,the current in amperes which will flow through the coil is1 by ,ohm's law using impedance in the same way as resistance4 volts #ajj volts current --------- --------- #aj amperes4 impedance #aj ohms ,the reactance is not always given but instead in some problems the frequency of the current and inductance of the circuit4 ,an expression to fit such cases is obtained by substituting #b;f,l for the reactance as follows3 7using symbols for impedance and resistance7 ,z 7,r 7#b;f,l77 7#b7 ,illustration3 ,,fig4 #a1bih4--;,diagram of circuit for example ,,ii4 ,,example ,,ii4--,if an alternating current1 having a frequency of #fj1 be impressed on a coil whose inductance is 4#je henry and whose resistance is #f ohms1 what is the impedance8 ,here ,r #f2 f #fj1 and ,l 4#je2 substituting these values in 7#b7 ,z 7#f 7#b #fj 4#je77 7#cic7 #ai4h ohms4 ,illustration3 ,,fig4 #a1bii4--;,diagram of circuit for example ,,iii4 ,,example ,,iii4--,if an alternating current1 having a frequency of #fj1 be impressed on a circuit whose inductance is 4#je henry1 and whose capacity reactance is #aj ohms1 what is the impedance8 ,x #b;f,l #b #c4adaf #fj 4#je #ah4he ohms ,z ,x - ,xc #ah4he - #aj #h4he ohms ,when a circuit contains besides resistance1 both inductance and capacity1 the formula for impedance as given in equation 7#a71 page #a1jeh1 must be modified to include the reactance due to capacity1 because1 as explained1 inductive and capacity reactances work in opposition to each other1 in the sense that the reactance of inductance acts in direct proportion to the quantity #b;f,l1 and the reactance of capacity in inverse proportion to the quantity #b;f,c4 ,the net reactance due to both1 when both are in the circuit1 is obtained by subtracting one from the other4 ,illustration3 ,,fig4 #a1cjj4--;,diagram of circuit for example ,,iv4 ,to properly estimate impedance then1 in such circuits1 the following equation is used3 impedance 7resistance 7inductance reactance - capacity reactance77 or using symbols1 ,z 7,r 7,x - ,xc77 7#c7 ,,example ,,iv4--,a current has a frequency of #ajj4 ,it passes through a circuit of #d ohms resistance1 of #aej milli-henrys inductance1 and of #bb microfarads capacity4 ,what is the impedance8 a4 ,the ohmic resistance ,r1 is #d ohms4 b4 ,the inductance reactance1 or ,x #b;f,l #b #c4adaf #ajj 4#ae #id4c ohms4 7note that #aej milli-henrys are reduced to 4#ae henry before substituting in the above equation74 ,illustration3 ,,fig4 #a1cja4--,simple choking coil4 ,there is an important difference in the obstruction offered to an alternating current by ordinary resistance and by reactance4 ,resistance obstructs the current by dissipating its energy1 which is converted into heat4 ,reactance obstructs the current by setting up a reverse pressure1 and so reduces the current in the circuit1 without wasting much energy1 except by hysteresis in any iron magnetized4 ,this may be regarded as one of the advantages of alternating over direct current1 for1 by introducing reactance into a circuit1 the current may be cut down with comparatively little loss of energy4 ,this is generally done by increasing the inductance in a circuit1 by means of a device called variously a reactance coil1 impedance coil1 choking coil1 or choker4 ,in the figure is a coil of thick wire provided with a laminated iron core1 which may be either fixed or movable4 ,in the first case1 the inductance1 and therefore also the reactance of the coil1 is invariable1 with a given frequency4 ,in the second case1 the inductance and consequent reactance may be respectively increased or diminished by inserting the core farther within the coil or by withdrawing it1 as was done in fig4 #a1bff1 the results of which are shown in fig4 #a1cjb4 ,illustration3 ,,fig4 #a1cjb4--;,impedance curve for coil with variable iron core4 ,the impedance of an inductive coil may be increased by moving an iron wire core into the coil4 ,in making a test of this kind1 the current should be kept constant with an adjustable resistance1 and voltmeter readings taken1 first without the iron core1 and again with #a1 #b1 #c1 #d1 etc41 inches of core inserted in the coil4 ,by plotting the voltmeter readings and the positions of the iron core on section paper as above1 the effect of inductance is clearly shown4 c4 ,the capacity reactance1 or #a #a ,xc ------ -------------------------- #gb4d ohms #b;f,c #b #c4adaf #ajj 4#jjjjbb 7note that #bb microfarads are reduced to 4#jjjjbb farad before substituting in the formula4 ,why8 ,see page #a1jdb74 ,substituting values as calculated in equation 7#c71 page #a1jfj4 ,z 7#d 7#id4b - #gb4d77 7#dia7 #bb4b ohms4 ,illustration3 ,,fig4 #a1cjc4--;,diagram of a resonant circuit4 ,a circuit is said to be resonant when the inductance and capacity are in such proportion that the one neutralizes the other1 the circuit then acting as though it contained only resistance4 ,in the above circuit ,x #b;f,l #b #c4adaf #ajj 4#ja #f4bh ohms2 ,xc #a 7#b #c4adaf #ajj 4#jjjbec7 #f4bh ohms whence the resultant reactance ,x - ,xc #f4bh - #f4bh #j ohms4 ,z 7,r 7,x - ,xc77 7#g #j7 #g ohms4 ,ques4 ,why is capacity reactance given a negative sign8 ,ans4 ,because it reacts in opposition to inductance1 that is it tends to reduce the spurious resistance due to inductance4 ,in circuits having both inductance and capacity1 the tangent of the angle of lag or lead as the case may be is the algebraic sum of the two reactances divided by resistance4 ,if the sign be positive1 it is an angle of lag2 if negative1 of lead4 ,resonance4--,the effects of inductance and capacity1 as already explained1 oppose each other4 ,if inductance and capacity be present in a circuit in such proportion that the effect of one neutralizes that of the other1 the circuit acts as though it were purely non-inductive and is said to be in a state of resonance4 ,for instance1 in a circuit containing resistance1 inductance1 and capacity1 if the resistance be1 say1 #h ohms1 the inductance #cj1 and the capacity #cj1 then the impedance is 7#h 7#cj - #cj77 7#h7 #h ohms4 ,illustration3 ,,fig4 #a1cjd4--;,application of a choking coil to a lighting circuit4 ,the coil is divided into sections with leads running to contacts similar to a rheostat4 ,each lamp is provided with an automatic short-circuiting cutout1 and should one1 two1 or more of them fail1 a corresponding number of sections of the choking apparatus is put in circuit to take the place of the broken lamp or lamps1 and thus keep the current constant4 ,it must not be supposed that this arrangement of lamps1 etc4 is a general one2 it being adopted to suit certain special conditions4 ,the formula for inductance reactance is ,x #b;f,l1 and for capacity reactance1 ,xc #a 7#b;f,c72 accordingly if capacity and inductance in a circuit be equal1 that is1 if the circuit be resonant #a #b;f,l ------ 7#a7 #b;f,c from which #a f ------- 7#b7 #b7;,,cl7 ,ques4 ,what does equation 7#a7 show8 ,ans4 ,it indicates that by varying the frequency in the proper way as by increasing or decreasing the speed of the alternator1 the circuit may be made resonant1 this condition being obtained when the frequency has the value indicated by equation 7#b74 ,ques4 ,what is the mutual effect of inductance and capacity8 ,ans4 ,one tends to neutralize the other4 ,ques4 ,what effect has resonance on the current8 ,ans4 ,it brings the current in phase with the impressed pressure4 ,illustration3 ,,fig4 #a1cje4--;,curve showing variation of current by increasing the frequency in a circuit having inductance and capacity4 ,the curve serves to illustrate the critical frequency or frequency producing the maximum current4 ,the curve is obtained by plotting current values corresponding to different frequencies1 the pressure being kept constant4 ,it is very seldom that a circuit is thus balanced unless intentionally brought about2 when this condition exists1 the effect is very marked1 the pressure rising excessively and bringing great strain upon the insulation of the circuit4 ,ques4 ,define critical frequency4 ,ans4 ,in bringing a circuit to a state of resonance by increasing the frequency1 the current will increase with increasing frequency until the critical frequency is reached1 and then the current will decrease in value for further increase of frequency4 ,the critical frequency occurs when the circuit reaches the condition of resonance4 ,ques4 ,how is the value of the current at the critical frequency determined8 ,ans4 ,by the resistance of the circuit4 ,skin ,effect4--,this is the tendency of alternating currents to avoid the central portions of solid conductors and to flow or pass mostly through the outer portions4 ,the so-called skin effect becomes more pronounced as the frequency is increased4 ,illustration3 ,,fig4 #a1cjf4--,section of conductor illustrating skin effect or tendency of the alternating current to distribute itself unequally through the cross section of the conductor as shown by the varied shading flowing most strongly in the outer portions of the conductor4 ,for this reason it has been proposed to use hollow or flat conductors instead of solid round wires4 ,however with frequency not exceeding #ajj the skin effect is negligibly small in copper conductors of the sizes usually employed4 ,where the conductor is large or the frequency high the effect may be judged by the following examples calculated by ,professor ,j4 ,j4 ,thomson3 ,in the case of a copper conductor exposed to an electromotive force making #ajj periods per second at #a centimetre from the surface1 the maximum current would be only 4#bjh times that at the surface2 at a depth of #b centimetres it would be only 4#jdc2 and at a depth of #d centimetres less than 4#jjb part of the value at the surface4 ,if the frequency be a million per second the current at a depth of #a millimetre is less than one six-millionth part of its surface value4 ,the case of an iron conductor is even more remarkable4 ,taking the permeability at #ajj and the frequency at #ajj per second the current at a depth of #a millimetre is only 4#ac times the surface value2 while at a depth of #e millimetres it is less than one twenty-thousandth part of its surface value4 ,the disturbance of current density may be looked upon as a self-induced eddy current in the conductor4 ,it necessarily results in an increase of ohmic loss2 as compared with a steady current3 proportional to the square of the total current flowing and consequently gives rise to an apparent increase of ohmic resistance4 ,the coefficient of increase of resistance depends upon the dimensions and the shape of the cross section1 the frequency and the specific resistance4 ,a similar but distinct effect is experienced in conductors due to the neighborhood of similar parallel currents4 ,for example in a heavy multicore cable the non-uniformity of current density in any core may be considered as partly due to eddy currents induced by the currents in the neighboring cores and partly to the self-induced eddy current4 ,it is only the latter effect which should rightly be considered as comprised under the term skin effect4 ,ques4 ,what is the explanation of skin effect8 ,ans4 ,it is due to eddy currents induced in the conductor4 ,consider the wire as being composed of several small insulated wires placed closely together4 ,now when a current is started along these separate wires1 mutual induction will take place between them1 giving rise to momentary reverse pressures4 ,those wires which are nearer the center1 since they are completely surrounded by neighboring wires1 will clearly have stronger reverse pressures set up in them than those on or near the outer surface1 so that the current will meet less opposition near the surface than at the center1 and consequently the flow will be greater in the outer portions4 ,ques4 ,what is the result of skin effect8 ,ans4 ,it results in an apparent increase of resistance4 ,the coefficient of increase of resistance depends upon the dimensions and the shape of the cross section1 the frequency1 and the specific resistance4 ,hughes1 about #ahhc1 called attention to the fact that the resistance of an iron telegraph wire was greater for rapid periodic currents than for steady currents4 ,in #ahhh ,kelvin showed that when alternating currents at moderately high frequency flow through massive conductors1 the current is practically confined to the skin1 the interior portions being largely useless for the purpose of conduction4 ,the mathematical theory of the subject has been developed by ,kelvin1 ,heaviside1 ,rayleigh1 and others4 ,,chapter ,,xlvii ,,alternating ,,current ,,diagrams ,whenever an alternating pressure is impressed on a circuit1 part of it is spent in overcoming the resistance1 and the rest goes to balance the reverse pressure due to self-induction4 ,the total pressure applied to the circuit is known as the impressed pressure1 as distinguished from that portion of it called the active pressure which is used to overcome the resistance1 and that portion called the self-induction pressure used to balance the reverse pressure of self-induction4 ,the intensity of the reverse pressure induced in a circuit due to self-induction is proportional to the rate of change in the current strength4 ,thus a current1 changing at the rate of one ampere per second1 in flowing through a coil having a coefficient of self-induction of one henry1 will induce a reverse pressure of one volt4 ,ques4 ,describe how the rate of change in current strength varies1 and how this affects the reverse pressure4 ,ans4 ,the alternating current varies from zero to maximum strength in one-quarter period1 that is1 in one-quarter revolution of the generating loop or #ij as represented by the sine curve in fig4 #a1cjg4 ,now1 during1 say1 the first #aj degrees of rotation 7from #j to ,a71 the current jumps from zero value to ,a'1 or #d amperes1 according to the scale2 during some intermediate #aj degrees of the quarter revolution1 as from ,b to ,c1 the current increases from ,b' to ,c' or #b amperes1 and during another #aj degrees as from ,d to ,e1 at the end of one-quarter revolution where the sine curve reaches its amplitude1 it rises and falls ampere4 ,it is thus seen that the rate of change varies from a maximum when the current is least1 to zero when the current is at its maximum4 ,accordingly1 the reverse pressure of self-induction being proportional to the rate of change in the current strength1 is greatest when the current is at zero value1 and zero when the current is at its maximum4 ,illustration3 ,,fig4 #a1cjg4--,sine curve showing that the rate of change in the strength of an alternating current is greatest when the current is least1 and zero when the current is at a maximum4 ,this is evident from the diagram1 since during say the first #aj as ,,oa1 the current increases #d amperes2 during ,,bc1 #b amperes2 during ,,de it rises and falls ampere4 ,the reverse pressure of self-induction being proportional to the rate of change of the current1 is a maximum when the current is zero1 and zero when the current is a maximum1 giving a phase difference of #ij between reverse pressure of self-induction and current4 ,this relation is shown by curves in fig4 #a1cjh1 and it should be noted that the reverse pressure and current are #ij apart in phase4 ,for this reason many alternating current problems may be solved graphically by the use of right angle triangles1 the sides1 drawn to some arbitrary scale1 to represent the quantities involved1 such as resistance1 reactance1 impedance1 etc4 ,properties of ,right ,angle ,triangles4--,in order to understand the graphical method of solving alternating current problems1 it is necessary to know why certain relations exist between the sides of a right angle triangle4 ,for instance1 in every right angle triangle3 ,the square of the hypothenuse is equal to the sum of the squares on the other two sides4 ,that is1 condensing this statement into the form of an equation3 hypothenuse base altitude 7#a7 the horizontal side being called the base and the vertical side1 the altitude4 ,this may be called the equation of the right angle triangle4 ,illustration3 ,,fig4 #a1cjh4--,sine curves showing phase relation between current and reverse pressure of self-induction4 ,this reverse pressure1 being proportional to the rate of change in the current strength1 is greatest when the current is at zero value1 and zero when the current is maximum1 and in phase is #ij behind the current4 ,illustration3 ,,fig4 #a1cji4--;,in a right angle triangle the square on the hypothenuse is equal to the sum of the squares on the other two sides4 ,that is3 hypothenuse base altitude4 ,draw ,,ab1 #d inches long1 and ,,bc1 #c inches long and at right angles to ,,ab4 ,join ,,ac1 which will be found to be #e inches long4 ,from the diagram1 it must be clear that the square on ,,ac sum of squares on ,,ab and ,,bc2 that is1 #e #d #c4 ,further1 #d #e - #c2 #c #e - #d2 #e 7#d #c72 #d 7#e - #c72 #c 7#e - #d74 ,ques4 ,why is the square of the hypothenuse of a right angle triangle equal to the sum of the squares of the other two sides8 ,ans4 ,this may be explained with the aid of fig4 #a1cji4 ,draw a line ,,ab1 #d inches in length and erect a perpendicular ,,bc1 #c inches in height2 connect ,a and ,c1 giving the right angle triangle ,,abc4 ,it will be found that ,,ac the hypothenuse of this triangle is #e inches long4 ,if squares be constructed on all three sides of the triangle1 the square on the hypothenuse will have an area of #be sq4 ins42 the square on the base1 #af sq4 ins41 and the square on the altitude1 #i sq4 ins4 ,then from the figure #e #d #c1 that is #be #af #i4 ,repeating equation 7#a71 it is evident from the figure that hypothenuse base altitude #e #d #c that is1 #be #af #i4 ,in the right angle triangle1 the following relations also hold3 base hypothenuse - altitude 7#b7 7#d #e - #c7 altitude hypothenuse - base 7#c7 7#c #e - #d7 ,in working impedance problems1 it is not the square of any of the quantities which the sides of the triangle are used to represent that is required1 but the quantities themselves1 that is1 the sides4 ,hence extracting the square root in equations 7#a71 7#b7 and 7#c71 the following are obtained3 hypothenuse 7base altitude7 7#d7 7#e 7#d #c77 base 7hypothenuse - altitude7 7#e7 7#d 7#e - #c77 altitude 7hypothenuse - base7 7#f7 7#c 7#e - #d77 ,representation of ,forces by ,lines4--,a single force may be represented in a drawing by a straight line1 #a1 the point of application of the force being indicated by an extremity of the line1 #b1 the intensity of the force by the length of the line1 and #c1 the direction of the force by the direction of the line1 an arrow head being placed at an extremity defining the direction4 ,thus in fig4 #a1caj1 the force necessary to balance the thrust on the steam piston may be represented by the straight line f whose length measured on any convenient scale represents the intensity of the force1 and whose direction represents the direction of the force4 ,illustration3 ,,fig4 #a1caj4--;,diagram illustrating the representation of forces by straight lines4 ,if #hj lbs4 of steam be applied to a piston of #d square inches area1 the total pressure acting on the piston is #d #hj #cbj lbs4 ,this may be balanced by an equal and opposite force4 ,to represent the latter by a line1 select any convenient scale whose divisions represent any convenient number of pounds--#a1 #c1 #e or1 as here taken1 #be lbs4 ,if the scale selected be divided into inches with -inch divisions1 then each inch represents a force of #be lbs42 or1 as usually stated1 #a #ajj lbs4 ,strictly speaking #a is equivalent to #ajj lbs4 ,draw the line f #c4b ins41 then its length represents the magnitude of the force or #cbj lbs41 that is1 #c4b #ajj #cbj lbs4 ,composition of ,forces4--,this is the operation of finding a single force whose effect is the same as the combined effect of two or more given forces4 ,the required force is called the resultant of the given forces4 ,the composition of forces may be illustrated by the effect of the wind and tide on a sailboat as in fig4 #a1caa4 ,supposing the boat be acted upon by the wind so that in a given time1 say half an hour1 it would be moved in the direction and a distance represented by the line ,,ab1 and that in the same time the tide would carry it from ,a to ,c4 ,now1 lay down ,,ab1 to any convenient scale1 representing the effect of the wind1 and ,,ac that of the tide1 and draw ,,bd equal and parallel to ,,ac1 and ,,cd equal and parallel to ,,ab1 then the diagonal ,,ad will represent the direction and distance the boat will move under the combined effect of wind and tide4 ,illustration3 ,,fig4 #a1caa4--,parallelogram of forces for boat acted upon by both wind and tide4 ,ques4 ,in fig4 #a1caa what is the line ,,ad called8 ,ans4 ,the resultant1 that is1 it represents the actual movement of the boat resulting from the combined forces of wind and tide4 ,ques4 ,what are the forces1 ,,ab and ,,ad in fig4 #a1caa1 represented by the sides of the parallelogram1 and which act upon a body to produce the resultant1 called8 ,ans4 ,the components4 ,illustration3 ,,fig4 #a1cab4--,parallelogram of forces2 method of obtaining the resultant of two components acting at right angles4 ,,example4--,two forces1 one of #c lbs4 and one of #d lbs4 act at a point a in a body and at right angles1 what is the resultant8 ,take any convenient scale1 say #a in4 #a lb41 and lay off 7fig4 #acab47 ,,ab #d ins4 #d lbs42 also1 ,,ac 7at right angles to ,,ab7 #c ins4 #c lbs4 ,draw ,,cd and ,,bd parallel to ,,ab and ,,ac respectively1 and join ,,ad4 ,the line ,,ad is the resultant of the components ,,ab and ,,ac1 and when measured on the same scale from which ,,ab and ,,ac were drawn will be found to be #e inches long1 which represents #e lbs4 acting in the direction ,,ad4 ,circuits containing ,resistance and ,inductance4--,in circuits of this kind where the impressed pressure encounters both resistance and inductance1 it may be looked upon as split up into two components1 as already explained1 one of which is necessary to overcome the resistance1 and the other1 the inductance4 ,that is1 the impressed pressure is split up into #a4 ,active pressure1 to overcome resistance2 #b4 ,self-induction pressure to overcome inductance4 ,illustration3 ,,fig4 #a1cac4--;,diagram illustrating the active1 and self-induction pressures1 or the two components of the impressed pressure in circuits containing resistance and inductance4 ,the active pressure is the volts required to overcome the resistance of the circuit4 ,in the figure only the portion from ,a to ,c is considered as having resistance 7the rest being negligibly small7 except at ,r1 a resistance equivalent to that of the inductive coil is inserted next to the non-inductive coil1 so ,p will give the total ohmic drop or active pressure1 that is1 the pressure necessary to force any equivalent direct current from ,a to ,c4 ,this active pressure ,p or component of the impressed pressure is in phase with the current4 ,the other component or self-induction pressure ,p that is the reactance drop necessary to overcome the reverse pressure of self-induction and is at right angles to the current and #ij ahead of the current in phase4 ,it is registered by a voltmeter between ,b and ,c1 less the pressure due to ohmic resistance of the inductive coil4 ,the impressed pressure ,p then or total pressure required to force electricity around the circuit not including the resistance ,r1 7which is removed from the circuit when the reading of the impressed pressure is taken71 is equal to the square root of the sum of the squares of the two components1 that is1 ,p 7,p ,p74 ,the active pressure is in phase with the current4 ,the self induction pressure is at right angles to the current and #ij degrees ahead of the current in phase4 ,ques4 ,why is the active pressure in phase with the current8 ,ans4 ,the pressure used in overcoming resistance is from ,ohm's law1 ,e ,,ri4 ,hence1 when the current is zero1 ,e is zero1 and when the current is a maximum ,e is a maximum4 ,hence1 that component of the impressed pressure necessary to overcome the resistance must be in phase with the current4 ,ques4 ,why is this8 ,ans4 ,since the reverse pressure of self induction is #ij behind the current1 the component of the impressed pressure necessary to overcome the reverse pressure of self induction1 being opposite to this1 will be represented as being #ij ahead of the current4 ,the distinction between the reverse pressure of self-induction1 that is1 the induced pressure1 and the pressure necessary to overcome self-induction should be carefully noted4 ,they are two equal and opposite forces1 that is1 two balancing forces just as is shown in fig4 #a1caj4 ,here1 in analogy1 the thrust of the piston may represent the induced pressure and the equal and opposite force indicated by the arrow f1 the component of the impressed pressure necessary to balance the induced pressure4 ,illustration3 ,,fig4 #a1cad4--;,graphical method of obtaining the impressed pressure in circuits containing resistance and inductance1 having given the ohmic drop1 and reactance drop due to inductance4 ,with any convenient scale lay off ,,ab ohmic drop and erect the perpendicular ,,bc reactance drop 7using same scale74 ,join ,,ac1 whose length 7measured with same scale7 will give the impressed pressure4 ,constructing a parallelogram with dotted lines ,,ad and ,,cd1 it is evident that ,,ac is the resultant of the two components ,,ab and ,,bc1 or its equal ,,ad4 ,the ,active ,pressure or ,ohmic ,drop4--,the component of the impressed pressure necessary to overcome resistance1 is from ,ohm's law3 active pressure ohmic resistance virtual current that is ,e ,r,i 7#a7 this is the ohmic drop and may be represented by a line ,,ab1 fig4 #a1cad drawn to any convenient scale1 as for instance1 #a in4 #aj volts4 ,the ,self-induction ,pressure or ,reactance ,drop4--,the component of the impressed pressure necessary to overcome the induced pressure1 is from ,ohm's law3 inductance pressure inductance reactance virtual current2 that is1 ,e ,x,i 7#b7 ,illustration3 ,,fig4 #a1cae4--;,diagram for impressed pressure on circuit containing #e volts ohmic drop and #ae volts reactance drop4 ,now the reactance ,x1 that is the spurious resistance1 is obtained from the formula ,x #b;f,l 7#c7 as explained on page #a1jch1 and in order to obtain the volts necessary to overcome this spurious resistance1 that is1 the reactance drop as it is called1 the value of ,x in equation 7#c7 must be substituted in equation 7#b71 giving ,e #b;f,,li 7#d7 writing simply ,i for the virtual pressure4 ,since the pressure impressed on a circuit is considered as made up of two components1 one in phase with the current and one at right angles to the current1 the component ,e or reactance drop as given in equation 7#d7 maybe represented by the line ,,bc in fig4 #a1cad1 at right angles to ,,ab1 and of a length ,,bc1 measured with the same scale as was measured ,,ab1 to correspond to the value indicated by equation 7#d74 ,,example4--,in an alternating circuit1 having an ohmic drop of #e volts1 and a reactance drop of #ae volts1 what is the impressed pressure8 ,with a scale of say1 inch one volt1 lay off1 in fig4 #a1cae1 ,,ab #e volts #a in41 and1 at right angles to it1 ,,bc #ae volts _/ or #c ins4 ,join ,,ac2 this measures #c4ie inches1 which is equivalent to #c4ie #d #ae4h volts1 the impressed pressure4 ,by using good paper1 such as bristol board1 a #f;,h pencil1 engineers' scale and triangles or square1 such problems are solved with precision4 ,by calculation impressed pressure 7#e #ae7 #ae4h volts4 ,note that the diagram is drawn with the side ,,bc horizontal instead of ,,ab--simply to save space4 ,illustration3 ,,fig4 #a1caf4--;,diagram of circuit containing #e volts ohmic drop1 and #ae volts reactance drop4 ,illustration3 ,,fig4 #a1cag4--;,diagram for obtaining reactance drop in circuit containing #e volts ohmic drop1 and #ae4h volts impressed pressure4 ,,example4--,in an alternating circuit1 having an ohmic drop of #e volts and an impressed pressure of #ae4h volts1 what is the reactance drop8 ,in fig4 #a1cag1 draw a horizontal line of indefinite length and at any point ,b erect a perpendicular ,,ab #e volts4 ,with ,a as center and radius of length equivalent to #ae4h volts1 describe an arc cutting the horizontal line at ,c4 ,this gives ,,bc1 the reactance drop required1 which by measurement is #ae volts4 ,illustration3 ,,fig4 #a1cah4--;,diagram for obtaining ohmic drop in the circuit fig4 #a1caf when impressed pressure and reactance drop are given4 ,lay off ,,bc to scale reactance drop2 draw ,,ab at right angle and of indefinite length2 with ,c as center and radius of length impressed pressure1 describe an arc cutting ohmic drop line at ,a1 then ,,ab ohmic drop #e volts by measurement4 ,illustration3 ,,fig4 #a1cai4--;,graphical method of finding angle of lag when the ohmic drop and reactance drop are given4 ,the angle of lag 1 is that angle included between the impressed pressure and the ohmic drop lines1 that is1 between ,,ac and ,,ab4 ,,example4--,an alternating current of #aj amperes having a frequency of #fj1 is impressed on a circuit containing a resistance of #e ohms and an inductance of #ae milli-henrys4 ,what is the impressed pressure8 ,the active pressure or ohmic drop is #e #aj #ej volts4 ,illustration3 ,,fig4 #a1cbj4--;,diagram of circuit containing #e ohms resistance1 #ae milli-henrys inductance1 with #c ampere #fj frequency current4 ,the inductance reactance or ,x is #b #c4adaf #fj 4#jae #e4ff ohms4 ,substituting this and the current value #aj amperes in the formula for inductance pressure or reactance drop 7equation #b on page #a1jgg7 gives ,e #e4fe #aj #ef4e volts4 ,illustration3 ,,fig4 #a1cba4--;,diagram for impressed pressure on circuit containing #e ohms resistance and inductance of #ae milli-henrys1 the current being #aj amperes with frequency of #fj4 ,in fig4 #a1cba1 lay off ,,ab #ej volts1 and ,,bc #ef4f volts4 ,using a scale of #bj volts to the inch gives ,,ab #b4e ins41 and ,,bc #b4hc ins4 ,joining ,,ac gives the impressed voltage1 which by measurement is #ge4d volts4 ,in some problems it is required to find the impedance of a circuit in which the ohmic and spurious resistances are given4 ,this is done in a manner similar to finding the impressed pressure4 ,illustration3 ,,fig4 #a1cbb4--;,graphical method of obtaining the impedance in circuits containing resistance and inductance1 having given the resistance and reactance1 that is1 the ohmic resistance and spurious resistance4 ,with any convenient scale lay off ,,ab resistance1 and erect the perpendicular ,,bc reactance 7using the same scale72 join ,,ac1 whose length 7measured with the same scale7 will give the impedance4 ,ohmic resistance and spurious resistance or inductance reactance both tend to reduce an alternating current4 ,their combined action or impedance is equal to the square root of the sum of their squares1 that is1 impedance 7resistance reactance7 ,this relation is represented graphically by the side of a right angle triangle as in fig4 #acbb1 in which the hypothenuse corresponds to the impedance1 and the sides to the resistance and reactance4 ,,example4--,in a certain circuit the resistance is #d ohms1 and the reactance #c ohms4 ,what is the impedance8 ,in fig4 #a1cbc1 lay off1 on any scale ,,ab #d ohms and erect the perpendicular ,,bc #c ohms4 ,join ,,ac1 which gives the impedance1 and which is1 measured with the same scale1 #e ohms4 ,,example4--,a coil of wire has a resistance of #bj ohms and an inductance of #ae milli-henrys4 ,what is its impedance for a current having a frequency of #ajj8 ,illustration3 ,,fig4 #a1cbc4--;,diagram for obtaining the impedance of a circuit containing #d ohms resistance and #c ohms reactance4 ,the ohmic value of the inductance1 that is1 the reactance is #b;f,l #b #c4adaf #ajj 4#jae #i4db ohms4 ,in fig4 #a1cbd1 lay off1 on any scale1 ,,ab #bj ohms1 and the perpendicular ,,bc to length #i4db ohms4 ,join ,,ac1 which gives the impedance1 which is1 measured on the same scale1 #bb4a ohms4 ,,example4--,what is the angle of lag in a circuit having a resistance of #d ohms and a reactance of #c ohms8 ,construct the impedance diagram in the usual way as in fig4 #a1cbe1 then the angle included between the impedance and resistance lines 7denoted by 7 is the angle of lag1 that is1 the angle ,,bac4 ,by measurement with a protractor it is #cg degrees4 ,by calculation the tangent of the angle of lag or ,,bc #c tan -- - or 4#ge ,,ab #d ,from the table on page #dea1 the angle is approximately #cg4 ,illustration3 ,,fig4 #a1cbd4--;,diagram for impedance of circuit containing #bj ohms resistance1 and inductance of #ae milli-henrys1 when the frequency is #ajj4 ,illustration3 ,,fig4 #a1cbe4--;,diagram showing angle of lag for current containing #d ohms resistance and #c ohms reactance4 ,circuits containing ,resistance and ,capacity4--,the effect of capacity in an alternating current circuit is to cause the current to lead the pressure1 since the reaction of a condenser1 instead of tending to prolong the current1 tends to drive it back4 ,careful distinction should be made between capacity in series with a circuit and capacity in parallel with a branch of a circuit4 ,the discussion here refers to capacity in series1 which means that the circuit is not continuous but the ends are joined to a condenser1 as shown at the right in fig4 #a1cbf1 so that no current can flow except into and out of the condenser4 ,illustration3 ,,fig4 #a1cbf1--;,circuit diagram illustrating the distinction between capacity in series and capacity in parallel4 ,the condition for capacity in series is that the circuit must be discontinuous as at ,m2 for capacity in parallel the main circuit must be continuous2 this means that the capacity must be inserted in a branch of the main circuit as at ,a4 ,in the figure the capacity ,s is connected in series with respect to the branch1 that is1 the branch is discontinuous1 but it is in parallel with respect to the main circuit1 when the latter is continuous1 that is1 when the switch ,w is closed4 ,if ,w be opened1 the main circuit becomes discontinuous and ,s is changed from in parallel to in series connection4 ,ques4 ,in circuits containing resistance and capacity upon what does the amount of lead depend8 ,ans4 ,upon the relative values of the resistance and the capacity reactance4 ,ques4 ,describe the action of a condenser when current is applied4 ,ans4 ,when the current begins to flow into a condenser1 that is1 when the flow is maximum1 the back pressure set up by the condenser 7called the condenser pressure7 is zero1 and when the flow finally becomes zero1 the condenser pressure is a maximum4 ,illustration3 ,,fig4 #a1cbg4--;,current and pressure curves showing that the condenser pressure is #ij ahead of the current4 ,a current flowing into a condenser encounters a gradually increasing pressure which opposes it1 beginning from zero pressure when the current enters at maximum flow and increasing to the same value as the current pressure1 at which time the current ceases to flow4 ,hence1 since the current varies from zero to maximum in one quarter period1 or #ij1 the phase difference between current and condenser pressure is #ij4 ,the condenser pressure reaching a positive maximum when the current starts from zero on the positive wave1 is #ij ahead of the current4 ,ques4 ,what does this indicate8 ,ans4 ,it shows that the phase difference between the wave representing the condenser pressure and the current is #ij1 as illustrated in fig4 #a1cbg4 ,ques4 ,is the condenser pressure ahead or behind the current and why8 ,ans4 ,it is ahead of the current4 ,the condenser pressure1 when the condenser is discharged being zero1 the current enters at maximum velocity as at ,a in fig4 #a1cbg1 and gradually decreases to zero as the condenser pressure rises to maximum at ,b1 this change taking place in one-quarter period4 ,thus the condenser pressure1 which opposes the current1 being at a maximum when the current begins its cycle is #ij ahead of the current1 as is more clearly seen in the last quarter of the cycle 7fig4 #a1cbg74 ,illustration3 ,,fig4 #a1cbh4--;,current and pressure curves1 showing phase relation between the current1 condenser pressure1 and impressed or capacity pressure necessary to overcome the condenser pressure4 ,the capacity pressure1 since it must overcome the condenser pressure1 is equal and opposite to the condenser pressure1 that is1 the phase difference is #ahj4 ,the condenser pressure being #ij ahead of the current1 the impressed pressure is #ij behind the current4 ,ques4 ,what is the phase relation between the condenser pressure and the pressure applied to the condenser to overcome the condenser pressure8 ,ans4 ,the pressure applied to the condenser to overcome the condenser pressure1 or as it is called1 the capacity pressure1 must be opposite to the condenser pressure1 or #ij behind the current4 ,in circuits containing resistance and capacity1 the total pressure impressed on the circuit1 or impressed pressure1 as it is called1 is made up of two components3 #a4 ,the active pressure1 or pressure necessary to overcome the resistance2 ,the active pressure is in phase with the current4 #b4 ,the capacity pressure1 or pressure necessary to overcome the condenser pressure1 ,the capacity pressure is #ij degrees behind the current4 ,illustration3 ,,fig4 #a1cbi4--;,graphical method of obtaining the impressed pressure in circuits containing resistance and capacity1 having given the ohmic drop and reactance drop due to capacity4 ,with any convenient scale1 lay off ,,ab ohmic drop1 and at right angles to ,,ab draw ,,bc reactance drop 7using the same scale74 ,join ,,ac1 whose length 7measured with the same scale7 will give the impressed pressure4 ,the mathematical expressions for the three quantities are given inside the triangle1 and explained in the text4 ,problems involving resistance and capacity are solved similarly to those including resistance and inductance4 ,the ,active ,pressure or ,ohmic ,drop4--,this1 as before explained is represented1 in fig4 #a1cbi1 by a line ,,ab1 which in magnitude equals1 by ,ohm's law1 the product of the resistance multiplied by the current1 that is1 ,e ,r,i 7#a7 ,illustration3 ,,fig4 #a1ccj4--;,diagram of circuit containing a resistance of #cj ohms and capacity of #abe microfarads4 ,the calculation for impressed pressure1 ohmic drop1 and reactance drop for a current of #h amperes at frequency #fj is given in the example on page #a1jhi1 the diagram for impressed pressure being given in fig4 #a1cca4 ,the ,capacity ,pressure or ,reactance ,drop4--,this component of the impressed pressure1 is1 applying ,ohm's law1 capacity pressure capacity reactance virtual current4 ,ec ,xc,i 7#b7 ,that is1 the expression for capacity reactance ,xc1 that is1 for the value of capacity in ohms is1 as explained on page #a1jdh1 #a ,xc ------ 7#c7 #b;f,c ,substituting this value of ,xc in equation 7#b7 and writing ,i for virtual current4 ,i ,ec ------- 7#d7 #b;f,c ,,caution--,the reader should distinguish between the #a 7one7 in 7#c7 and the letter ,i in 7#d72 both look alike4 ,since the capacity pressure is #ij behind the current1 it is represented in fig4 #a1cbi1 by a line ,,bc1 drawn downward1 at right angles to ,,ab1 and of a length corresponding to the capacity pressure1 that is1 to the reactance drop4 ,the ,impressed ,pressure4--,having determined the ohmic and reactance drops and represented them in the diagram1 fig4 #a1cbi1 by lines ,,ab and ,,bc respectively1 a line ,,ac joining ,a and ,c1 will then be the resultant of the two component pressures1 that is1 it will represent the impressed pressure or total pressure applied to the circuit4 ,in the diagram it should be noted that the active pressure is called the ohmic drop1 and the capacity pressure1 the reactance drop4 ,,example4--,a circuit as shown in fig4 #a1ccj contains a resistance of #cj ohms1 and a capacity of #abe microfarads4 ,if an alternating current of #h amperes with frequency #fj be flowing in the circuit1 what is the ohmic drop1 the reactance drop1 and the impressed pressure8 ,the ohmic drop or active pressure is1 substituting in formula 7#a7 on page #a1jhg1 ,e #cj #h #bdj volts which is the reading of voltmeter ,a in fig4 #a1ccj4 ,illustration3 ,,fig4 #a1cca4--;,diagram for obtaining the impressed pressure of the circuit shown in fig4 #a1ccj4 ,the reactance drop or ,i #h ,ec ------ ------------------------- #agj volts #b;f,c #b #c4adaf #fj 4#jjjabe in substituting1 note that the capacity ,c of #abe microfarads is reduced to 4#jjjabe farad4 ,using a scale of say #a inch #hj volts1 lay off in fig4 #a1cca1 ,,ab equal to the ohmic drop of #bdj volts2 on this scale ,,ab #c inches4 ,lay off at right angles1 ,,bc reactance drop #agj volts #b4abe inches4 ,join ,,ac1 which gives the impressed voltage1 7that is the reading of voltmeter ,i in fig4 #a1ccj17 which measures #bid volts4 ,by calculation1 impressed pressure 7#bdj #agj7 #bid volts4 ,,example4--,in the circuit shown in fig4 #a1ccj1 what is the angle of lead8 ,the tangent of the angle of lead is given by the quotient of the reactance divided by the resistance of the circuit4 ,that is1 reactance reactance drop tan ------------ ----------------- resistance resistance drop ,ec ,i tan -- ------ ,e 7#a7 ,e #b;f,c ,the tangent is given a negative sign because lead is opposed to lag and because the positive value is assigned to lag4 ,substituting in 7#a7 #agj #b4abe tan --- or ------ -4#ga #bdj #c the angle corresponding is approximately #ce 7see table page #dea74 ,illustration3 ,,figs4 #a1ccb and #a1ccc4--;,diagrams for circuits containing inductance and capacity4 ,since inductance and capacity act #ahj apart1 their reactances1 or their ohmic drops may be represented by oppositely directed lines4 ,these may be drawn above and below a reference line1 as in fig4 #a1ccb1 and their algebraic sum taken1 or both may be drawn on the same side of the reference line and their difference in lengths1 as ,,cd1 fig4 #a1ccc1 measured4 ,recourse to a diagram for obtaining the resultant reactance in circuits containing inductance and capacity is unnecessary as it is simply a matter of taking the difference of two quantities4 ,circuits ,containing ,inductance and ,capacity4--,the effect of capacity in a circuit is exactly the opposite of inductance1 that is1 one tends to neutralize the other4 ,the method of representing each graphically has been shown in the preceding figures4 ,since they act oppositely1 that is #ahj apart1 the reactance due to each may be calculated and the values thus found1 represented by oppositely directed vertical lines3 the inductance resistance upward from a reference line1 and the capacity resistance downward from the same reference line4 ,the difference then is the resultant impedance4 ,this method is shown in fig4 #a1ccb1 but it is more conveniently done as in fig4 #a1ccc4 ,illustration3 ,,fig4 #a1ccd4--;,diagram of circuit containing #cj milli-henrys inductance and #abe microfarads capacity1 with current of #bj amperes1 #ajj frequency4 ,,example4--,in a circuit1 as in fig4 #a1ccd1 containing an inductance of #cj milli-henrys and a capacity of #abe microfarads1 how many volts must be impressed on the circuit to produce a current of #bj amperes having a frequency of #ajj4 ,the inductance reactance is ,x #b;f,l #b #c4adaf #ajj 4#jc #ah4he ohms4 ,substituting this and the current value of #bj amperes in the formula for inductance pressure ,e ,r,i #ah4he #bj #cgg volts4 ,reducing #abe microfarads to 4#jjjabe farad1 and substituting in the formula for capacity pressure ,i #bj ,ec ------ -------------------------- #bee volts4 #b;f,c #b #c4adaf #ajj 4#jjjabe ,a diagram is unnecessary in obtaining the impressed pressure since it is simply the difference between inductance pressure and capacity pressure 7the circuit being assumed to have no resistance71 that is impressed pressure ,e - ,ec #cgg - #bee #abb volts4 ,,example4--,a circuit in which a current of #bj amperes is flowing at a frequency of #ajj1 has an inductance reactance of #ah4be ohms1 and a capacity of #abe microfarads4 ,what is the impedance8 ,the reactance due to capacity is #a #a ,xc ------ -------------------------- #ab4gf ohms4 #b;f,c #b #c4adaf #ajj 4#jjjabe ,the impedance of the circuit then is the difference between the two reactances1 that is impedance inductance reactance - capacity reactance1 or ,z ,x - ,xc #ah4be - #ab4gf #e4di ohms4 ,illustration3 ,,fig4 #a1cce4--;,impedance diagram for circuit 7of above example7 containing inductance and capacity4 ,with any convenient scale1 erect a perpendicular ,,ab #ah4be ohms1 and ,,cd #ab4gf ohms4 ,continue ,,cd by dotted line to ,d' so that ,,cd' ,,ab1 then ,,dd' ,,ab - ,,cd inductance reactance - capacity reactance1 which is equal to the impedance4 ,expressed by letters ,z ,x - ,xc ,,dd'1 which by measurement #e4di ohms4 ,circuits ,containing ,resistance1 ,inductance1 and ,capacity4--,when the three quantities resistance1 inductance1 and capacity1 are present in a circuit1 the combined effect is easily understood by remembering that inductance and capacity always act oppositely1 that is1 they tend to neutralize each other4 ,hence1 in problems involving the three quantities1 the resultant of inductance and capacity is first obtained1 which1 together with the resistance1 is used in determining the final effect4 ,capacity introduced into a circuit containing inductance reduces the latter and if enough be introduced1 inductance will be neutralized1 giving a resonant circuit which will act as though only resistance were present4 ,illustration3 ,,fig4 #a1ccf4--;,impedance diagram for circuit containing resistance1 inductance and capacity4 ,the symbols correspond to those used in equation 7#a7 below4 ,in constructing the diagram from the given values1 lay off ,,ab resistance2 at ,b1 draw a line at right angles1 on which lay off above the resistance line1 ,,bc inductive reactance1 and below1 ,,bd capacity reactance1 then the resultant reactance ,,bc - ,,bd ,,bd'4 ,join ,a and ,d'1 then ,,ad' impedance4 ,ques4 ,what is the expression for impedance of a circuit containing resistance1 inductance and capacity8 ,ans4 ,it is equal to the square root of the sum of the resistance squared plus the square of inductance reactance minus capacity reactance4 ,this is expressed plainer in the form of an equation as follows3 impedance 7resistance 7inductance reactance - capacity reactance77 or1 using symbols1 ,z 7,r 7,x - ,xc77 7#a7 ,ques4 ,if the capacity reactance be larger than the inductance reactance1 how does this affect the sign of 7,x-,xc78 ,ans4 ,the sign of the resultant reactance of inductance and capacity will be negative if capacity be the greater1 but since in the formula the reactance is squared1 the sign will be positive4 ,illustration3 ,,fig4 #a1ccg4--;,impedance diagram of a circuit containing #be ohms resistance1 #cj ohms inductance1 and #dj ohms capacity4 ,the resultant reactance being due to excess of capacity1 the impedance line ,,ac' falls below the horizontal line ,,ab1 indicating that the current leads pressure4 ,,example4--,what is the impedance in a circuit having #be ohms resistance1 #cj ohms inductance reactance1 and #dj ohms capacity reactance8 ,to solve this problem graphically1 draw the line ,,ab1 in fig4 #a1ccg1 equal to #be ohms resistance1 using any convenient scale4 ,at ,b draw upward at right angles ,,bc #cj ohms2 draw from ,c downward ,,cc' #dj ohms4 ,this gives -,,bc' 7 ,,bc - ,,cc'7 showing the capacity reactance to be #aj ohms in excess of the inductance reactance4 ,such a circuit is equivalent to one having no inductance but the same resistance and #aj ohms capacity reactance4 ,the diagram is completed in the usual way by joining ,,ac giving the required impedance1 which by measurement is #bf4i ohms4 ,by calculation1 ,z 7#be 7#cj - #dj77 7#be 7-#aj77 #bf4i4 ,form of ,impedance ,equation without ,ohmic ,values4-- ,using the expressions #b;f,l for inductance reactance and #a _/ 7#b;f,c7 for capacity reactance1 and substituting in equation 7#a7 on page #a1jic gives the following3 ,z 7,r 7#b;f,l - #a _/ 7#b;f,c777 7#b7 which is the proper form of equation 7#a7 to use in solving problems in which the ohmic values of inductance and capacity must be calculated4 ,illustration3 ,,fig4 #a1cch4--;,,example3 ,a resistance of #bj ohms and an inductance of 4#jb henry are connected in parallel as in the diagram4 ,what is the impedance1 and how many volts are required for #ej amperes1 when the frequency is #gh4f8 ,,solution3 ,the time constants are not alike1 hence the geometric sum of the reciprocals must be taken as the reciprocal of the required impedance4 ,that is1 the combined conductivity will be the hypothenuse of the right triangle1 of which the ohmic conductivity and the reactive conductivity are the two sides1 respectively4 ,accordingly3 #a _/ ,r #a _/ #bj 4#je1 and #a _/ 7#b;f,l7 #a _/ #aj 4#a1 from which1 #a _/ ,r 77#a _/ ,r7 7#a _/ 7#b;f,l777 4#aaa4 ,whence ,z #a _/ 4#aaa #i ohms4 ,illustration3 ,,fig4 #a1cci4--;,diagram of circuit containing #bc ohms resistance1 #da milli-henrys inductance1 and #ea microfarads capacity1 with current supplied at a frequency of #aej4 ,,example4--,a current has a frequency of #aej4 ,it passes through a circuit1 as in fig4 #a1cci1 of #bc ohms resistance1 of #da milli-henrys inductance1 and of #ea microfarads capacity4 ,what is the impedance8 ,the inductance reactance or ,x #b;f,l #b #c4adaf #aej 4#jda #ch4fd ohms 7note that #da milli-henrys are reduced to 4#jda henry before substituting in the above equation74 ,the capacity reactance1 or #a #a ,xc ------ -------------------------- #bj4h ohms #b;f,c #b #c4adaf #aej 4#jjjjea 7note that #ea microfarads are reduced to 4#jjjjea farad before substituting in the above equation74 ,substituting the values as calculated for #b;f,l and #a _/ 7#b;f,c7 in equation 7#b7 ,z 7#bc 7#ch4fd - #bj4h77 #bi4a ohms4 ,to solve the problem graphically1 lay off in fig4 #a1cdj1 the line ,,ab equal to #bc ohms resistance1 using any convenient scale4 ,draw upward and at right angles to ,,ab the line ,,bc #ch4fd ohms inductance reactance1 and from ,c lay off downward ,,cc' #bj4h ohms capacity reactance4 ,the resultant reactance is ,,bc' and being above the horizontal line ,,ab shows that inductance reactance is in excess of capacity reactance by the amount ,,bc'4 ,join ,,ac' which gives the impedance sought1 and which by measurement is #bi4a ohms4 ,in order to obtain the impressed pressure in circuits containing resistance1 inductance and reactance1 an equation similar to 7#b7 on page #a1jie is used which is made up from the following3 ,e ,,ri 7#c7 ,e #b;f,,li 7#d7 ,i ,ec ------ 7#e7 #b;f,c ,illustration3 ,,fig4 #a1cdj4--;,impedance diagram for the circuit shown in fig4 #a1cci4 ,note that the resultant reactance being due to excess of inductance1 the impedance line ,,ac' falls above the horizontal line ,,ab4 ,this indicates that the current lags behind the pressure4 ,when all three quantities1 resistance1 inductance1 and capacity are present1 the equation is as follows3 impressed pressure 7ohmic drop 7inductive drop - capacity drop77 ,e 7,e 7,e - ,ec77 7#f7 ,substituting in this last equation 7#f71 the values given in 7#c71 7#d7 and 7#e7 ,e 7,r,i 7#b;f,,li - 7,i _/ 7#b;f,c7777 ,i 7,r 7#b;f,l - 7#a _/ 7#b;f,c7777 7#g7 ,illustration ,,fig4 #a1cda4--;,diagram of circuit containing #be ohms resistance1 4#ae henry inductance1 and #abe microfarads capacity1 with current of #h amperes at #fj frequency4 ,ques4 ,what does the quantity under the square root sign in equation 7#g7 represent8 ,ans4 ,it is the impedance of a circuit possessing resistance1 inductance1 and capacity4 ,ques4 ,why8 ,ans4 ,because it is that quantity which multiplied by the current gives the pressure1 which is in accordance with ,ohm's law4 ,illustration3 ,fig4 #a1cdb4--;,diagram for finding the pressure necessary to be impressed on the circuit shown in fig4 #a1cda1 to produce a current of #h amperes4 ,,example4--,an alternator is connected to a circuit having1 as in fig4 #a1cda1 #be ohms resistance1 an inductance of 4#ae henry1 and a capacity of #abe microfarads4 ,what pressure must be impressed on the circuit to allow #h amperes to flow at a frequency of #fj8 ,the ohmic drop is ,e ,,ri #be #h #bjj volts4 ,the inductance drop is ,e #b;f,,li #b #c4adaf #fj 4#ae #h #deb volts ,the capacity drop is ,i #h ,ec ------ ------------------------- #agj volts4 #b;f,c #b #c4adaf #fj 4#jjjabe ,substituting the values thus found1 impressed pressure 7,e 7,e - ,ec77 7#bjj 7#deb - #agj77 7#bjj #bhb7 7#aaiebd7 #cde4g volts4 ,,chapter ,,xlviii ,,the ,,power ,,factor ,the determination of the power in a direct current circuit is a simple matter since it is only necessary to multiply together the volts and amperes to obtain the output in watts4 ,in the case of alternating current circuits1 this holds true only when the current is in phase with the pressure--a condition rarely found in practice4 ,when the current is not in phase with the pressure1 the product of volts and amperes as indicated by the voltmeter and ammeter must be multiplied by a coefficient called the power factor in order to obtain the true watts1 or actual power available4 ,there are several ways of defining the power factor1 any of which requires some explanation4 ,the power factor may be defined as3 ,the number of watts indicated by a wattmeter1 divided by the apparent watts1 the latter being the watts as measured by a voltmeter and ammeter4 ,the power factor may be expressed as being equal to true power true watts true watts ---------------- ---------------- ------------------- apparent power apparent watts volts amperes ,ques4 ,what are the true watts8 ,ans4 ,the watts as measured by a wattmeter4 ,ques4 ,what are the apparent watts8 ,ans4 ,the watts obtained by multiplying together the simultaneous voltmeter and ammeter readings4 ,ques4 ,what is usually meant by power factor8 ,ans4 ,the multiplier used with the apparent watts to determine how much of the power supplied is available4 ,illustration3 ,,fig4 #a1cdc4--,marine analogy of power factor4 ,a ferry boat in crossing a river to a slip ,c would head for some point ,b up stream from ,c to allow for the effect of the tide4 ,under such conditions the actual motion 7referred to the water7 would be from ,a to ,b1 and the apparent motion1 from ,a to ,c4 ,accordingly1 the energy expended in propelling the boat from ,a to ,b in still water1 will propel it from ,a to ,c when the tide is running in the direction of the arrow4 ,the effect of the tide is the same as that of inductance or capacity in an alternating circuit1 that is1 it puts the applied force or thrust 7impressed volts7 out of phase with the motion of the boat 7amperes71 this phase difference being indicated by the angle ,,bac or 4 ,now1 work 7watts7 is the product of two factors1 pressure 7volts7 and distance 7amperes72 accordingly1 the apparent work done in propelling the boat from ,a to ,c is the product of the thrust of the paddle wheels multiplied by ,,ac1 which in analogy corresponds to the product of voltmeter and ammeter readings at the alternator1 called kva4 ,actually1 however1 the power is only applied from ,a to ,b1 the boat being carried sidewise by the tide1 as it crosses1 a distance ,,bc which represents no energy expended by the paddle wheels4 ,in analogy1 the actual power1 expended in propelling boat from ,a to ,b corresponds to the wattmeter reading in an alternating current power circuit4 ,to obtain the actual work done on the boat1 the product of its apparent motion thrust must be multiplied by a coefficient or power factor because the thrust is applied at an angle to the apparent motion1 the power factor being equal to the cosine of this angle1 77 or ,,ab ,,ac4 ,similarly1 when there is phase difference between pressure and alternating current1 the voltmeter and ammeter readings must be multiplied by the power factor or cos to give the output of an alternator available for external work1 the excess power indicated by ammeter and voltmeter readings1 performing no external work1 but causing objectionable heating of the alternator4 ,ques4 ,upon what does the power factor depend8 ,ans4 ,upon the relative amounts of resistance inductance and capacity contained in the circuit4 ,ques4 ,how does the power factor vary in value8 ,ans4 ,it varies from one to zero4 ,the power factor1 as will be shown later1 is equal to the cosine of the angle of phase difference2 its range then is from one to zero because these are the limiting values of the cosine of an angle 7neglecting the or-sign74 ,ques4 ,what is the effect of lag or lead of the current on the power factor8 ,ans4 ,it causes it to become less than one4 ,illustration3 ,,fig4 #a1cdd4--,method of drawing the power curve from the pressure and current curves4 ,as shown1 the same scale is used for all curves4 ,this as a rule1 makes the power curve inconveniently high1 hence it is usually drawn to smaller scale as in fig4 #a1cde4 ,how to ,obtain the ,power ,curve4--,since under any phase condition1 the power at any instant is equal to the product of the pressure multiplied by the current at that instant1 a curve may be easily plotted from the pressure and current curves1 giving the instantaneous values of the power through a complete cycle4 ,in fig4 #a1cdd1 from the zero line of the current and pressure curves1 draw any ordinate as at ,f cutting the current curve at ,g and the pressure curve at ,g'4 ,the values for current and pressure at this point are from the scale1 #b amperes and #c4g volts4 ,since watts amperes volts1 the ordinate ,,fg is to be multiplied by ordinate ,,fg' that is1 #b #c4g #g4d4 ,project up through ,f the ordinate ,,fg #g4d1 and this will give one point on the power curve4 ,similarly at another point1 say ,m1 where the current and pressure are maximum ,,ms ,,ms' ,,ms1 that is #c #e #ae giving ,s another point on the curve4 ,obtaining several points in this way the power curve is then drawn through them as shown4 ,illustration3 ,,fig4 #a1cde4--,usual method of drawing power curve from the pressure and current curves4 ,a smaller scale is employed for the power curve in order to reduce its height4 ,ques4 ,why is the power curve positive in the second half of the period when there are negative values of current and pressure8 ,ans4 ,because the product of two negative quantities is positive4 ,ques4 ,does fig4 #a1cdd represent the usual way of drawing a power curve8 ,ans4 ,since ordinates of the power curve are products of the current and pressure ordinates1 they will be of inconvenient length if drawn to the same scale2 it is therefore customary to use a different scale for the power ordinates1 as in fig4 #a1cde4 ,the illustration is lettered identical with fig4 #a1cdd1 with which it should be compared4 ,synchronism of ,current and ,pressure2 ,power ,factor ,unity4--,the current and pressure would be in phase as represented in fig4 #a1cdf were it possible to have a circuit containing resistance only4 ,in actual practice all circuits contain at least a small amount of reactance4 ,illustration3 ,,fig4 #a1cdf4--,synchronism of current and pressure4 ,power curve showing that the power factor is unity4 ,this is indicated by the fact that the power curve does not project below the base or zero line4 ,a circuit supplying nothing but incandescent lamps comes very nearly being all resistance1 and may be so considered in the discussion here4 ,fig4 #a1cdg illustrates a circuit containing only resistance4 ,in such a circuit the pressure and current 7as shown in fig4 #a1cdf7 pass through zero and through their maximum values together4 ,multiplying instantaneous values of volts and amperes will give the power curve1 as before explained1 whose average value is half-way between the zero line and the maximum of the curve2 that part of the power curve above the line of average power ,,ww1 exactly filling the open space below the line ,,ww4 ,that is1 average power maximum power #b maximum voltage maximum current _/ #b virtual voltage virtual current4 ,this latter is simply the product of the voltmeter and ammeter readings which gives the watts just the same as in direct current4 ,illustration3 ,,fig4 #a1cdg4--;,diagram of circuit containing only resistance2 in such a circuit the power factor is unity4 ,ques4 ,what should be noticed about the power curve8 ,ans4 ,its position with respect to the zero line2 it lies wholly above the zero line which denotes that all the power delivered to the circuit except that dissipated by friction is useful1 that is1 the power factor is unity4 ,hence1 to keep the power factor as near unity as possible is one of the chief problems in alternating current distribution4 ,ques4 ,can the power factor be less than unity if the current and pressure be in phase8 ,ans4 ,yes1 if the waves of current and voltage be distorted as in fig4 #a1cdh4 ,effect of ,lag and ,lead4--,in an alternating circuit the amount of power supplied depends on the phase relationship of the current and pressure4 ,as just explained1 when there is synchronism of current and pressure1 that is1 when they are in phase 7as in fig4 #a1cdf7 the power factor is unity1 assuming no distortion of current and pressure waves4 ,in all other cases the power factor is less than unity that is1 the effect of lag or lead is to make the power factor less than unity4 ,illustration3 ,,fig4 #a1cdh4--;,case of synchronism of current and pressure with power factor less than unity4 ,suppose the waves of current and voltage to be in phase1 but distorted in form1 and not symmetrical1 so that they do not run uniformly together1 as shown in the figure4 ,then the real power factor may not be unity1 although indicated as such by the power factor meter4 ,however1 the switchboard instruments are made to show the angle of lag as the power factor1 because the error due to wave distortion is generally too small to be considered4 ,illustration3 ,,fig4 #a1cdi4--;,effect of lag on the power factor4 ,when the current lags behind the pressure the power factor becomes less than unity4 ,it will be seen that the power curve projects below the zero line giving the shaded area which represents negative power which must be subtracted from the areas above the zero line to get the net power4 ,in the figure the line ,,ww' is drawn at a height corresponding to the average power1 and ,,hn at a height corresponding to the average power that would be developed if the current were in phase with the pressure4 ,the power factor then is represented by ,m ,s1 and by inspection of the figure it is seen that this is less than unity4 ,illustration3 ,,fig4 #a1cej4--;,effect of lead on the power factor4 ,when the current is in advance of the pressure the power factor becomes less than unity4 ,the curve1 as shown1 projects below the zero line1 giving the shaded area which represents negative power which must be subtracted from the areas above the zero line to get the net power4 ,as in fig4 #a1cdi1 the line ,,ww' at a height ,m represents the average power1 and ,,hn the average power for synchronism of current and pressure4 ,the power factor then is ,m ,s which is less than unity4 ,the effect of lag on the power factor may be illustrated by fig4 #a1cdi1 in which the angle between the pressure and current1 or the angle of lag is taken as #dj1 corresponding to a power factor of 4#gff4 ,plotting the power curve from the products of instantaneous volts and amperes taken at various points1 the power curve is obtained1 a portion of which lies below the horizontal line4 ,the significance of this is that at certain times1 the current is flowing in the opposite direction to that in which the impressed pressure would send it4 ,during this part of the period conditions are reversed1 and the power 7indicated by the shaded area71 instead of being supplied by the source to the circuit1 is being supplied by the circuit to the source4 ,illustration3 ,,fig4 #a1cea4--,steam engine analogy of power factor4 ,the figure represents an indicator card of an engine in which the steam distribution is such that the steam is expanded below the back pressure line1 that is below the pressure of the exhaust4 ,this results in negative work which must be overcome by the momentum or kinetic energy previously stored in the fly wheel1 and which is represented on the diagram by the shaded loop ,s4 ,if the exhaust valve had opened at ,g1 the amount of work done during the revolution would be represented by the area ,m1 but continuing the expansion below the back pressure line1 the work done is ,m - ,s4 ,this latter case as compared with the first when expansion does not continue below the back pressure line gives an efficiency 7power factor7 of 7,m - ,s7 ,m1 the shaded area representing so much loss4 ,this condition is exactly analogous to the case of a steam engine1 expanding the steam below the back or exhaust pressure1 a condition sometimes caused by the action of the governor in considerably reducing the cut off for very light load4 ,an indicator diagram of such steam distribution is shown in fig4 #a1cea4 ,this gives a negative loop in the diagram indicated by the shaded section4 ,it must be evident that the average pressure of the shaded loop portion of the diagram must be subtracted from that of the other portion1 because during the expansion below the exhaust pressure line1 the back pressure is in excess of the forward pressure exerted on the piston by the expanding steam1 and the engine would accordingly reverse its motion1 were it not for the energy previously stored up in the fly wheel in the form of momentum1 which keeps the engine moving during this period of back thrust4 ,evidently the shaded area must be subtracted from the positive area to obtain the net work done during the stroke4 ,hence following the analogy as far as possible if ,m work 7watts7 be done during each revolution 7cycle7 when steam does not expand below back pressure 7when current and pressure are in phase71 and ,s negative work 7negative watts7 be done when steam expands below back pressure 7when there is lag71 the efficiency 7power factor7 is 7,m - ,s7 ,m4 ,illustration3 ,,fig4 #a1ceb4--,power curve illustrating the so-called wattless current in which case the power factor is zero4 ,by noting that the curve projects equally on each side of the zero line1 the power areas equal the negative power areas1 hence the summation of these areas for the period is zero1 that is1 the two areas minus the two shaded areas equal zero4 ,it should be noted that the line of average power ,,ww'1 which is visible in the other figures1 here coincides with the zero line1 and the average power then is zero1 since the positive part above the zero line is equal to and offsets the negative 7shaded7 part below the line4 ,this is the case of wattless current and 7considering a circuit with resistance so small that it may be considered as zero7 shows plainly the possibility of having full load current and voltage on a circuit yet delivering no power1 the current simply surging to and fro without an actual transfer of power4 ,wattless ,current2 ,power ,factor ,zero4--,when the power factor is zero1 it means that the phase difference between the current and the pressure is #ij4 ,the term wattless current1 as understood1 does not indicate an absence of electrical energy in the circuit2 its elements are there1 but not in an available form for external work4 ,the false power due to the so called wattless current pulsates in and out of the circuit without accomplishing any useful work4 ,an example of wattless current1 showing that the power factor is zero is illustrated in fig4 #a1cec4 ,here the angle of lag is #ij1 that is1 the current is #ij behind the pressure4 ,the power curve is constructed from the current and pressure curves1 and1 as shown in the diagram1 it lies as much below the zero line as above1 that is1 the two plus power areas which occur during each period are equal to the two negative 7shaded7 power areas1 showing that the circuit returns as much energy as is sent out4 ,hence1 the total work done during each period is zero1 indicating that although a current be flowing1 this current is not capable of doing external work4 ,illustration3 ,,fig4 #a1cec4--;,example of wattless current showing that the power factor is zero when the phase difference between current and pressure is #ij4 ,for zero power factor the current may lead #ij as in fig4 #a1ceb1 or lag #ij as here shown4 ,since the shaded or negative areas the plus areas1 the average power 7indicated by ,,ww' which coincides with the zero line7 is zero1 that is the circuit is carrying current under pressure yet delivering no power1 hence1 the power factor is zero4 ,ques4 ,is the condition as just described met with in practice8 ,ans4 ,no4 ,ques4 ,why not8 ,ans4 ,the condition just described involves that the circuit have no resistance1 all the load being reactance1 but it is impossible to have a circuit without some resistance1 though the resistance may be made very small in comparison to the reactance so that a close approach to wattless current is possible4 ,ques4 ,give some examples where the phase difference is very nearly #ij4 ,ans4 ,if an alternator supplies current to a circuit having a very small resistance and very large inductance1 the current would lag nearly #ij behind the pressure4 ,the primary current of a transformer working with its secondary on an open circuit is a practical example of a current which represents very little energy4 ,illustration3 ,,fig4 #a1ced4--,performance curves of ,general ,electric single phase repulsion induction motor4 ,ques4 ,when the phase difference between the current and pressure is #ij1 why is the current called wattless8 ,ans4 ,because the product of such a current multiplied by the pressure does not represent any watts expended4 ,a man lifting a weight1 and then allowing it to descend the same distance to its initial position1 as shown in figs4 #a1cee to #a1ceg1 presents a mechanical analogy of wattless current4 ,let the movement of the weight represent the current and the weight the pressure4 ,then calling the weight #aj pounds 7volts71 and the distance two feet 7amperes74 ,the work done by the man 7alternator7 on the weight in lifting it is #aj pounds #b feet #bj foot pounds 7#a7 7#aj volts #b amperes #bj watts47 ,the work done on the man by the weight in forcing his hand down as his muscles relax is #aj pounds #b feet #bj foot pounds 7#b7 7#aj volts #b amperes #bj watts47 ,from 7#a7 and 7#b7 it is seen that the work done by the man on the weight is equal to the work done by the weight on the man1 hence no useful work has been accomplished2 that is1 the potential energy of the weight which it originally possessed has not been increased4 ,illustration3 ,,figs4 #a1cee to #a1ceg4--,mechanical analogy of wattless current4 ,if a man lift a weight any distance1 as from the position of fig4 #a1cee to position of fig4 #a1cef1 he does a certain amount of work on the weight giving it potential energy4 ,when he lowers it to its original position1 as in fig4 #a1ceg1 the weight loses the potential energy previously acquired1 that is1 it is given back to the man1 the system 7man and weight7 having returned to its original condition as in fig4 #a1cee4 ,during such a cycle1 the work done by the man on the weight is equal to the work done by the weight on the man and no useful external work has been accomplished4 ,why the ,power ,factor is equal to ,cos 4--,in the preceding figures showing power curves for various phase relations between current and pressure1 the curves show the instantaneous values of the fluctuating power1 but what is of more importance1 is to determine the average power developed4 ,when the current is in phase with the pressure1 it is a simple matter1 because the power or watts amperes volts that is1 the product of the ammeter and voltmeter readings will give the power4 ,however1 the condition of synchronism of current and pressure hardly ever exists in practice1 there being more or less phase difference4 ,illustration3 ,,fig4 #a1ceh4--,method of obtaining the active component of the current2 diagram illustrating why the power factor is equal to cos 4 ,if ,,ab and ,,ac be respectively the given current and pressure1 or readings of the ammeter and voltmeter1 and the angle of phase difference between current and pressure1 then drawing from ,b1 ,,bd perpendicular to ,,ac will give ,,ad the active component4 ,now1 true power ,,ac ,,ad1 but ,,ad ,,ab cos 1 hence true power ,,ac ,,ab cos 4 ,again1 apparent power ,,ac ,,ab1 and since true power apparent power power factor1 the power factor cos 4 ,when the current is not in phase with the pressure1 it is considered as made up of two components at right angles to each other4 #a4 ,the active component1 in phase with the pressure2 #b4 ,the wattless component1 at right angles to the pressure4 ,with phase difference between current and pressure the product of ammeter and voltmeter readings do not give the true power1 and in order to obtain the latter1 the active component of the current in phase with the pressure must be considered1 that is1 true power volts active amperes 7#a7 ,the active component of the current is easily obtained graphically as in fig4 #a1ceh4 ,with any convenient scale draw ,,ab equal to the current as given or read on the ammeter1 and ,,ac1 equal to the pressure1 making the angle between ,,ab and ,,ac equal to the phase difference between the current and pressure4 ,from ,b1 draw the line ,,bd perpendicular to ,,ac1 then ,,bd will be the wattless component1 and ,,ad 7measured with the same scale as was used for ,,ab7 the active component of the current1 or that component in phase with the pressure4 ,hence from equation 7#a7 true power ,,ac ,,ad 7#b7 ,now in the right triangle ,,abd ,,ad -- cos ,,ab from which ,,ad ,,ab cos 7#c7 ,substituting this value of ,,ad in equation 7#b7 gives true power ,,ac ,,ab cos 7#d7 ,now the power factor may be defined as3 that quantity by which the apparent watts must be multiplied in order to give the true power4 ,that is true power apparent watts power factor 7#e7 ,comparing equations 7#d7 and 7#e71 ,,ac ,,ab in 7#d7 is equal to the apparent watts1 hence1 the power factor in 7#e7 is equal to cos 4 ,that is1 the power factor is numerically equal to the cosine of the angle of phase difference between current and pressure4 ,,example ,i4--,an alternator supplies a current of #bjj amperes at a pressure of #a1jjj volts4 ,if the phase difference between the current and pressure be #cj1 what is the true power developed8 ,in fig4 #a1cei1 draw ,,ab to scale1 equal to #bjj amperes1 and draw ,,ac of indefinite length making an angle of #cj with ,,ab4 ,from ,b1 draw ,,bd perpendicular to ,,ac which gives ,,ad1 the active component1 and which measured with the same scale as was used in laying off ,,ab1 measures #agc4b amperes4 ,the true power developed then is true watts #agc4b #a1jjj #agc4b kw4 ,the true power may be calculated thus3 ,from the table cos #cj 4#hff1 hence true watts #bjj #a1jjj 4#hff #agc4b kw4 ,illustration3 ,,fig4 #a1cei4--;,diagram for obtaining the active component of the current in a circuit having a current of #bjj amperes and angle of lag of #cj4 ,,example ,,ii4--,if in an alternating current circuit1 the voltmeter and ammeter readings be #aaj and #bj and the angle of lag #de1 what is the apparent power and true power8 ,the apparent power is simply the product of the current and pressure readings or apparent power #bj #aaj #b1bjj watts ,the true power is the product of the apparent power multiplied by the cosine of the angle of lag4 ,cos #de 4#gjg1 hence true power #b1bjj 4#gjg #a1eee4d watts4 ,ques4 ,does the power factor apply to capacity reactance in the same way as to inductance reactance8 ,ans4 ,yes4 ,the angles of lag and of lead1 are from the practical standpoint1 treated as if they lay in the first quadrant of the circle4 ,even the negative sign of the tangent when it occurs is simply used to determine whether the angle be one of lag or of lead1 but in finding the value of the angle from a table it is treated as a positive quantity4 ,illustration3 ,,fig4 #a1cfj4--;,diagram for obtaining the power factor for example ,,ii4 ,with convenient scale1 lay off ,,ab #bj amperes4 ,from ,a draw ,,ac at #de to ,,ab1 and from ,b1 draw ,,bd perpendicular to ,,ac4 ,then1 the power factor which is equal to cosine of angle of lag1 ,,ad ,,ab 7by measurement7 #ad4ae #bj 4#gjg4 ,ques4 ,in introducing capacity into a circuit to increase the power factor what should be considered8 ,ans4 ,the cost and upkeep of the added apparatus as well as the power lost in same4 ,ques4 ,how is power lost in a condenser8 ,ans4 ,the loss is principally due to a phenomenon known as dielectric hysteresis1 which is somewhat analogous to magnetic hysteresis4 ,the rapidly alternating charges in a condenser placed in an alternating circuit may be said to cause alternating polarization of the dielectric1 and consequent heating and loss of energy4 ,ques4 ,when is inductance introduced into a circuit to increase the power factor8 ,ans4 ,when the phase difference is due to an excess of capacity4 ,,example4--,a circuit having a resistance of #c ohms1 and a resultant reactance of #d ohms1 is connected to a #ajj volt line4 ,what is3 #a1 the impedance1 #b1 the current1 #c1 the apparent power1 #d1 the angle of lag1 #e1 the power factor1 and #f1 the true power8 #a4 ,the impedance of the circuit4 ,z 7#c #d7 #e ohms4 #b4 ,the current4 current volts impedance #ajj #e #bj amperes4 #c4 ,the apparent power4 apparent power volts amperes #ajj #bj #b1jjj watts4 #d4 ,the tangent of the angle of lag4 tan reactance resistance #d #c #a4cc4 ,from table of natural tangents 7page #dea7 #ec4 #e4 ,the power factor4 ,the power factor is equal to the cosine of the angle of lag1 that is1 power factor cos #ec 4#fjb 7from table74 #f4 ,the true power4 ,the true power is equal to the apparent watts multiplied by the power factor1 or true power volts amperes cos #ajj #bj 4#fjb #a1bjd watts4 ,ques4 ,prove that the power factor is unity when there is no resultant reactance in a circuit4 ,ans4 ,when there is no reactance1 tan which is equal to reactance resistance becomes #j ,r #j4 ,the angle 7the phase difference angle7 whose tangent is #j is the angle of #j degrees4 ,hence1 the power factor which is equal to cos cos #j #a4 ,illustration3 ,,figs4 #a1cfa to #a1cfe4--;,diagrams illustrating why the power factor is unity or one when there is no resultant reactance in the circuit1 that is1 when the circuit is resonant or has only resistance4 ,the power factor is equal to the cosine of the angle of lag 7or lead74 ,in the figures this angle is ,,bac or and the value of the natural cosine ,,ac gives the power factor4 ,by inspection of the figures1 it is evident that decreasing the reactance decreases the angle and increases cos or the power factor4 ,the circular arc in each figure being at unity distance from the center ,a1 the power factor with decreasing reactance evidently approaches unity as its limit1 this limit being shown in fig4 #a1cfe where the reactance ,b',c' #j4 ,ques4 ,what is the usual value of the power factor in practice8 ,ans4 ,slightly less than one4 ,ques4 ,why is it desirable to keep the power factor near unity8 ,ans4 ,because with a low power factor1 while the alternator may be carrying its full load and operating at a moderate temperature1 the consumer is paying only for the actual watts which are sent over the line to him4 ,illustration3 ,,fig4 #a1cff4--;,diagram illustrating power factor test1 when on non-inductive and inductive circuits4 ,the instruments are connected as shown and by means of the double throw switch can be put on either the non-inductive or inductive circuit4 ,first turn switch to left so that current passes through the lamps2 for illustration1 the following readings are assumed3 ammeter #aj1 voltmeter #aaj1 and wattmeter #a1ajj4 ,the power factor then is wattmeter reading volts amperes #a1ajj actual watts #a1ajj apparent watts #a1 that is1 on non-inductive circuit the power factor is unity4 ,now throwing the switch to the right connecting instruments with the inductive circuits1 then for illustration the following readings may be assumed3 ammeter #h1 voltmeter #aaj1 and wattmeter #fhd4 ,now1 as before1 power factor wattmeter reading volts amperes #fhd 7#h #aaj7 #fhd #hhj 4#gh4 ,for instance1 if a large alternator supplying #a1jjj kilowatts at #f1fjj volts in a town where a number of induction motors are used on the line be operating with a power factor of say 4#fbe during a great portion of the time1 the switchboard instruments connected to the alternator will give the following readings3 ,voltmeter #f1fjj volts2 ammeter #bdb4d amperes2 power factor meter 4#fbe4 ,the apparent watts would equal #a1fjj1jjj watts or #a1fjj kilowatts1 which1 if multiplied by the power factor 4#fbe would give #ajj1jjj1jjj watts or #a1jjj kilowatts which is the actual watts supplied4 ,the alternator and line must carry #bdb4d amperes instead of #aea amperes and the difference #bdb4d - #aea #ia4d amperes represents a wattless current flowing in the circuit which causes useless heating of the alternator4 ,the mechanical power which is required to drive the alternator is equivalent to the actual watts produced1 since that portion of the current which lags1 is out of phase with the pressure and therefore requires no energy4 ,ques4 ,how are alternators rated by manufacturers in order to avoid disputes8 ,ans4 ,they usually rate their alternators as producing so many kilovolt amperes instead of kilowatts4 ,illustration3 ,,fig4 #a1cfg4--;,ayrton and ,sumpner method of alternating current power measurement4 ,three voltmeters are required1 and accordingly the method is sometimes called the three voltmeter method4 ,it is a good method where the voltage can be regulated to suit the load4 ,in the figure1 let the non-inductive resistance ,r be placed in series with the load ,,ab4 ,measure the following voltages3 ,v across the terminals of ,r1 ,v across the load ,,ab1 and ,v across both1 that is from ,a to ,c4 ,then1 true watts 7,v - ,v - ,v7 #b,r4 ,the best conditions are when ,v ,v1 and1 if ,r ohm1 then ,w ,v - ,v - ,v4 ,ques4 ,what is a kilovolt ampere 7kva78 ,ans4 ,a unit of apparent power in an alternating current circuit which is equal to one kilowatt when the power factor is equal to one4 ,the machine mentioned on page #a1abj would be designed to carry #aea amperes without overheating and also carry slight overloads for short periods4 ,it would be rated as #f4f kilo volts and #aea amperes which would equal approximately #a1jjj kilowatts when the power factor is #a or unity1 and it should operate without undue heating4 ,now the lower the power factor becomes1 the greater the heating trouble will be in trying to produce the #a1jjj actual kilowatts4 ,illustration3 ,,fig4 #a1cfh--;,curves illustrating power factor4 ,in a circuit having no capacity or inductance1 the power is given by the product of the respective readings of the voltmeter and ammeter1 as in the case of a direct current4 ,in the case of a circuit having capacity or inductance1 this product is higher than the true value as found by a wattmeter1 and is known as the apparent watts4 ,the ratio true watts apparent watts is known as the power factor4 ,the current flowing in an inductive circuit1 such as the primary of a transformer1 is really made up of two components1 as already explained1 one of which 7the load or active component71 is in phase with the pressure1 while the other the magnetizing component1 is at right angles to it1 that is1 it attains its crest value when the other is at zero1 and vice versa4 ,to illustrate1 take a complete cycle divided into #cfj degrees and lay out on it the current required to correspond to a given load on the secondary of a transformer1 say a crest value of #ajj amperes1 and at right angles to this lay out the current required for exciting the magnetic circuit of the transformer1 giving ,a1 merely for purposes of illustration1 a crest value of #be amperes4 ,combining these curves1 the dotted curve in the figure is obtained and which represents the resultant current that would be indicated by an ammeter placed in the primary circuit of the transformer4 ,it will be noted that this current attains its maximum at a point #ad #b later than the load current1 giving the angle of lag4 ,multiplying the apparent watts by the cosine of the angle of lag gives the true watts4 ,now assuming the diagram to show the full load condition of the transformer1 the angle of lag being #ad #b1 the power factor at full load is 4#ig 74#ig being the value of the natural cosine of #ad #b as obtained from table1 such as on page #dea74 ,with no external load on the transformer1 the load component of the current is that necessary to make up the core losses4 ,for instance1 at #e amperes1 while the magnetizing current remains as before at #be amperes1 the angle of lag becomes #gh #da and the power factor 4#aif4 ,it is thus seen that in transformers1 induction motors1 etc41 the power factor is a function of the load4 ,ques4 ,how can the power factor be kept high8 ,ans4 ,by carefully designing the motors and other apparatus and even making changes in the field current of motors which are already installed4 ,ques4 ,how is the power factor determined in station operation8 ,ans4 ,not by calculation1 but by reading a meter which forms one of the switchboard instruments4 ,illustration3 ,,fig4 #a1cfh4--;,fleming's combined voltmeter and ammeter method of measuring power in alternating current circuits4 ,it is quite accurate and enables instruments in use to be checked4 ,in the figure1 ,r is a non-inductive resistance connected in shunt to the inductive load4 ,the voltmeter ,v measures the pressure across the resistance ,,xy4 ,a and ,a are ammeters connected as shown4 ,then1 true watts 7,a - ,a - 7,v_/,r77 ,r _/ #b4 ,if the volt meter ,v take an appreciable amount of current1 it may be tested as follows3 disconnect ,r and ,v at ,y1 and see that ,a and ,a are alike2 then connect ,r and ,v at ,y again1 and disconnect the load4 ,a will equal current taken by ,r and ,v in parallel4 ,ques4 ,when is the power factor meter of importance in station operation1 and why8 ,ans4 ,when rotary converters are used on alternating current lines for supplying direct currents and the sub-station operators are kept busy adjusting the field rheostat of the rotary to maintain a high power factor and prevent overheating of the alternators during the time of day when there is the maximum demand for current or the peak of the load4 ,,example4--,an alternator delivers current at #hjj volts pressure at a frequency of #fj1 to a circuit of which the resistance is #ge ohms and 4#be henry4 ,determine3 a1 the value of the current1 b1 angle of lag1 c1 apparent watts1 d1 power factor1 e1 true power4 a4 ,value of current pressure ,e current --------- ----------------- impedance 7,r 7#b;f,l77 #hjj --------------------------------- #f4g amperes 7#ge 7#b #c4adaf #fj 4#be77 b4 ,the angle of lag reactance #b;f,l #b #c4adaf #fj 4#be tan ---------- ------ --------------------- #a4be resistance ,r #ge angle of lag #ea #ae 7from table1 page #dea74 c4 ,the apparent power apparent power volts amperes #hjj #f4g #e1cfj watts #e4cf kva4 d4 ,the power factor power factor cosine of the angle of lag cos #ea #ae 4#fbf4 e4 ,the true power true power apparent power power factor #e1cfj 4#fbf #c1cee watts4 ,illustration3 ,,fig4 #a1cfi4--,wattmeter method of three phase power measurement4 ,two wattmeters are required in unbalanced systems as shown in the illustration4 ,the total power transmitted is then the algebraic sum of the readings of the two wattmeters4 ,if the power factor be greater than 4#e1 the power is the arithmetical sum1 and if it be less than 4#e1 the power is the arithmetical difference of the readings4 ,,chapter ,,xlix ,,alternators ,use of ,alternators4--,the great increase in the application of electricity for supplying power and for lighting purposes in industry1 commerce1 and in the home1 is due chiefly to the economy of distribution of alternating current4 ,direct current may be used to advantage in densely populated districts1 but where the load is scattered1 it requires1 on account of its low voltage1 too great an investment in distributing lines4 ,in such cases the alternator is used to advantage1 for while commutators can be built for collecting direct current up to #a1jjj volts1 alternators can be built up to #ab1jjj volts or more1 and this voltage increased1 by step up transformers of high economy1 up to #ge1jjj or #ajj1jjj volts4 ,since the copper cost is inversely as the square of the voltage1 the great advantage of alternating current systems is clearly apparent4 ,the use of alternating current thus permits a large amount of energy to be economically distributed over a wide area from a single station1 not only reducing the cost of the wiring1 but securing greater economy by the use of one large station1 instead of several small stations4 ,the higher voltages generated by alternators enables the transmission of electrical energy to vastly greater distances than possible by a direct current system1 so that the energy from many waterfalls that otherwise would go to waste may be utilized4 ,classes of ,alternator4--,there are various ways of classifying alternators4 ,they may be divided into groups1 according to3 #a1 the nature of the current produced2 #b1 type of drive2 #c1 method of construction2 #d1 field excitation2 #e1 service requirements1 etc4 ,from these several points of view1 alternators then may be classified3 #a4 ,with respect to the current1 as3 a4 ,single phase2 b4 ,polyphase4 #b4 ,with respect to the type of drive1 as3 a4 ,belt or chain driven2 b4 ,direct connected4 #c4 ,with respect to construction1 as3 a4 ,revolving armature2 b4 ,revolving field2 c4 ,inductor4 ,homopolar and heteropolar4 #d4 ,with respect to mode of field excitation1 as3 a4 ,self-exciting2 b4 ,separately excited2 ,exciter direct connected1 or gear driven4 c4 ,compositely excited4 #e4 ,with respect to service requirements1 as3 a4 ,slow speed2 b4 ,fly wheel2 c4 ,high speed2 d4 ,water wheel type2 e4 ,turbine driven4 ,single ,phase ,alternators4--,as a general rule1 when alternators are employed for lighting circuits1 the single phase machines are preferable1 as they are simpler in construction and do not generate the unbalancing voltages often occurring in polyphase work4 ,illustration3 ,,fig4 #a1cgj4--;,elementary four pole single phase alternator4 ,it has four inductors whose pitch is the same as the pole pitch4 ,they are connected in series and terminate at the two collector rings as shown4 ,the poles being alternate ,n and ,s1 it is evident that there will be two cycles of the current per revolution of the armature4 ,for any number of poles then the number of cycles equals the number of poles divided by two4 ,applying ,fleming's rule for induced currents1 the direction of the current induced in the inductors is easily found as indicated by the arrows4 ,the field magnets are excited by coils supplied with direct current1 usually furnished from an external source2 for simplicity this is not shown4 ,the magnets may be considered as of the permanent type4 ,ques4 ,what are the essential features of a single phase alternator8 ,ans4 ,fig4 #a1cgj shows an elementary single phase alternator4 ,it consists of an armature1 with single phase winding1 field magnets1 and two collector rings and brushes through which the current generated in the armature passes to the external circuit4 ,ques4 ,in what respect do commercial machines differ mostly from the elementary alternator shown in fig4 #a1cgj1 and why8 ,ans4 ,they have a large number of poles and inductors in order to obtain the desired frequency1 without excessive speed1 and electromagnets instead of permanent magnets4 ,illustration3 ,,fig4 #a1cga4--;,developed view of elementary single phase four pole alternator and sine curve showing the alternating current or pressure generated during one revolution4 ,the armature is here shown as a flat surface upon which a complete view of the winding is seen4 ,if ,m be any position of an inductor1 by projecting up to the curve gives ,n1 the corresponding value of the current or pressure4 ,magnetic lines are shown at the poles representing a field decreasing in intensity from a maximum at the center to zero at points half way between the poles1 this being the field condition corresponding to the sine form of wave4 ,in actual machines the variation from the sine curve is considerable in some alternators4 ,see figs4 #a1bdg and #a1bdh4 ,ques4 ,in actual machines1 why must the magnet cores be spaced out around the armature with considerable distance between them8 ,ans4 ,in order to get the necessary field winding on the cores1 and also to prevent undue magnetic leakage taking place1 laterally from one limb to the next of opposite sign4 ,ques4 ,is there any gain in making the width of the armature coils any greater than the pole pitch1 and why8 ,ans4 ,no1 because any additional width will not produce more voltage1 but on the contrary will increase the resistance and inductance of the armature4 ,illustration3 ,,fig4 #a1cgb4--;,elementary four pole two phase alternator4 ,the winding consists of one inductor per phase per pole1 that is1 four inductors per phase1 the inductors of each phase being connected in series by the connectors and terminating at the collector rings4 ,this arrangement requires four collector rings1 giving two independent circuits4 ,the pitch of the inductors of each phase is equal to the pole pitch1 and the phase difference is equal to one-half the pole pitch1 that is1 phase ,b winding begins at ,b1 a point half-way between inductors ,a and ,a' of phase ,a winding4 ,hence when the current or pressure in phase ,a is at a maximum1 in the ideal case1 when inductor ,a for instance is under the center of a pole1 the current or pressure in ,b is zero1 because ,b is then half-way between the poles4 ,polyphase ,alternators4--,a multiphase or polyphase alternator is one which delivers two or more alternating currents differing in phase by a definite amount4 ,for example1 if two armatures of the same number of turns each be connected to a shaft at #ij degrees from each other and revolved in a bipolar field1 and each terminal be connected to a collector ring1 two separate alternating currents1 differing in phase by #ij degrees1 will be delivered to the external circuit4 ,thus a two phase alternator will deliver two currents differing in phase by one-quarter of a cycle1 and similarly a three phase alternator 7the three armatures of which are set #abj degrees from each other7 will deliver three currents differing in phase by one-third of a cycle4 ,in practice1 instead of separate armatures for each phase1 the several windings are all placed on one armature and in such sequence that the currents are generated with the desired phase difference between them as shown in the elementary diagrams #a1cgb and #a1cgc for two phase current1 and figs4 #a1cgd and #a1cge for three phase current4 ,illustration3 ,,fig4 #a1cgc4--;,developed view of elementary two phase four pole alternator and sine curves1 showing the alternating current or pressure generated during one revolution of the armature4 ,the complete winding for the three phases are here visible1 the field magnets being represented as transparent so that all of the inductors may be seen4 ,by applying ,fleming's rule1 as the inductors progress under the poles1 the directions and reversals of current are easily determined1 as indicated by the sine curves4 ,it will be seen from the curves that four poles give two cycles per revolution4 ,inductors ,a1 and ,b are lettered to correspond with fig4 #a1cgb1 with which they should be compared4 ,ques4 ,what use is made of two and three phase current8 ,ans4 ,they are employed rather for power purposes than for lighting1 but such systems are often installed for both services4 ,ques4 ,how are they employed in each case8 ,ans4 ,for lighting purposes the phases are isolated in separate circuits1 that is1 each is used as a single phase current4 ,for driving motors the circuits are combined4 ,illustration3 ,,fig4 #a1cgd4--;,elementary four pole three phase alternator4 ,there are three sets of inductors1 each set connected in series and spaced on the drum with respect to each other two-thirds pole pitch apart4 ,as shown1 six collector rings are used1 but on actual three phase machines only three rings are employed1 as previously explained4 ,the inductors have distinctive coverings for the different phases4 ,the arrows indicate the direction in which the induced pressures tend to cause currents4 ,ques4 ,why are they combined for power purposes8 ,ans4 ,on account of the difficulty encountered in starting a motor with single phase current4 ,ferarris1 of ,italy1 in #ahhh discovered the important principle of the production of a rotating magnetic field by means of two or more ,illustration3 ,,fig4 #a1cge4--;,elementary four pole three-phase alternator and sine curves showing current or pressure conditions for one revolution4 ,six collector rings are shown giving three independent circuits4 ,the pitch of the inductors for each phase is the same as the pole pitch1 and the phase difference is equal to two-thirds of the pole pitch1 giving the sequence of current or pressure waves as indicated by the sine curves4 ,the waves follow each other at period1 that is1 the phase difference is #abj degrees4 ,inductors ,a1 ,b1 and ,c1 the beginning of each phase winding1 are lettered to correspond with fig4 #a1cgd1 with which they should be compared4 _/ alternating currents displaced in phase from one another1 and he thus made possible by means of the induction motor1 the use of polyphase currents for power purposes4 ,ques4 ,what is the difficulty encountered in starting a motor with single phase current8 ,ans4 ,a single phase current requires either a synchronous motor to develop mechanical power from it1 or a specially constructed motor of dual type1 the idea of which is to provide a method of getting rotation by foreign means and then to throw in the single phase current for power4 ,illustration3 ,,fig4 #a1cgf4--;,diagram of six phase winding with star grouping1 being equivalent to a three phase winding in which the three phases are disconnected from each other and their middle points united at a common junction4 ,illustration3 ,,fig4 #a1cgg4--;,diagram of six phase winding with mesh grouping4 ,six ,phase and ,twelve ,phase ,windings4--,these are required for the operation of rotary converters4 ,the phase difference in a six phase winding is #fj degrees and in a twelve phase winding #cj degrees4 ,a six phase winding can be made out of a three phase winding by disconnecting the three phases from each other1 uniting their middle points at a common junction1 as shown by diagram fig4 #a1cgf4 ,this will give a star grouping with six terminals4 ,in the case of a mesh grouping1 each of the three phases must be cut into two parts and then reconnected as shown in fig4 #a1cgg4 ,illustration3 ,,fig4 #a1cgh4--;,diagram of twelve phase winding star grouping4 ,illustration3 ,,fig4 #a1cgi4--;,diagram of six phase winding consisting of combination of mesh and star grouping4 ,as the phase difference of a twelve phase winding is one-half that of a six phase winding1 the twelve phases may be regarded as a star grouping of six pairs crossed at the middle point of each pair as shown in fig4 #a1cgh1 or in mesh grouping for converters they may be arranged as a twelve pointed polygon4 ,they may also be grouped as a combination of mesh and star as shown in fig4 #a1cgi1 which1 however1 is not of general interest4 ,belt or ,chain ,driven ,alternators4--,the mode in which power is transmitted to an alternator for the generation of current is governed chiefly by conditions met with where the machine is to be installed4 ,in many small power stations and isolated plants the use of a belt drive is unavoidable4 ,in some cases the prime mover is already installed and cannot be conveniently arranged for direct connection1 in others the advantage to be gained by an increase in speed more than compensates for the loss involved in belt transmission4 ,illustration3 ,,fig4 #a1chj4--;,belt-driven alternator4 ,by use of a belt1 any desired speed ratio is obtained1 enabling the use of a high speed alternator which1 being smaller than one of slow speed1 is cheaper4 ,it affords means of drive for line shaft and has other advantages1 but requires considerable space and is not a positive drive4 ,belting exerts a side pull which results in friction and wear of bearings4 ,means for tightening the belt as shown in fig4 #a1cha1 or equivalent1 must be provided4 ,there are many places where belted machines may be used advantageously and economically4 ,they are easily connected to an existing source of power1 as1 for instance1 a line shaft used for driving other machinery1 and for comparatively small installations they are lower in first cost than direct connected machines4 ,moreover1 when connected to line shaft they are run by the main engine which as a rule is more efficient than a small engine direct connected4 ,where there is sufficient room between pulley centers1 a belt is a satisfactory medium for power transmission1 and one that is largely used4 ,it is important that there be liberal distance between centers1 especially in the case of generators or motors belted to a medium or slow speed engine1 because1 owing to the high speed of rotation of the electric machines1 there is considerable difference in their pulley diameters and the drive pulley diameter2 hence1 if they were close together1 the arc of contact of the belt with the smaller pulley would be appreciably reduced1 thus diminishing the tractive power of the belt4 ,illustration3 ,,fig4 #a1cha4--,sub-base and ratchet device for moving alternator to tighten belt4 ,a ratchet ,a1 operated by lever ,b1 works the block ,c by screw connection1 causing it to move the block4 ,the latter1 engaging with the frame1 causes it to move1 thus providing adjustment for belt4 ,after tightening belt1 the bolts ,d1 which pass through the slots in the sub-base1 are tightened1 thus securing the machine firmly in position4 ,ques4 ,what provision should be made in the design of an alternator to adapt it to belt drive8 ,ans4 ,provision should be made for tightening the belt4 ,illustration3 ,,fig4 #a1chb4--;,allis-,chalmers pedestal type1 belted alternator4 ,the bearings are of the ring oiling form with large oil reservoirs4 ,the bearings have spherical seats and are self aligning4 ,ques4 ,how is this done8 ,ans4 ,sometimes by an idler pulley1 but usually by mounting the machine on a sub-base provided with slide rails1 as in fig4 #a1cha1 the belt being tightened by use of a ratchet screw which moves the machine along the base4 ,illustration3 ,,fig4 #a1chc4--;,diagram illustrating rule for horse power transmitted by belts4 ,a single belt travelling at a speed of #a1jjj feet per minute will transmit one horse power2 a double belt will transmit twice that amount1 assuming that the thickness of a double belt is twice that of a single belt4 ,this is conservative practice1 and a belt so proportioned will do the work in practically all cases4 ,the above rule corresponds to a pull of #cc lbs4 per inch of width4 ,many designers proportion single belts for a pull of #de lbs4 ,for double belts of average thickness1 some writers say that the transmitting efficiency is to that of single belts as #aj is to #g4 ,this should not be applied to the above rule for single belts1 as it will give an unnecessarily large belt4 ,ques4 ,give a rule for obtaining the proper size of belt to deliver a given horse power4 ,ans4 ,a single belt travelling at a speed of one thousand feet per minute will transmit one horse power2 a double belt will transmit twice that amount4 ,this corresponds to a working strain of #cc lbs4 per inch of width for single belt1 or #ff lbs4 for double belt4 ,many writers give as safe practice for single belts in good condition a working tension of #de lbs4 per inch of width4 ,ques4 ,what is the best speed for maximum belt economy8 ,ans4 ,from #d1jjj to #d1ejj feet per minute4 ,,example4--,what is the proper size of double belt for an alternator having a #af inch pulley1 and which requires #ej horse power to drive it at #a1jjj revolutions per minute full load8 ,the velocity of the belt is circumference in feet revolutions feet per minute #af -- #c4adaf #a1jjj #d1ahh4 #ab ,horse power transmitted per inch width of double belt at #d1ahh feet speed #d1ahh #b ----- #h4ch4 #a1jjj ,illustration3 ,,fig4 #a1chd4--;,fort ,wayne revolving field belt driven alternator4 ,it is designed for belted exciter1 having a shaft extension at the collector ring end for exciter driving pulley4 ,width of double belt for #ej horse power #ej #h4ch #e4ig1 say #f inch4 ,ques4 ,what are the advantages of chain drive8 ,ans4 ,the space required is much less than with belt drive1 as the distance between centers may be reduced to a minimum4 ,it is a positive drive1 that is1 there can be no slip4 ,less liability of becoming detached1 and1 because it is not dependent on frictional contact1 the diameters of the sprockets may be much less than pulley diameter for belt drive4 ,illustration3 ,,figs4 #a1che and #a1chf4--;,diagram showing the distinction between direct connected and direct coupled units4 ,in a direct connected unit1 fig4 #a1che1 the engine and generator are permanently connected on one shaft1 there being one bed plate upon which both are mounted4 ,an engine and generator are said to be direct coupled when each is independent1 as in fig4 #a1chf being connected solely by a jaw or friction clutch or equivalent at times when it is desired to run the generator4 ,at other times the generator may be disconnected and the engine run to supply power for other purposes4 ,ques4 ,what are some objections8 ,ans4 ,a lubricant is required for satisfactory operation1 which causes more or less dirt to collect on the chain1 requiring frequent cleaning2 climbing of teeth when links and teeth become worn2 noise and friction4 ,illustration3 ,,fig4 #a1chg4--;,engberg direct connected1 or engine type alternator4 ,in many places direct connected units are used1 owing to the great saving in floor space1 convenience of operation1 and absence of belts4 ,direct ,connected ,alternators4--,there are a large number of cases where economy of space is of prime importance1 and to meet this condition the alternator and engine are direct connected1 meaning1 that there is no intermediate gearing such as belt1 chain1 etc41 between engine and alternator4 ,one difficulty encountered in the direct connection of engine and alternator is the fact that the most desirable rotative speed of the engine is less than that of the alternator4 ,accordingly a compromise is made by raising the engine speed and lowering the alternator speed4 ,the insistent demand for direct connected units in the small and medium sizes1 especially for direct current units1 was the chief cause resulting in the rapid and high development of what is known as the high speed automatic engine4 ,increasing the engine speed means that more horse power is developed for any given cylinder dimensions1 while reducing the speed of the generator involves that the machine must be larger for a given output1 and in the case of an alternator more poles are required to obtain a given frequency1 resulting in increased cost4 ,the compactness of the unit as a whole1 simplicity1 and general advantages are usually so great as to more than offset any additional cost of the generator4 ,illustration3 ,,fig4 #a1chh4--;,crocker-,wheeler #b1jjj kva4 #b1djj volt coupled type alternator4 ,the coupled type of alternator is desirable for use with steam1 gas1 and oil engines1 and water wheels where it is inconvenient to mount the alternator on the engine shaft or to extend the engine base to accommodate a bearing4 ,this type consists of alternator complete with shaft and bearings similar to belt type machines1 but with bearings not necessary designed for the side pull of belts4 ,ques4 ,what is the difference between a direct connected and a direct coupled unit8 ,ans4 ,a direct connected unit comprises an engine and generator permanently connected2 direct coupling signifies that engine and generator are each complete in itself1 that is1 having two bearings1 and are connected by some device such as friction clutch1 jaw clutch1 or shaft coupling4 ,revolving ,armature ,alternators4--,this type of alternator is one which has its parts arranged in a manner similar to a dynamo1 that is1 the armature is mounted on a shaft so it can revolve while the field magnets are attached to a circular frame and arranged radially around the armature1 as shown in fig4 #a1chi4 ,it may be single or polyphase1 belt driven1 or direct connected4 ,illustration3 ,,fig4 #a1chi4--,revolving armature alternator4 ,revolving armatures are suitable for machines generating current at comparatively low pressure1 as no difficulty is experienced in collecting such current4 ,revolving armature alternators are also suitable for small power plants1 isolated lighting plants1 where medium or small size machines are required4 ,ques4 ,when is the revolving type of armature used and why8 ,ans4 ,it is used on machines of small size because the pressure generated is comparatively low and the current transmitted by the brushes small1 no difficulty being experienced in collecting such a current4 ,illustration3 ,,fig4 #a1cij4--,ring wound dynamo arranged as alternator by replacing commutator with collector rings connected to the winding at points #ahj apart4 ,ques4 ,could a dynamo be converted into an alternator8 ,ans4 ,yes4 ,ques4 ,how can this be done8 ,ans4 ,by placing two collector rings on one end of the armature and connecting these two rings to points in the armature winding #ahj apart1 as shown in fig4 #a1cij4 ,ques4 ,would such arrangement as shown in fig4 #a1cij make a desirable alternator8 ,ans4 ,no4 ,alternating current windings are usually different from those used for direct currents4 ,one distinction is the fact that a simple open coil winding may be1 and often is1 employed1 but the chief difference is the intermittent action of the inductors4 ,in a direct current ,gramme ring winding a certain number of coils are always active1 while those in the space between the pole pieces are not generating4 ,in this way a practically steady pressure is produced by a large fraction of the coils4 ,in the case of an alternator all of the coils are either active or inactive at one time4 ,hence1 the winding need cover only as much of the armature as is covered by the pole pieces4 ,illustration3 ,,fig4 #a1cia4--;,engberg alternating current generating set2 shown also in cross section in fig4 #a1chg4 ,the set comprises a vertical engine and alternator1 direct connected and placed on one base4 ,the lubrication system comprises an oil pump situated in the base of the engine1 pumping the oil from an oil reservoir up into a sight feed oil cup which leads to a distributing oil trough on the inside of the engine frame1 from here oil pipes lead to all movable bearings1 which are grooved to insure proper distribution of oil4 ,the oil is drained from bearings into the base1 filtered and re-pumped4 ,a water shed partition is provided in the engine frame1 preventing any water passing from the cylinder down into the engine base and mixing with the oil1 consequently leaving good1 clean oil in the oil reservoir at all times4 ,the details of the lubrication system are shown in fig4 #a1chg4 ,revolving ,field ,alternators4--,in generating an electric current by causing an inductor to cut magnetic lines1 it makes no difference whether the cutting of the magnetic lines is effected by moving an inductor across a magnetic field or moving the magnetic field across the inductor4 ,illustration3 ,,fig4 #a1cib4--;,allis-,chalmers revolving field self-contained belted type alternator4 ,motion is purely a relative matter1 that is1 an object is said to move when it changes its position with some other object regarded as stationary2 it may be moving with respect to a second object1 and at the same time be at rest with respect to a third object4 ,thus1 a dory has a speed of four miles per hour in still water2 if it be run up stream against a current flowing four miles per hour it would move at that speed with respect to the water1 yet remain at rest with respect to the earth4 ,it must be evident then that motion1 as stated1 being a purely relative matter1 it makes no difference whether the armature of a generator move with respect to the field magnets1 or the field magnets move with respect to the armature1 so far as inducing an electric current is concerned4 ,illustration3 ,,fig4 #a1cic4--,marine view1 showing that motion is purely a relative matter4 ,in order that there may be motion something must be regarded as being stationary4 ,in the above illustration a catboat is shown at anchor in a stream which is flowing at a rate of four miles per hour in the direction of the arrow4 ,the small dory running at a speed of four miles per hour against the current is moving at that velocity relative to the current1 yet is at a standstill relative to the catboat4 ,in this instance both catboat and dory are moving with respect to the water if the latter be regarded as stationary4 ,again if the earth be regarded as being stationary1 the two boats are at rest and the water is moving relative to the earth4 ,for alternators of medium and large size there are several reasons why the armature should be stationary and the field magnets revolve1 as follows3 #a4 ,by making the armature stationary1 superior insulation methods may be employed1 enabling the generation of current at very much higher voltage than in the revolving armature type4 #b4 ,because the difficulty of taking current at very high pressures from collector rings is avoided4 ,the field current only passes through the collector rings4 ,since the field current is of low voltage and small in comparison with the main current1 small brushes are sufficient and sparking troubles are avoided4 ,illustration3 ,,fig4 #a1cid4--;,diagram showing essential parts of a revolving field alternator and method of joining the parts in assembling4 #c4 ,only two collector rings are required4 #d4 ,the armature terminals1 being stationary1 may be enclosed permanently so that no one can come in contact with them4 ,ques4 ,what names are usually applied to the armature and field magnets with respect to which moves8 ,ans4 ,the stator and the rotor4 ,the terms armature and field magnets are to be preferred to such expressions4 ,an armature is an armature1 no matter whether it move or be fixed1 and the same applies to the field magnets4 ,there is no good reason to apply other terms which do not define the parts4 ,ques4 ,explain the essential features of a revolving field alternator4 ,ans4 ,the construction of such alternators is indicated in the diagram1 fig4 #a1cid4 ,attached to the shaft is a field core1 which carries the latter1 consisting of field coils fitted on pole pieces which are dovetailed to the field core4 ,the armature is built into the frame and surrounds the magnets as shown4 ,the field current1 which is transmitted to the magnets by slip rings and brushes1 consists of direct current of comparatively low pressure1 obtained from some external source4 ,illustration3 ,,fig4 #a1cie4--,western ,electric stationary armature and frame of engine driven alternator4 ,it is of cast iron and surrounds the laminated iron core in which the armature windings are embedded4 ,heavy steel clamping fingers hold the core punchings in place and numerous ventilating ducts are provided in the core at frequent intervals to allow free circulation of cool air4 ,the armature coils are form wound1 insulated1 and retained in the core slots by means of wedges4 ,inductor ,alternators4--,in this class of alternator both armature and field magnets are stationary1 a current being induced in the armature winding by the action of a so called inductor in moving through the magnetic field so as to periodically vary its intensity4 ,illustration3 ,,figs4 #a1cif and #a1cig4--;,elementary inductor alternator2 diagram showing principle of operation4 ,it consists of a field magnet1 at the polar extremities of which is an armature winding both being stationary as shown4 ,inductors consisting of iron discs are arranged on a shaft to rotate through the air gap of the magnet poles4 ,now in the rotation of the inductors1 when any one of them passes through the air gap as in fig4 #a1cif1 the reluctance or magnetic resistance of the air gap is greatly reduced1 which causes a corresponding increase in the number of magnetic lines passing through the armature winding4 ,again as an inductor passes out of the air gap as in fig4 #a1cig1 the number of magnetic lines is greatly reduced2 that is1 when an inductor is in the air gap1 the magnetic field is dense1 and when no inductor is in the gap1 the field is weak2 a variable flux is thus made to pass through the armature winding1 inducing current therein4 ,the essential feature of the inductor alternator is that iron only is revolving1 and as the design is usually homopolar1 the magnetic flux in its field coils is not alternating1 but undulating in character4 ,thus1 with a given maximum flux through each polar mass1 the total number of armature turns required to produce a given voltage is just twice that which is required in an alternator having an alternating instead of an undulating flux through its field windings4 ,the above and the one shown in figs4 #a1cih and #a1cii are examples of real inductor alternators1 those shown in the other cuts are simply so called inductor alternators1 the distinction being that1 as above1 the inductor constitutes no part of the field magnet4 ,ques4 ,what influence have the inductors on the field flux8 ,ans4 ,they cause it to undulate2 that is1 the flux rises to a maximum and falls to a minimum value1 but does not reverse4 ,ques4 ,how does this affect the design of the machine as compared with other types of alternator8 ,ans4 ,with a given maximum magnetic flux through each polar mass1 the total number of armature turns necessary to produce a given pressure is twice that which is required in an alternator having an alternating flux through its armature windings4 ,illustration3 ,,figs4 #a1cih and #a1cii4--;,a low tension ignition system with an inductor magneto of the oscillating type4 ,the inductor ,e is rotated to and fro by means of a link ,r1 one end of which is attached to the inductor crank1 and the other to the igniter cam ,c4 ,two views are shown3 immediately before and after sparking4 ,s is the grounded electrode of the igniter2 ,t an adjustable hammer which is secured in position by a lock nut ,n4 ,ques4 ,is the disadvantage due to the necessity of doubling the number of armature turns compensated in any way8 ,ans4 ,yes1 the magnetic flux is not reversed or entirely changed in each cycle through the whole mass of iron in the armature1 the abrupt changes being largely confined to the projections on the armature surface between the coils4 ,ques4 ,what benefit results from this peculiarity8 ,ans4 ,it enables the use of a very high magnetic flux density in the armature without excessive core loss1 and also the use of a large flux without an excessive increase in the amount of magnetic iron4 ,the use of a large flux permits a reduction in the number of armature turns1 thus compensating1 more or less1 for the disadvantage due to the operation of only one-half of the armature coils at a time4 ,illustration3 ,,figs4 #a1djj and #a1dja4--,one form of inductor alternator4 ,as shown1 the frame carries the stationary armature1 which is of the slotted type4 ,inside of the armature is the revolving inductor1 provided with the projections built up of wrought iron or steel laminations4 ,the circular exciting coil is also stationary and encircles the inductor1 thus setting up a magnetic flux around the path indicated by the dotted line1 fig4 #a1dja4 ,the projecting poles are all1 therefore1 of the same polarity1 and as they revolve1 the magnetic flux sweeps over the coils4 ,although this arrangement does away with collector rings1 the machines are not so easily constructed as other types1 especially in the large sizes4 ,the magnetizing coil becomes large and difficult to support in place1 and would be hard to repair in case of breakdown4 ,inductor alternators have become practically obsolete1 except in special cases1 as inductor magnetos used for ignition and other purposes requiring a very small size machine4 ,the reasons for the type being displaced by other forms of alternator are chiefly because only half as great a pressure is obtained by a flux of given amount1 as would be obtained in the ordinary type of machine4 ,it is also more expensive to build two armatures1 to give the same power1 than to build one armature4 ,this type has still other grave defects1 among which may be mentioned enormous magnetic leakage1 heavy eddy current losses1 inferior heat emissivity1 and bad regulation4 ,classes of ,inductor ,alternator4--,there are two classes into which inductor alternators may be divided1 based on the mode of setting of their polar projections3 #a4 ,homopolar machines2 #b4 ,heteropolar machines4 ,homopolar ,inductor ,alternators4--,in this type the positive polar projections of the inductors are set opposite the negative polar projections as shown in fig4 #a1djb4 ,when the polar projections are set in this manner1 the armature coils must be staggered or set displaced along the circumference with respect to one another at a distance equal to half the distance from the positive pole to the next positive pole4 ,illustration3 ,,figs4 #a1djb and #a1djc4--;,homopolar and heteropolar inductors4 ,homopolar inductors have their ,n and ,s poles opposite each other1 while in the heteropolar type1 they are staggered as shown4 ,heteropolar ,inductor ,alternators4--,machines of this class are those in which the polar projections are themselves staggered1 as shown in fig4 #a1djc1 and therefore1 do not require the staggering of the armature coils4 ,in this case1 a single armature of double width may be used1 and the rotating inductor then acts as a heteropolar magnet1 or a magnet which presents alternatively positive and negative poles to the armature1 instead of presenting a series of poles of the same polarity as in the case of a homopolar magnet4 ,use of ,inductor ,alternators4--,morday originally designed and introduced inductor alternators in #ahff4 ,they are not the prevailing type1 as their field of application is comparatively narrow4 ,they have to be very carefully designed with regard to magnetic leakage in order to prevent them being relatively too heavy and costly for their output1 and too defective with respect to their pressure regulation1 other defects being heavy eddy current losses and inferior heat conductance4 ,hunting or ,singing in ,alternators4--,hunting is a term applied to the state of two parallel connected alternators running out of step1 or not synchronously1 that is1 see sawing4 ,when the current wave of an alternator is peaked and two machines are operated in parallel it is very difficult to keep them in step1 that is in synchronism4 ,any difference in the phase relation which is set up by the alternation will cause a local or synchronizing current to flow between the two machines and at times it becomes so great that they must be disconnected4 ,illustration3 ,,fig4 #a1djd4--,revolving field of ,fort ,wayne alternator equipped with amortisseur winding4 ,the object of this winding is to check any tendency toward hunting when the alternator is to be run as a synchronous motor1 either for rotary condenser or power service4 ,the amortisseur winding consists of heavy copper bars1 placed around and through the pole faces and short circuited at the ends by heavy copper rings2 it serves as a starting winding to bring the rotor up to speed as an induction motor1 and also serves as a damping device to neutralize any tendency toward hunting caused by variation in speed of the generator supplying the current4 ,alternators which produce a smooth current wave and are maintained at uniform speed by properly designed governors1 operate fairly well in parallel1 but are not entirely free from hunting1 and other means are provided to overcome the difficulty4 ,when heavy copper flanges1 called dampers1 are put over the polar projections or copper bars laid in grooves on the pole face and short circuited by connecting rings 7called amortisseur winding71 the powerful induced currents which are produced when the alternators get out of step tend to quickly re-establish the phase relation4 ,illustration3 ,,fig4 #a1dje4--,westinghouse field with amortisseur or damper winding for #ge kva4 and larger belted alternators1 which prevents hunting and reduces eddy currents in the pole pieces4 ,the copper bars of the amortisseur cage winding are arranged in partially closed slots in the pole pieces4 ,two examples of a field provided with amortisseur#d winding are shown in figs4 #a1djd and #a1dje4 #d ,,note4--,amortisseur windings are often erroneously called squirrel cage windings on account of similarity of construction4 ,the latter term should be reserved for its proper significance as being the name of the type of armature winding generally used for induction motors1 the name being suggested by the resemblance of the finished armature to the wheel of a squirrel cage4 ,a comparison of figs4 #a1dje and #a1gdf will show the distinction4 ,in a squirrel cage winding there is a large number of bars uniformly spaced2 an amortisseur winding consists of a comparatively small number of bars1 usually unevenly spaced1 that is they are divided into groups with considerable space between the groups1 as in fig4 #a1dje1 and less pronounced in fig4 #a1djd4 ,the bars are short circuited by rings the same as in squirrel cage winding4 ,illustration3 ,,fig4 #a1djf4--;,diagram of monocyclic system1 showing monocyclic armature and transformer connections4 ,the monocyclic system is a single phase system primarily intended for the distribution of lights with an incidental load of motors4 ,the lighting load is entirely connected to one single phase circuit1 and the motors are started and operated from this circuit with the assistance of the teazer wire4 ,the long coil indicates the main winding of the armature1 which is similar in its arrangement and size to the ordinary armature winding of a single phase alternator4 ,the short coil which connects at one end to the middle point of the coil above mentioned1 and at the other to a third collector ring is called the teazer coil4 ,its use is to generate a pressure in quadrature with that of the main coil4 ,this pressure is combined with the main pressure of the alternator by transformers1 so as to give suitable phase relations for operating induction motors4 ,in the diagram the voltage has been assumed to be #b1jhj volts1 and the voltages marked to correspond with the generated pressure4 ,the coils of the alternator armature are connected1 as shown1 to two main leads and to a teazer wire4 ,between each end of the main coil and the end of the teazer coils1 a resultant pressure is generated4 ,these resultants are about #ab per cent4 larger than half the main pressure4 ,they also have a phase difference4 ,monocyclic ,alternators4--,this type of alternator was designed prior to the introduction of the polyphase systems1 to overcome the difficulties encountered in the operation of single phase alternators as motors4 ,a single phase alternator will not start from rest as a motor1 but must first be started and brought up to the proper speed before being connected with single phase mains4 ,this condition constituted a serious difficulty in all cases where the motor had to be stopped and started at comparatively frequent intervals4 ,illustration3 ,,fig4 #a1djg4--,monocyclic system diagram showing transformer connections4 ,illustration3 ,,fig4 #a1djh4--;,diagram showing section of monocyclic alternator armature illustrating the armature winding4 ,the main coils are wound on every other tooth1 and the teazer coils are placed in quadrature with them1 as shown4 ,the monocyclic alternator is a single phase machine provided with an additional coil1 called a teaser coil1 wound in two phase relationship with1 and connected to the center of the main single phase coil4 ,it is provided with three collector rings2 two for the single phase coil1 and one for the free end of the teaser coil4 ,illustration3 ,,fig4 #a1dji4--;,diagram showing connections of ,general ,electric ,monocyclic alternator4 ,for #b1cjj volt machine1 connect as shown by solid lines4 ,for #a1aej volt machine1 omit connections ,a to ,b1 ,c to ,d1 ,e to ,f1 and ,g to ,h1 and connect as shown by dotted lines4 ,the armature of a standard monocyclic alternator rotates in a counter clockwise direction facing the commutator4 ,when the alternator is loaded1 the voltage between the teazer coil and the two terminals of the main coil may be different2 therefore1 it is necessary to have the commutator connected in corresponding ends of the main coil4 ,if the machine has not been arranged for clockwise rotation1 the following change in the connections on the commutator-collector must be made if the machine is to be run in parallel with another4 ,fig4 #a1daj shows the connections of monocyclic alternators4 ,in fig4 #a1dji1 the studs on the commutator-collector marked #a and #f are the terminals of the main coil4 ,these should be reversed4 ,the numbers are stamped on the ends of the stud and may be seen with the assistance of a mirror4 ,by reference to this diagram it is a simple matter to trace out the connections with a magneto1 after the armature leads are disconnected and the brushes raised4 ,by this arrangement ordinary single phase incandescent lighting can be accomplished by means of a single pair of wires taken from the single phase coil4 ,where three phase motors have to be operated1 however1 a third wire1 called the power wire1 which is usually smaller than the main single phase wires is carried to the point at which the motor is located1 and by the use of two suitably connected transformers three phase currents are obtained from the combined single phase and power wires for operating the motors4 ,illustration3 ,,fig4 #a1daj4--;,diagram showing connections of ,general ,electric monocyclic alternator4 ,the solid lines show standard connections for counter-clockwise rotation2 the broken lines show connection changed for clockwise rotation4 ,fig4 #a1djf shows the connections of the monocyclic system and it is only necessary to carry the teaser wire into buildings where motors are to be used4 ,armature ,reaction4--,every conductor carrying a current creates a magnetic field around itself1 whether it be embedded in iron or lie in air4 ,armature inductors1 therefore1 create magnetic fluxes around themselves1 and these fluxes will1 in part1 interfere with the main flux from the poles of the field magnet4 ,the effect of these fluxes is3 #a4 ,to distort the field1 or #b4 ,to weaken the field4 ,these disturbing fluxes form1 in part1 stray fluxes linked around the armature inductors tending to choke the armature current4 ,illustration3 ,,figs4 #a1daa and #a1dab4--,section of armature and field showing distorting effect of armature reaction on the field4 ,when a coil is opposite a pole as in fig4 #a1daa1 no current is flowing 7assuming no self induction7 and the field is undisturbed1 but1 as the inductors pass under a pole face as in fig4 #a1dab1 current is induced in them1 and lines of force are set up as indicated by the dotted lines4 ,this distorts the main field so that the lines of force are crowded toward the forward part of the pole face as shown4 ,ques4 ,explain how the field becomes distorted by armature reaction4 ,ans4 ,considering a slotted armature and analyzing the electrical conditions as the inductors move past a pole piece1 it will be observed3 #a1 when the coil is in the position shown in fig4 #a1daa1 the current will be zero1 assuming no armature self-induction1 consequently for this position the armature coil has no disturbing effect upon the field set up by the field magnet2 #b1 when the inductors have moved under the pole face1 as in fig4 #a1dab1 currents will be induced in them1 and they will tend to set up a magnetic field as indicated by the dotted lines1 and in direction1 by the arrow heads4 ,the effect of this field will be to distort the main field1 strengthening one side of the pole and weakening the other side4 ,illustration3 ,,fig4 #a1dac4--,section of armature and field showing weakening effect of armature reaction in the field4 ,self-induction being present 7as it almost always is71 the current lags more or less behind the pressure1 so that when the coil is in the position of zero induction1 as shown1 the current has not yet come to rest4 ,accordingly1 lines of force 7indicated by the dotted lines7 are set up by the current flowing through the coils which are in opposition to the field1 thus weakening the latter4 ,the dots and crosses in inductor sections1 have their usual significance in defining the direction of current1 representing respectively the heads and tails of arrows4 ,ques4 ,explain how the field becomes weakened by armature reaction4 ,ans4 ,in all armatures there is more or less inductance which causes the current to lag behind the pressure a corresponding amount4 ,accordingly1 the current does not stop flowing at the same instant that the pressure becomes zero1 therefore1 when the coil is in the position of zero pressure1 as in fig4 #a1dac1 the current is still flowing and sets up a magnetic field which opposes the main field as indicated by the dotted arrows1 thus weakening the main field4 ,ques4 ,in what kind of armature is this effect especially pronounced8 ,ans4 ,in slotted armatures provided with coils of a large number of turns4 ,illustration3 ,,fig4 #a1dad4--,section of armature and field showing strengthening effect of armature reaction when the current leads the pressure4 ,if the circuit contain an excess of capacity the current will lead the pressure1 so that when the coil is in the position of zero induction1 as shown1 the current will have come to rest and reversed4 ,accordingly1 lines of force 7indicated by the dotted lines7 are set up by the current flowing through the coil and which are in the same direction as the lines of force of the field1 thus strengthening the latter4 ,ques4 ,what would be the effect if the current lead the pressure8 ,ans4 ,it would tend to strengthen the field as shown in fig4 #a1dad4 ,the value of the armature ampere turns which tend to distort and to diminish or augment the effect of the ampere turns on the field magnet is sometimes calculated as follows3 4#gjg ,i ,t ,p ,a ---------------- s in which ,a armature ampere turns2 ,i current per phase2 ,t turns per pole per phase2 ,p number of phases2 s product of the distribution and pitch factors of the winding4 ,this value of ampere turns1 combined at the proper phase angle with the field ampere turns gives the value of the ampere turns available for producing useful flux4 ,illustration3 ,,fig4 #a1dae4--;,fort ,wayne separately excited belt driven alternator1 a form adapted for installation in small plants where low power factor is to be encountered4 ,this condition exists in a line where power is supplied to induction motors1 transformers or other inductive apparatus4 ,the type here shown is built in sizes from #cg kw4 to #bjj kw41 #fj cycles1 two or three phases and voltages of #bdj1 #dhj1 #fjj1 #a1aej or #b1cjj volts4 ,they may be operated as single phase alternators by using two of the phases and may then be rated at #gj per cent4 of the polyphase rating4 ,the field is excited by direct current at a pressure of #abe volts4 ,these alternators may be used as synchronous motors and for this duty are fitted with amortisseur winding in the pole faces which does not interfere with their use as alternators4 ,single ,phase ,reactions4--,unlike three phase currents1 a single phase current in an alternator armature produces a periodic disturbance of the flux through the machine4 ,in the magnet system this disturbance is of twice the normal frequency1 while in the armature core it is the ,illustration3 ,,figs4 #a1daf to #a1dbe4--;,diagrams illustrating superposition of fields4 ,in the figures magnetic curves representing the effect of the armature currents in several different cases are superposed upon the magnetic curves assumed to be due to the field magnet4 ,the uppermost line shows the primary field due to the exciting coils on the magnet poles4 ,they are shown passing into the armature teeth in two principal positions1 where the middle of a pole is3 #a1 opposite a tooth1 and #b1 opposite a slot4 ,in the second line is shown the field due to the armature currents assuming no lag1 and that the magnets are not excited4 ,if there be no lag1 the places of strongest current will be opposite the poles4 ,as shown in the right hand figure when the current in one phase ,c1 is at its maximum1 those in the other phases ,a and ,b will be of half strength4 ,in the left hand figure when the current in one phase ,b1 is at its zero value1 those in the other phases will be of equal value1 or #hg per cent4 of the maximum4 ,in the third line is shown the effect of superposing these fields due to the current upon those due to the magnets as depicted in the first line4 ,inspection of this resultant field shows how the armature current distorts the field without altering the total number of lines per pole4 ,in the fourth and fifth lines are shown the effects of a lagging current4 ,a lag of #ij is assumed2 and in that case the maximum current occurs in any inductor one quarter period after the pole has passed1 or at a distance of half a pole pitch behind the middle point of the pole1 as in the fourth line4 ,when these armature fields are superposed on those of the magnets in the first line the resultant fields are those depicted in the fifth line4 ,on inspection it will be seen that in this case there is no distortion1 but a diminution of the flux from each pole1 as the lines due to the armature currents1 tending to pass through the pole cores in the sense opposite to those of the primary magnetism1 must be deducted from the total4 ,the twelve lines per pole are correspondingly reduced to eight2 and1 of these eight1 four go astray constituting a leakage field4 ,this illustrates the effect of a lagging current in demagnetizing the field magnets and in increasing the dispersion4 _/ same as the normal frequency4 ,in both cases the eddy currents which are set up1 produce a marked increase in the load losses1 and thus tend to give the machine a higher temperature rise on single phase loading4 ,designers continue to be singularly heedless of these single phase reactions1 resulting in many cases of unsatisfactory single phase alternators4 ,single phase reactions distort the wave form of the machine4 ,three ,phase ,reactions4--,the action of the three phase currents in an alternator is to produce a resultant field which is practically uniform1 and which revolves in synchronism with the field system4 ,the resultant three phase reaction1 because of its uniformity1 produces no great increase in the load losses of the machine1 the small additional losses which are present being due to windings not being placed actually in space at #abj1 and to the local leakage in the teeth4 ,illustration3 ,,fig4 #a1dbf4--;,diagram showing lateral field between adjacent poles4 ,magnetic ,leakage4--,in the design of alternators the drop of voltage on an inductive load is mainly dependent upon the magnetic leakages1 primary and secondary4 ,they increase with the load1 and1 what is of more importance1 they increase with the fall of the power factor of the circuit on which they may be working4 ,this is one reason why certain types of alternator1 though satisfactory on a lighting circuit1 have proved themselves unsatisfactory when applied to a load consisting chiefly of motors4 ,the designer must know the various causes which contribute to leakage and make proper allowance4 ,in general1 to keep the leakage small1 the pole cores should be short1 and of minimum surface1 the pole shoes should not have too wide a span nor be too thick1 nor present needless corners1 and the axial length of the pole face and of the armature core should not be too great in proportion to the diameter of the working face4 ,illustration3 ,,figs4 #a1dbg and #a1dbh4--;,diagram showing respectively the character of stray field between adjacent straight poles1 and between adjacent poles with shoes4 ,across the slightly ,v-shaped spaces the stray field passes in lines that1 save near the outer part1 are nearly straight4 ,quite straight they would not be1 even were the sides parallel1 because the difference of magnetic pressure increases from the roots towards the pole ends4 ,at the roots1 where the cores are attached to the yoke1 the magnetic pressure difference is almost zero4 ,it would be exactly zero if there were not a perceptible reluctance offered by the joints and by the metal of the yoke4 ,the reluctance of the joint causes a few of the lines to take paths through the air by a leakage which adds to the useful flux4 ,at the tops of the cores there is a difference of magnetic pressure equal to the sum of the ampere turns on the two cores1 tending to drive magnetic lines across4 ,this difference of magnetic pressure increases regularly all the way up the cores from root to top2 hence1 the average value may be taken as equal to the ampere turns on one core4 ,the stray field1 therefore1 will steadily increase in density from the bottom upwards4 ,in addition to this stray field between the pole cores there is also a stray field between the projecting tips or edges of the pole shoes1 as shown in fig4 #a1dbh4 ,in some machines the dispersion due to the pole shoes is greater than that between the flanks of the cores4 ,to keep the increase of leakage between no load and full load from undue magnitude1 it is required that armature reactions shall be relatively small1 that the peripheral density of the armature current 7ampere-conductors per inch7 be not too great1 and that the pole cores be not too highly saturated when excited for no load4 ,illustration3 ,,fig4 #a1dbi4--,lincoln revolving field alternator4 ,the frame has openings for ventilation1 the fanning action of the pole pieces causing a current of air to pass not only over the end of the windings1 as is usual with other designs1 but also through ventilating slots in the windings themselves4 ,the armature core laminations are annealed after punching and before assembling to guard against the crystalizing effect of the punching4 ,the armature coils are form wound and insulated before being placed in the slot4 ,there is also slot insulation which is put in the slot previous to inserting the coil4 ,when the winding is completed1 it is tested with a pressure of #d to #aj times the normal voltage of the machine4 ,the bearings are self-aligning4 ,the machine is normally designed to operate at a power factor of approximately #gj per cent41 which means that at that power factor1 the armature and fields at full load will heat equally4 ,if it have a higher power factor than #gj per cent4 it means that the field windings will run considerably cooler than the armature windings with full load4 ,if the power factor be lower than this1 it will mean that the field windings will run hotter than the armature on full load2 however1 the machine is designed so that harmful heating does not occur on full load with greater power factor than #dj per cent4 ,the general character of the stray field between adjacent poles is shown in figs4 #a1dbg and #a1dbh for straight poles and those having shoes4 ,field ,excitation of ,alternators4--,the fields of alternators require a separate source of direct current for their excitation1 and this current should be preferably automatically controlled4 ,in the case of alternators that are not self exciting1 the dynamo which generates the field current is called the exciter4 ,the excitation of an alternator at its rated overload and 4#h power factor would not1 in some cases1 if controlled by hand1 exceed #abe volts1 although1 in order to make its armature voltage respond quickly to changes in the load and speed1 the excitation of its fields may at times be momentarily varied by an automatic regulator between the limits of #gj and #adj volts4 ,illustration3 ,,fig4 #a1dcj4--,western ,electric armature for self-excited alternator4 ,the main winding is placed at the bottom of the slots1 each coil being surrounded by an armour of horn fibre4 ,the exciter winding occupies a very small portion of the slot1 being placed on top of the main winding1 and connected to the commutator immediately in front of the core and between core and collector rings as shown4 ,the exciter should1 in turn1 respond at once to this demand upon its armature1 and experience has shown that to do this its shunt fields must have sufficient margin at full load to deliver momentarily a range from #be to #afj volts at its armature terminals4 ,it is obvious from the above that an exciter suitable for use with an automatic regulator must commutate successfully over a wide range in voltage1 and1 if properly designed1 have liberal margins in its shunt fields and magnetic circuits4 ,alternator fields designed for and operated at unity power factor have often proved unsatisfactory when the machines were called upon to deliver their rated kva4 at 4#h power factor or lower4 ,this is due to the increased field current required at the latter condition and results1 first1 in the overheating of the fields and1 second1 in the necessity of raising the direct current exciting voltage above #abe volts1 which often requires the purchase of new exciters4 ,ques4 ,what is a self-excited alternator8 ,ans4 ,one whose armature has1 in addition to the main winding1 another winding connected to a commutator for furnishing direct field exciting current1 as shown in fig4 #a1dcj4 ,illustration3 ,,fig4 #a1dca4--;,frame1 bed plate and armature winding for ,westinghouse bracket bearing polyphase alternator4 ,ques4 ,how is a direct connected exciter arranged8 ,ans4 ,the exciter armature is mounted on the shaft of the alternator close to the spider hub1 or in some cases at a distance sufficient to permit a pedestal and bearing to be mounted between the exciter and hub4 ,in other designs the exciter is placed between the bearing and hub4 ,figs4 #a1dcb and #a1dcc are examples of direct connected exciter alternators1 in fig4 #a1dcb the exciter being placed between the field hub and bearing1 and in fig4 #a1dcc1 beyond the bearing4 ,ques4 ,what is the advantage of a direct connected exciter8 ,ans4 ,economy of space4 ,this is apparent by comparing figs4 #a1dcb and #a1dcc with fig4 #a1dcd1 which shows a belted exciter4 ,illustration3 ,,fig4 #a1dcb4--;,general ,electric alternator with direct connected exciter mounted on shaft between field hub and bearing4 ,in the smaller sizes1 the magnet frame is bolted to the bearing bracket1 but in the larger sizes special construction is used depending upon the conditions to be met4 ,the exciters are capable of furnishing the desired excitation for low power factors4 ,ques4 ,what is the disadvantage of a direct connected exciter8 ,ans4 ,it must run at the same speed as the alternator1 which is slower than desirable1 hence the exciter must be larger for a given output than the gear driven type1 because the latter can be run at high speed and accordingly be made proportionally smaller4 ,ques4 ,what form of gear is generally used on gear driven exciters8 ,ans4 ,belt gear4 ,illustration3 ,,fig4 #a1dcc4--;,fort ,wayne alternator with direct connected exciter mounted on the field shaft at such distance as to permit a pedestal and bearing to be mounted between the exciter and revolving field4 ,in the view1 the bearing is hidden by the exciter1 only the foot of the pedestal being visible4 ,ques4 ,what are the advantages of gear driven exciters8 ,ans4 ,being geared to run at high speed1 they are smaller and therefore less costly than direct connected exciters4 ,in large plants containing a number of alternators one exciter may be used having sufficient capacity to excite all the alternators1 and which can be located at any convenient place4 ,ques4 ,what is the disadvantage of gear driven exciters8 ,ans4 ,the space occupied by the gear4 ,illustration3 ,,fig4 #a1dcd4--;,diagram showing a ,westinghouse #ej kva41 #b1djj volt1 three phase1 #fj cycle revolving field separately excited alternator direct connected to a steam engine4 ,the exciter is belted to the alternator shaft1 the driving pulley being located outside the main bearing4 ,the small pulley on the exciter gives an indication of its high speed as compared with that of the alternator4 ,in the case of a chain drive very little space is required1 but for belts1 the drive generally used1 there must be considerable distance between centers for satisfactory transmission4 ,slow ,speed ,alternators4--,by slow speed is here understood relatively slow speed1 such as the usual speeds of reciprocating engines4 ,a slow speed alternator is one designed to run at a speed slow enough that it may be direct connected to an engine4 ,such alternators are of the revolving field type and a little consideration will show that they must have a multiplicity of field magnets to attain the required frequency4 ,in order that there be room for the magnets1 the machine evidently must be of large size1 especially for high frequency4 ,illustration3 ,,fig4 #a1dce4--;,crocker-,wheeler #cej kva41 slow speed alternator direct connected to a ,corliss engine4 ,in front is seen a belted exciter driven from a pulley on the main shaft between the alternator and the large band wheel4 ,the latter serves to give the additional fly wheel effect needed for close speed regulation4 ,,example4--,how many field magnets are required on a two phase alternator direct connected to an engine running #bdj revolutions per minute1 for a frequency of #fj8 ,an engine running #bdj revolutions per minute will turn #bdj #fj #d revolutions per second4 ,a frequency of #fj requires #fj #d #ae cycles per phase per revolution1 or #ae #b #cj poles per phase4 ,hence for a two phase alternator the total number of poles required is #cj #b #fj4 ,it is thus seen that a considerable length of spider rim is required to attach the numerous poles1 the exact size depending upon their dimensions and clearance4 ,illustration3 ,,fig4 #a1dcf4--,three ,crocker-,wheeler #ge kva41 slow speed alternators direct connected to high speed engines4 ,the alternator is styled slow speed although connected to a high speed engine1 because what is considered high engine speed is slow speed for alternator operation4 ,the alternators have direct connected exciters which are plainly seen in the illustration placed on an extension of bearing pedestal4 ,direct connected exciters on units of this kind do not1 as a rule1 assume too bulky proportions1 because of the high engine speed4 ,fly ,wheel ,alternators4--,the diameter of the revolving fields on direct connected alternators of very large sizes becomes so great that considerable fly wheel effect is obtained1 although the revolutions be low4 ,by giving liberal thickness to the rim of the spider1 the rotor then answers the purpose of a fly wheel1 hence no separate fly wheel is required4 ,in fact1 the revolving element resembles very closely an ordinary fly wheel with magnets mounted on its rim1 as illustrated in fig1 #a1dcg4 ,illustration3 ,,fig4 #a1dcg4--;,general ,electric #dh pole #gej kw41 three phase fly wheel type alternator4 ,it runs at a speed of #aej revolutions per minute1 giving a frequency of #fj cycles per second and a full load pressure of #b1cjj volts4 ,the slip rings and leads to the field winding are clearly shown in the figure4 ,the field magnets are mounted directly on the rim of the spider1 which resembles very closely a fly wheel1 and which in fact it is--hence the name fly wheel alternator4 ,high ,speed ,alternators4--,since alternators may be run at speeds far in excess of desirable engine speeds1 it must be evident that both size and cost may be reduced by designing them for high speed operation4 ,since the desired velocity ratio or multiplication of speed is so easily obtained by belt drive1 that form of transmission is generally used for high speed alternators1 the chief objection being the space required4 ,accordingly where economy of space is not of prime importance1 a high speed alternator is usually installed1 except in the large sizes where the conditions naturally suggest a direct connected unit4 ,illustration3 ,,fig4 #a1dch4--;,allis-,chalmers high speed belted type alternator4 ,the small pulley at the right and the angle of the belt suggest the high speed at which such alternators are run1 a #ej kva4 machine turning #a1bjj revolutions per minute4 ,an example of high speed alternator is shown in fig4 #a1dch4 ,machines of this class run at speeds of #a1bjj to #a1hjj or more1 according to size4 ,no one would think of connecting an alternator running at any such speed direct to an engine1 the necessary speed reduction proper for engine operation being easily obtained by means of a belt drive4 ,water ,wheel ,alternators4--,in order to meet most successfully the requirements of the modern hydro-electric plant1 the alternators must combine those characteristics which result in high electrical efficiency with a mechanical strength of the moving elements which will insure uninterrupted service1 and an ample factor of safety when operating at the relatively high speeds often used with this class of machine4 ,illustration3 ,,fig4 #a1dci4--;,allis-,chalmers #e1jjj kva41 #dej ,r4 ,p4 ,m41 #f1fjj volt1 #fj cycle1 #c phase1 horizontal water wheel alternator4 ,the shaft is extended for the reception of a flange coupling for direct connection to water wheel4 ,owing to the wide range in output of the generating units and also in the speed at which they must operate to suit varying conditions of head1 types of wheels used1 and other features pertaining to water power developments1 it has been necessary to design a very complete line of machines for this work4 ,the bearings are of the ring oiling type with large oil reservoirs4 ,when selecting an alternator for water wheel operation a careful analysis of the details of construction should be made in order to determine the relative values which have been assigned by the designers to the properties of the various materials used4 ,such analysis will permit the selection of a type of machine best adapted to the intended service and which possesses the required characteristics of safety1 durability and efficiency4 ,illustration3 ,,fig4 #a1ddj4--,stator of #ejj k4w4 ,allis-,chalmers alternator for direct connection to vertical shaft hydraulic turbine4 ,the large use of electric power transmitted by means of high pressure alternating current has led to the development of a large number of water powers and created a corresponding demand for alternators suitable for direct connection to water wheels4 ,ques4 ,name two forms of water wheel alternator4 ,ans4 ,horizontal and vertical4 ,examples of horizontal and vertical forms of water wheel alternator are shown in figs4 #a1dci and #a1ddj4 ,ques4 ,how should the rotor be designed8 ,ans4 ,it should be of very substantial construction4 ,ques4 ,why8 ,ans4 ,because water wheel alternators are frequently required to operate safely at speeds considerably in excess of normal4 ,illustration3 ,,fig4 #a1dda4--;,allis-,chalmers revolving field for water wheel alternator4 ,in this type of alternator it is essential that the rotating part be designed to have a liberal factor of safety not only at the ordinary operating speed1 but also at speeds much in excess of normal4 ,frequently machines are required to operate safely at a speed #ej to #ge per cent4 in excess of normal1 so that there may be no danger in case the water wheel races4 ,in most machines the field spider is of steel cast in a single piece for the smaller alternators and in two or more parts for the larger sizes4 ,for alternators running at high peripheral speed1 the rim is built up of steel laminations supported by a cast steel spider2 the latter serves merely to rotate the rim1 which is in itself able to withstand all stresses due to the high speed4 ,the field poles are laminated1 being built up of steel punchings held between malleable iron or bronze end plates1 the latter being used on high speed machines4 ,with but very few exceptions the poles are attached by dovetail projections that fit into corresponding slots4 ,steel tapered keys are driven in alongside the dovetails1 and the pole pieces cannot become loose4 ,all field coils1 except on a few of the smallest machines1 are of edgewise wound copper strip4 ,this style of coil is essential for revolving field alternators where the pressure on the insulation1 due to centrifugal force1 is so great that cotton insulation on round wire will not stand4 ,current is led into the rings by means of carbon brushes1 the number of brushes being such that the current density at the rubbing contact is kept within conservative limits4 ,at least two brushes per ring are always provided so that one can be removed for inspection without interrupting the exciting current4 ,in large machines the brush holder studs are mounted on a stand supported from the base2 in small alternators they are usually fastened to the cap of one of the bearing pedestals4 ,illustration3 ,,figs4 #a1ddb to #a1ddd4--;,diagram of turbine alternator windings for revolving armature4 ,fig4 #a1ddb illustrates a two pole design in which all overlapping is avoided4 ,it has #gb slots of which only #dh are filled1 giving #h slots per phase4 ,the projecting claws from the brass end shield which hold the coils in position are shown in section4 ,fig4 #a1ddc shows a four pole design having #dh slots or #d slots per phase per pole1 the coils being made up of #h inductors per slot taped together1 the end bends forming two ranges4 ,fig4 #a1ddd shows a two pole design for a two phase armature with #ah slots per pole per phase4 ,the core discs are spaced out as for #ajh slots1 but of these1 #d lots of #g each are not stamped out1 and #h of those stamped are left empty1 so that there are #gb slots filled4 ,ques4 ,what special provision is made for cooling the bearings8 ,ans4 ,they are in some cases water cooled4 ,turbine ,driven ,alternators4--,although the principle of operation of the steam turbine and that of the reciprocating engine are decidedly unlike1 the principle of operation of the high speed turbine driven alternator does not differ from that of generators designed for being driven by other types of engine or by water wheels4 ,there are1 therefore1 with the turbine driven alternator no new ideas for the operator who is familiar with the older forms to acquire4 ,it must be obvious that the proportions of such extra high speed machines must be very different from those permissible in generators of much slower speeds4 ,ques4 ,how does a turbine rotor differ from the ordinary construction8 ,ans4 ,it is made very small in diameter and unusually long4 ,ques4 ,why8 ,ans4 ,to reduce vibration and centrifugal stresses4 ,ques4 ,what are the two classes of turbine driven alternators8 ,ans4 ,they are classed as vertical or horizontal4 ,ques4 ,how do they compare8 ,ans4 ,the vertical type requires less floor space than the horizontal design1 and while a step bearing is necessary to carry the weight of the moving element1 there is very little friction in the main bearings4 ,the horizontal machine1 while it occupies more space1 does not require a step bearing4 ,ques4 ,describe a step bearing4 ,ans4 ,it consists of two cylindrical cast iron plates bearing upon each other and having a central recess between them into which lubricating oil is forced under considerable pressure by a steam or electrically driven pump1 the oil passing up from beneath4 ,ques4 ,what auxiliary is generally used in connection with a step bearing8 ,ans4 ,a weighted accumulator is sometimes installed in ,illustration3 ,,fig4 #a1dde4--e1jjj kw4 ,curtis turbine alternators installed for the ,new ,york ,central ,r4 ,r4 at ,yonkers1 ,n4 ,y4 ,the illustration shows also the auxiliary apparatus consisting of condensers1 vacuum augmenters1 circulating pumps1 air pumps1 etc4 ,the augmenter of the first machine is plainly seen between the condenser and centrifugal circulating pump4 connection with the oil pipe as a convenient device for governing the step bearing pumps1 and also as a safety device in case the pumps fail4 ,alternators of ,exceptional ,character4--,there are a few types of alternator less frequently encountered than those already described4 ,the essentials of such machines are here briefly given4 ,asynchronous ,alternators4--,in these machines1 the rotating magnet1 which1 with definite poles1 is replaced by a rotor having closed circuits4 ,in general construction1 they are similar to asynchronous induction motors having short circuited rotors2 for these alternators1 when operating as motors1 run at a speed slightly below synchronism and act as generators when the speed is increased above that of synchronism4 ,machines of this class are not self-exciting1 but require an alternating or polyphase current previously supplied to the mains to which the stationary armature is connected4 ,asynchronous alternators may be advantageously used in central stations that may be required to sustain a very sudden increase of load4 ,in such cases1 one or more asynchronous machines might be kept in operation as a non-loaded motor at a speed just below synchronism until its output as a generator is required2 when by merely increasing the speed of the engine it will be made to act as a generator1 thus avoiding the delays usually occurring before switching in a new alternator4 ,image ,current ,alternators4--,when the generated frequency of alternators excited by low frequency currents is either the sum or the difference of the excitation and rotation frequencies1 any load current flowing through the armature of the machine is exactly reproduced in its field circuit4 ,these reproduced currents are characteristic of all types of asynchronous machines1 and are called image currents1 as they are actually the reflection from the load currents delivered by the armature circuit4 ,as the exciter of a machine of this type carries image currents proportional to the generated currents1 its size must be proportional to the capacity of the machine multiplied by the ratio of the excitation and generated frequencies2 therefore1 in the commercial machines1 the excitation frequency is reduced to the minimum value possible2 from two to five cycles per second being suitable for convenient employment4 ,these machines as heretofore constructed are not self-exciting1 but as the principle of image current enables the construction of self-exciting alternators1 it will be of advantage to have a general understanding of the separately excited machine under different conditions of excitation4 ,illustration3 ,,fig4 #addf4--;,diagram of constant pressure image current alternator connections4 ,the image or reproduced currents are characteristic of all types of asynchronous machines1 and are called image currents because they are actually the reflection from the load currents delivered by the armature circuit4 ,the principle of operation is explained in the accompanying text4 ,when the generated frequency of the machine is equal to the difference of the excitation and rotation frequencies1 the magnetization of the machine is higher under a non-inductive load than under no load4 ,this is principally due to the ohmic resistance of the field circuit1 which prevents the image current from entirely neutralizing the magnetomotive force of the armature current4 ,in other words1 the result of the magnetomotive force of the armature and image currents not only tends to increase the no load magnetization of the machine at non-inductive load1 but depresses the original magnetization at inductive load1 so that the terminal voltage of the machine increases with non-inductive load1 and decreases with inductive load4 ,again1 the generated frequency is equal to the sum of the excitation and rotation frequencies1 the resistance of the field circuit reacts positively2 that is1 it tends to decrease the magnetization1 and consequently the terminal voltage of the machine at both inductive and non-inductive loads4 ,in the constant pressure machine1 the two effects are combined and opposed to one another4 ,the connections of two alternators with diphase excitation are shown by fig4 #a1ddf4 ,extra ,high ,frequency ,alternators4--,alternators generating currents having a frequency up to #aj1jjj or #ae1jjj cycles per second have been proposed several times for special purposes1 such as high frequency experiments1 etc4 ,in #aijb ,nikola ,tesla proposed some forms of alternators having a large number of small poles1 which would generate currents up to a frequency of #ae1jjj cycles per second4 ,later1 the ,westinghouse ,company constructed an experimental machine of the inductor alternator type for generating currents having a frequency of #aj1jjj cycles per second4 ,this machine was designed by ,samms4 ,it had #bjj polar projections with a pole pitch of only #j4be inch1 and a peripheral speed of #be1jjj feet per minute4 ,the armature core was built up of steel ribbon #b inches wide and #c mils thick4 ,the armature had #djj slots with one wire per slot1 and a bore of about #be inches4 ,the air gap was only #j4jcabe inch4 ,on constant excitation the voltage dropped from #aej volts at no-load to #abc volts with an output of #h amperes4 ,self-,exciting ,image ,current ,alternators4--,the type of machine described in the preceding paragraph can be made self-exciting by connecting each pair of brushes1 which collect the current from the armature1 with a field coil so located that the flux it produces will be displaced by a predetermined angle depending on the number of phases required1 as shown by fig4 #a1ddg4 ,the direction of the residual magnetism of the machine is shown by the arrows ,a1 ,a4 ,illustration3 ,,fig4 #a1ddg4--;,diagram of connections of self-exciting image current alternator4 ,when the armature is rotated1 a pressure will be generated between the brushes #b and #d1 and a current will flow from ,c through the coils ,,xx to ,b1 producing a flux through the armature at right angles to the residual magnetism and establishing a resultant magnetic field between ,d1 ,b1 and ,d1 ,c4 ,this field will generate a pressure between the brushes #a and #c1 and a current will flow ,d through ,,xx to ,e in such a direction that it will at first be opposed to the residual magnetism1 and afterward reverse the direction of the latter4 ,at the moment the residual magnetism becomes zero1 the only magnetism left in the machine will be due to the currents from the brushes #b and #d1 and their field combining with the vertical reversed field will produce a resultant polar line between ,b and ,e4 ,as these operations are cyclic1 they will recur at periodic intervals1 and the phenomena will become continuous4 ,the negative field thus set up in the air gap of the machine will cut the conductors of the stator and will be cut by the conductors of the rotor in such a manner that the electromotive forces generated between the brushes of the armature will be equal and opposite to those between the terminals of the stator4 ,,chapter ,l ,,construction ,,of ,,alternators ,the construction of alternators follows much the same lines as dynamos1 especially in the case of machines of the revolving armature type4 ,usually1 however1 more poles are provided than on direct current machines1 in order to obtain the required frequency without being driven at excessive speed4 ,the essential parts of an alternator are3 #a4 ,field magnets2 #b4 ,armature2 #c4 ,collector rings2 and in actual construction1 in order that these necessary parts may be retained in proper co-relation1 and the machine operate properly there must also be included3 #d4 ,frame2 #e4 ,bed plate2 #f4 ,pulley4 ,field ,magnets4--,the early forms of alternator were built with permanently magnetized steel magnets1 but these were later discarded for electromagnets4 ,alternators are built with three kinds of electromagnets1 classed according to the manner in which they are excited1 the machines being known as1 #a4 ,self-excited2 #b4 ,separately excited2 #c4 ,compositely excited4 ,illustration3 ,,figs4 #a1ddh and #a1ddi4--,westinghouse laminated hub and laminated pole piece for revolving field having squirrel cage winding4 ,thin steel is used for the laminations of both hub and pole piece2 these are assembled and firmly riveted together under hydraulic pressure4 ,the laminations are of the same thickness in both hub and spider4 ,illustration3 ,,figs4 #a1dej to #a1deb4--,views of ,triumph pole pieces4 ,these consist of laminated punchings securely clamped between two cast steel end plates4 ,the laminations are shaped with polar horns or shoes as shown1 and which serve to keep the field coils securely wedged in position4 ,in some designs the horns are separate4 ,the two holes in each pole piece are for through bolts which secure the pole piece and coil to the spider run4 ,dovetail joints are sometimes used instead of through bolts1 as in figs4 #a1ddh and #a1ddi4 ,ques4 ,what is a self-excited alternator8 ,ans4 ,one in which the field magnets are excited by current from one or more of the armature coils1 or from a separate winding 7small in comparison with the main winding71 the current being transformed into direct current by passing it through a commutator4 ,illustration3 ,,fig4 #a1dec4--;,fort ,wayne armature for self-excited alternator4 ,there are two independent windings1 one for the main current1 and one for the exciting current4 ,the winding for the latter current occupies a very small amount of space1 and is placed in the slots on top the main winding4 ,the commutator to which the exciter winding is connected1 is located between the collector rings and the core4 ,it is of standard construction with end clamps holding the bars in place on the insulated commutator drum4 ,the armature coils are form wound and the core is built of sheet steel laminations1 annealed and japanned to prevent hysteresis and eddy current losses4 ,ventilated openings are provided to allow a free circulation of air both around the ends of the windings and through ducts in the laminated core4 ,the core is clamped by bolts between the flanges of the armature spider which is keyed to the shaft4 ,these flanges have cylindrical extensions with ribbed surfaces1 which form a support for the ends of the armature coils4 ,the ribbed surfaces form air passages from the core outward around the ends of the coils1 thus ventilating both core and coils4 ,fig4 #a1dec shows an armature of a self-excited machine1 the exciting current being generated in a separate winding and passed through a commutator4 ,ques4 ,for what class of service are self-exciting alternators used8 ,illustration3 ,,fig4 #a1ded4--;,allis-,chalmers three bearing type alternator with exciter direct connected4 ,the bearing pedestals are bolted to a substantial cast iron base having1 in the large sizes1 sufficient length to permit shifting frame sideways along the base to give access to the field and armature coils4 ,the field coils are designed for #abj volt excitation1 and are wound edgewise with copper strip4 ,there is a liberal margin of field excitation to take care of overloads or for operation on loads of low power factor4 ,the regulating qualities are as good as can be obtained without making the machine unnecessarily large and expensive4 ,by regulation is meant the percentage rise in voltage when full load is thrown off1 field excitation and speed being held constant2 the percentage is referred to normal full load voltage4 ,an alternator with poor regulation will show large variations in voltage with changes in load1 the pressure falling whenever a load is thrown on and rising when it is thrown off4 ,these changes will be especially pronounced if the load be inductive4 ,a badly designed alternator might show very fair regulation on non-inductive load and yet be unable to give full voltage on inductive load4 ,ans4 ,they are employed in small power plants and isolated lighting plants where inductive loads are encountered4 ,ques4 ,what is a separately excited alternator8 ,ans4 ,one in which the field magnets are excited from a small dynamo independently driven or driven by the alternator shaft1 either direct connected or by belt as shown in fig4 #a1dee4 ,illustration3 ,,fig4 #a1dee4--;,diagram of separately excited alternator4 ,the field winding is supplied with direct current1 usually at #abe volts pressure by a small dynamo called the exciter4 ,the latter may be driven by independent power1 or by belt connection with the main shaft1 and in some cases the exciter is directly connected to the alternator shaft4 ,ques4 ,what is a compositely excited alternator8 ,ans4 ,a composite alternator is similar to a compound wound dynamo in that it has two field windings4 ,in addition to the regular field coils which carry the main magnetizing current from the exciter1 there is a second winding upon two or upon all of the pole pieces1 carrying a rectified current from the alternator which strengthens the field to balance the losses in the machine1 and also if so desired1 the losses on the line as shown in fig4 #a1def4 ,illustration3 ,,fig4 #a1def4--;,diagram of compositely excited alternator4 ,the current for exciting the field magnets is obtained1 partly from an exciter and partly from the windings of the alternator1 being transformed into direct current by the rectifier4 ,the connections are as shown4 ,one end of the armature winding is connected to one of the collector rings2 the other end1 to the light part of the rectifier1 as shown1 the solid black part of the rectifier being connected to the other collector ring4 ,two brushes bear on adjacent teeth of the rectifier and are connected to the compensating winding circuit across which is a shunt4 ,these connections are shown more clearly in fig4 #a1deg4 ,in operation the separately excited coils set up the magnetism necessary for the generation of the voltage at no load4 ,the main current coming from the armature is shunted1 part going through the shunts and the remainder around the compensating winding1 furnishing the additional magnetism necessary to supply the voltage to overcome the armature impedance4 ,this composite method of field excitation is very similar to that used on a compound wound dynamo4 ,as shown1 both field windings encircle every pole1 but in some machines the rectified current will traverse a few poles only1 the current from the exciter traversing the remainder4 ,ques4 ,what is a magneto8 ,ans4 ,a special form of alternator having permanent magnets for its field1 and used chiefly to furnish current for gas engine ignition and for telephone call bells4 ,details of construction and operation are shown in figs4 #a1deh to #a1dfa4 ,illustration3 ,,fig4 #a1deg4--;,diagram showing construction of rectifier and connections of compositely excited alternator4 ,the rectifier consists of two castings ,m and ,s with teeth which fit together as shown1 being insulated so they do not come in contact with each other4 ,every alternate tooth being of the same casting is connected together1 the same as though joined by a conducting wire4 ,there are as many teeth as there are poles4 ,one end of the armature winding is connected direct to one of the collector rings1 while the other is connected to ,m of the rectifier1 the circuit being through brushes ,p and ,q1 the shunt1 and compensating winding to the other collector ring4 ,the brushes ,p and ,q contact with adjacent teeth1 when one is in contact with the solid black casting the other touches the light casting4 ,the principle of action is the same as a commutator1 briefly3 to reverse the connections terminating at the brushes ,p and ,q in synchronism with the reversals of the alternating current induced in the armature winding1 thus obtaining direct current for the compensating field winding4 ,the shunt resistance placed across the compensating winding circuit permits adjusting the compounding of the machine to the circuit on which it is to work1 since by varying the resistance the percentage of the total current passing through the compensating winding can be changed4 ,it will be seen by tracing the path of the current for each direction in the armature winding that while the rectifier causes the current to flow in the same direction in the compensating field winding1 it still remains alternating in the external circuit4 ,illustration3 ,,fig4 #a1deh4--;,connecticut magneto2 view showing permanent magnets in dotted lines4 ,it consists of three permanent ,u shape magnets1 between the poles of which is a shuttle type armature4 ,the latter is geared to a hand crank in sufficient velocity ratio to give the desired speed without too rapid turning of the crank4 ,this type of magneto is used to generate current for operation of telephone call bells4 ,illustration3 ,,figs4 #a1dei to #a1dfa4--;,diagram illustrating the operation of a magneto4 ,the shuttle shaped armature is wound from end to end with insulated wire1 so that when rotated1 a powerful alternating current is produced in the windings by cutting the magnetic lines1 whose varying strength is shown by the shaded portions in the two views4 ,when in the position shown in the first diagram1 the lines of force mostly converge at the top and bottom1 finding a direct path through the metal end flanges of the shuttle4 ,when in the position shown in the second diagram1 the lines are converged so as to pass through the armature core4 ,fig4 #a1dfj shows detail of the armature core4 ,ques4 ,what are the two principal types of field magnet8 ,ans4 ,stationary and revolving4 ,ques4 ,what is the usual construction of stationary field magnets8 ,ans4 ,laminated pole pieces are used1 each pole being made up of a number of steel stampings riveted together and bolted or preferably cast into the frame of the machine4 ,the field coils are machine wound and carefully insulated4 ,after winding they are taped to protect them from mechanical injury4 ,each coil is then dipped in an insulating compound and afterwards baked to render it impervious to moisture4 ,illustration3 ,,fig4 #a1dfb4--,stationary field of ,fort ,wayne multiphase revolving armature alternator2 view showing brass girds on pole pieces for synchronous motor operation4 ,when designed for this use the machine is provided with amortisseur winding on the poles4 ,as shown in the illustration this winding consists of a brass collar around the pole tip with a cross rib integral with the collar1 fitting in a slot in the pole face parallel to the shaft4 ,this construction assists in bringing the machine up to synchronous speed as an induction motor1 ordinarily checks any tendency toward hunting and does not in any way affect the operation of the machine as an alternator4 ,the main field winding should be connected through switches on the field frame in order that the field circuit may be broken up to eliminate any danger that might arise from induced voltage4 ,it is not advisable to throw on a full rated voltage and a compensator should1 therefore1 be provided to reduce the pressure4 ,illustration3 ,,fig4 #a1dfc4--,triumph #cf pole fly wheel type revolving field4 ,the spider has the form of a fly wheel having spokes and rim to which the field magnets are attached by through bolts4 ,the field coils are of copper strap bent on end1 the kind generally used on large machines4 ,the series connection of the coils is plainly shown1 also the two cables leading via one of the spokes to the slip rings4 ,illustration3 ,,fig4 #a1dfd4--,wagner cast steel hub with dovetail grooves for attaching the revolving field magnets4 ,such construction is generally used on machines of small and medium size4 ,illustration3 ,,fig4 #a1dfe4--,wagner laminated pole piece with horns stamped in one piece4 ,the laminations are held together between two end pieces by through rivets1 as shown4 ,ques4 ,describe the construction of a revolving field4 ,ans4 ,the entire structure or rotor consists of a shaft1 hub or spider1 field magnets and slip rings4 ,the magnet poles consist of laminated iron stampings clamped in place by means of through bolts which1 acting through the agency of steel end plates1 force the laminated stampings into a uniform1 rigid mass4 ,this mass is magnetically subdivided into so many small parts that the heating effect of eddy currents is reduced to a minimum4 ,the cores are mounted upon a hub or spider either by dovetail construction or by means of through bolts1 according to the centrifugal force which they must withstand in operation1 either method permitting the easy removal of any particular field pole if necessary4 ,the field coils are secured upon the pole pieces either by horns in one piece with the laminations1 or separate and bolted4 ,all the coils are connected in series1 cable leads connecting them to slip rings placed on the shaft4 ,illustration3 ,,fig4 #a1dff4--,wagner revolving field of #cjj kilowatt alternator during construction1 illustrating the method of attaching the field magnets to the hub by dovetail joints4 ,after the notched ends of the pole pieces are slid into the grooves in the hub1 tapered keys1 which are plainly seen1 are driven in1 thus making a tight joint which will not shake loose4 ,ques4 ,what are slip rings8 ,ans4 ,insulated rings mounted upon the alternator shaft to receive direct current for the revolving field1 as distinguished from collector rings which collect the alternating currents generated in an alternator of the revolving armature type4 ,in construction provision is made for attaching the field winding leads4 ,the rings are usually made of cast iron and are supported mechanically upon the shaft1 but are insulated from it and from one another4 ,the current is introduced by means of brushes as with a commutator4 ,carbon brushes are generally used4 ,a good design of slip ring should provide for air circulation underneath and between the rings4 ,illustration3 ,,fig4 #a1dfg4--;,general ,electric field coil1 showing one method of winding4 ,in the smaller machines the wire is wound on spools which are slipped over the pole pieces1 which are built of sheet iron1 spreading at the pole face so as to secure not only a wide polar arc for the proper distribution of the magnetic flux1 but also to hold the field windings in place4 ,ques4 ,what form of spider is used on large alternators8 ,ans4 ,it is practically the same form as a fly wheel1 consisting of hub1 spokes1 and rim to which the magnets are bolted4 ,illustration3 ,,fig4 #a1dfh4--;,general ,electric field coil showing another method of winding4 ,the field coils on the larger machines consist of a single strip of flat copper1 wound on edge as shown1 so that the surface of every turn is exposed to the air for cooling4 ,the flat sides of the copper strip rest against each other and the entire coil forms a structure of great solidity which can be easily removed for inspection and repair4 ,illustration3 ,,fig4 #a1dfi4--;,allis-,chalmers #fj kva4 belted two bearing alternator on base arranged so the armature can be shifted sideways as shown1 to give access to the field and armature coils4 ,on alternators of the fly wheel type the spider rim is made of sufficient weight to obtain full fly wheel effect1 thus making a separate fly wheel unnecessary4 ,illustration3 ,,fig4 #a1dgj4--,revolving field of ,fort ,wayne #aj pole alternator4 ,in construction1 the cores of the field poles are built up from punchings of laminated steel1 and assembled under considerable pressure between malleable iron or steel end plates and riveted together4 ,substantial insulation is placed on the pole cores and over this is wound the field coils of cotton covered wire4 ,after the wire is in place1 the completed poles are baked to expel any moisture and are then treated with insulating varnish4 ,they are then assembled on a laminated spider1 being held in place by dovetail joints made tight by the use of taper keys4 ,special casting plates are finally fastened in place over the dove tails effectually closing them4 ,the assembly of the field is completed by the insertion of the shaft into the field spider under heavy hydraulic pressure4 ,all the coils are connected in series1 cable leads connecting them to slip rings placed on the shaft4 ,each slip ring is provided with a double type brush holder1 making it possible to clean brushes while the alternator is in service1 by simply removing one brush at a time4 ,illustration3 ,,fig4 #a1dga4--;,general ,electric slip rings2 view showing construction and attachment of cable leads to field winding4 ,they are so designed that all surfaces of the rings have easy access to the air1 in order to obtain good ventilation4 ,slip rings1 through which current is transmitted to a revolving field1 are to be distinguished from collector rings whose function it is to collect or transmit the alternating currents induced in the armature to the brushes4 ,armatures4--,in construction1 armatures for alternators are similar to those employed on dynamos2 they are in most cases simpler than direct current armatures due to the smaller number of coils1 absence of commutator with its multi-connections1 etc4 ,alternator armatures may be classified in several ways3 #a4 ,with respect to operation1 as a4 ,revolving2 b4 ,stationary4 ,illustration3 ,,fig4 #a1dgb4--;,allis-,chalmers brush holder and slip rings4 ,the latter are made of cast copper1 which the builders claim to be more satisfactory than cast iron4 ,on some of the large low speed machines the collector rings are split1 but on the majority of alternators they are in one piece4 ,current is led into the rings by means of carbon brushes1 the number of brushes being such that the current density at the rubbing contact is kept within conservative limits4 ,at least two brushes per ring are provided1 so that one can be removed for inspection without interrupting the exciting current4 ,in large machines the brush holder studs are mounted on a stand supported from the base2 on small alternators they are usually fastened to the cap of one of the bearing pedestals4 ,illustration3 ,,fig4 #a1dgc4--;,fort ,wayne multiphase revolving armature alternator1 designed for use in small power plants and isolated lighting plants where inductive loads are encountered4 ,built for pressures of #abj1 #bdj1 #dhj1 and #fjj volts4 ,these voltages have been recommended by the ,american ,institute of ,electrical ,engineers1 and will cover the needs of any set of conditions ordinarily met with4 ,these standard voltages not only permit economical distribution1 but they are such that no transformers are necessary to reduce the line pressure for ordinary cases4 ,for transmitting power relatively long distances1 #fjj volts is usually employed4 ,where there is a demand for #dhj volt service1 a #dhj volt alternator should be selected and if lower voltages are also desired an auto-transformer may be furnished by means of which #bdj volts can be obtained4 ,when #abj volt circuits are necessary for lighting1 etc41 the #bdj volt pressure can be still further reduced to #abj volts by means of another auto-transformer4 ,however1 this double reduction will rarely be found necessary4 ,illustration3 ,,fig4 #a1dgd4--,western ,electric stationary armature4 ,in this type of armature1 the core upon which the winding is placed1 is built into the frame as shown1 the core teeth projecting inwardly like internal gear teeth1 forming a cylindrical chamber for the revolving field4 ,the core is built up of iron1 laminated and japanned to prevent eddy currents and hysteresis losses4 ,the laminations are rigidly bolted between two heavy end plates4 ,the armature coils are of copper bar impregnated with insulating compound4 ,they are held in the slots by wedges which allow their ready removal for inspection or repairs4 ,illustration3 ,,figs4 #a1dgd to #a1dgg4--,various types of armature2 fig4 #a1dgd ring armature2 fig4 #a1dge disc armature2 fig4 #a1dgf drum armature4 ,the latter type is now almost universally used1 the others being practically obsolete4 ,a ,gramme ring wound and connected to collector rings as in fig4 #a1dgd1 will yield an alternating current4 ,in a multipolar field1 the ring will need multipolar connections alternated at points corresponding to the pitch of the poles4 ,fig4 #a1dge illustrates the so-called ,siemens disc armature4 ,the armature coils are arranged around the periphery of a thin disc4 ,the field magnets consist of two crowns of fixed coils1 with iron cores arranged so that their free poles are opposite one another4 ,this type was created in #ahgh by ,herr von ,hefner1 engineer to ,messrs4 ,siemens and ,halske4 ,fig1 #a1dgf shows a modern drum armature of a three phase machine4 ,it is similar in appearance to a direct current armature except for the absence of the commutator and its connections4 ,the drum armature is the prevailing type4 #b4 ,with respect to the core1 as a4 ,ring2 b4 ,disc2 c4 ,drum4 ,ring and disc armatures are practically obsolete and need not be further considered4 ,a ring armature has the inherent defect that the copper inside the ring is inactive4 ,disc armatures were employed by ,pacinotti in #ahgh1 and afterwards adopted by ,brush in his arc lighting dynamos4 ,the design failed for mechanical reasons1 but electrically it is1 in a sense1 an improvement upon the ,gramme ring1 in that inductors on both sides of the ring are active1 these being connected together by circumferential connectors from pole to pole1 thus1 corresponding to the end connectors on modern drum armatures4 #c4 ,with respect to the core surface1 as a4 ,smooth core2 b4 ,slotted core4 ,in early dynamos the armature windings were placed upon an iron core with a smooth surface4 ,a chief disadvantage of this arrangement is that the magnetic drag comes upon the inductors and tends to displace them around the armature4 ,to prevent ,illustration3 ,,fig4 #a1dgh4--;,a style of disc largely used for armature cores4 ,the teeth are provided with dovetail grooves near the circumference4 ,after the coil is inserted in a groove1 a wooden wedge is driven in the groove which encloses the coil and secures it firmly in position4 ,this obviates the necessity of bands to resist the centrifugal force acting on the inductors4 ,illustration3 ,,fig4 #a1dgi4--,large revolving armature construction with segmental discs dovetailed to spider spokes4 ,illustration3 ,,fig4 #a1dhj4--;,construction of large stationary armature2 view showing section of core and frame4 ,the core discs are in segments and are attached to the frame by dovetail joints as shown4 ,the joints are staggered in building up the core1 that is1 they are overlapped so as not to unduly increase the reluctance of the magnetic circuit4 ,dovetail joints obviate the use of through bolts which1 if not insulated1 are liable to give rise to eddy currents by short circuiting the discs4 _/ this1 projecting metal pieces called driving horns were fixed into the core so as to take the pressure1 but they proved unsatisfactory4 ,this defect together with the long air gap necessary in smooth core construction resulted in the type being displaced by slotted core armatures4 ,a slotted core is one whose surface is provided with slots or teeth which carry the inductors1 as shown in the accompanying illustrations1 and is the type almost universally used4 ,the inductors are laid in the slots1 the sides and bottoms of which are first carefully insulated by troughs of mica-canvas1 micanite or other suitable insulating material4 ,ques4 ,what are the advantages of slotted core armatures8 ,ans4 ,the teeth protect the inductors1 retain them in place against the electrical drag and centrifugal force1 and the construction permits a reduction of air gap to a minimum1 thus reducing the amount of copper required for the field4 ,illustration3 ,,fig4 #a1dha4--;,general ,electric revolving field and exciter armature4 ,this is an example of direct connected exciter construction4 ,in this arrangement the armature of the exciter is carried on the alternator shaft at the end farthest from the pulley4 ,in the smaller sizes the magnet frame is bolted to the bearing bracket1 but in the larger sizes special construction is used depending upon the conditions to be met4 ,on all alternators of standard design1 the field is built for #abe volts excitation and on account of the increased danger from induced voltage1 in case the machine is used as a synchronous motor1 the builders consider any higher voltage undesirable4 ,illustration3 ,,fig4 #a1dhb4--,section of ,general ,electric ,alternator showing method of dovetailing core laminations to frame4 ,the latter is made in two general styles1 known as the box type and skeleton type4 ,the box type consists of a single casting for the smaller sizes1 but for large capacity alternators the frame castings are usually divided into upper and lower sections4 ,the skeleton type consists of two side castings between which substantial spacing rods are set at regular intervals4 ,the core consists of the usual sheet iron lamination slotted and assembled2 they are mounted on the inner periphery of the frame1 making lap joints 7that is staggered as in fig4 #a1dhj71 each section being dovetailed to the frame4 ,heavy clamping rings or end plates are mounted on both sides of the core by means of bolts1 and supporting fingers extend along the slot projections4 ,the design is such as to provide for air circulation as shown in figs4 #a1dhc and #a1dhd4 ,armature ,windings4--,in general1 the schemes for armature windings for alternators are simpler than those for direct current machines1 as in the majority of cases the inductors are an even multiple of the number of poles1 and the groupings are usually symmetrical with respect to each pole or each pair of poles4 ,furthermore1 as a general rule1 all the inductors of any one phase are in series with one another2 therefore1 there is only one circuit per phase1 and this is as it should be1 since alternators are usually required to generate high voltages4 ,these general principles establish the rule1 that in the circuit in a single phase armature1 and in the individual circuits in a polyphase armature1 the winding is never re-entrant1 but the circuits have definite endings and beginnings4 ,in exceptional cases1 as those of polyphase converters1 re-entrant circuits are employed1 and the armature windings are so constructed that a commutator can be connected to them exactly as in direct current machines4 ,these armatures are usually of the lap wound drum type4 ,illustration3 ,,fig4 #a1dhc4--,section of ,general ,electric alternator frame showing air ducts and supporting fingers extending along the slot projections4 ,the air circulation is provided for by means of ducts formed by suitable spacing blocks inserted at intervals between the laminations1 as shown here and in fig4 #a1dhd4 ,the armature coils are form wound and designed so they can be readily replaced in case of injury4 ,they are taped and treated with an impregnating compound1 in the usual way1 then inserted in the armature slots in an armour of horn fibre and retaining wedges of wood are dovetailed into the slot walls4 ,alternator windings are usually described in terms of the number of slots per phase per pole4 ,for instance1 if the armature of a #bj pole three phase machine have #cjj slots1 it has #ae slots per pole or #e slots per each phase per pole1 and will be described as a five slot winding4 ,therefore1 in order to trace the connections of a winding1 it is necessary to consider the number of slots per pole for any one phase on one of the following assumptions3 #a1 that each slot holds one inductor2 #b1 that there is one side of a coil in each slot2 and #c1 that one side of a coil is subdivided so as to permit of its distribution in two or more adjacent slots4 ,the voltage depends upon the number of inductors in a slot1 but the breadth coefficient and wave form are influenced by the number of slots per pole1 and not by the number of inductors within the slots4 ,illustration3 ,,fig4 #a1dhd4--,section of ,general ,electric stationary armature showing method of assembling the coils4 ,these are form wound and are held in the slots by suitable wedges1 the open slot construction permitting the use of form wound coils that can be easily removed and replaced in case of damage4 ,where heavy windings project beyond the laminations1 an additional support is provided by means of an insulated metal ring1 to which the outer ends of the coils are fastened2 the coils are thereby protected from mechanical displacement1 or distortion due to the magnetic disturbances caused by violent fluctuations of the load or short circuits4 ,the figure shows a section of a supporting ring of this type and indicates the method of connecting the coils to it4 ,in order to admit of the prompt replacement of damaged coils1 sufficient space is usually provided between the alternator bearings to allow ample movement of the armature to permit of ready access to both armature and field coils4 ,where space necessitates the use of a short shaft1 access to the windings may be had by disconnecting some of the coils and lifting the upper half of the armature4 ,classification of ,windings4--,the fact that alternators are built in so many different types1 gives rise to numerous kinds of armature winding to meet the varied conditions of operation4 ,in dividing these forms of winding into distinctive groups1 they may be classified1 according to several points of view1 as follows3 #a4 ,with respect to the form of the armature1 as3 a4 ,revolving2 b4 ,stationary4 #b4 ,with respect to the mode of progression1 as3 a4 ,lap winding2 b4 ,wave winding4 #c4 ,with respect to the relation between number of poles and number of coils1 as3 a4 ,half coil winding2 b4 ,whole coil winding4 #d4 ,with respect to the number of slots1 as3 a4 ,concentrated or uni-coil winding2 b4 ,distributed or multi-coil winding4 ,partially distributed2 ,fully distributed4 #e4 ,with respect to the form of the inductors1 as3 a4 ,wire winding2 b4 ,strap winding2 c4 ,bar winding4 #f4 ,with respect to the number of coils per phase per pole1 as3 a4 ,one slot winding2 b4 ,two slot winding2 etc4 #g4 ,with respect to the kind of current delivered1 as3 a4 ,single phase winding2 b4 ,two phase winding2 c4 ,three phase winding4 ,illustration3 ,,fig4 #a1dhe4--,section of ,western ,electric stationary armature core showing laminations clamped in place1 and ventilating ducts4 ,the stator or stationary armature consists of soft iron laminations assembled in the magnet frame with stator coils embedded in the core slots4 ,the laminations are punched separately and then carefully annealed to reduce hysteresis losses4 ,after annealing1 a coat of japan is applied1 effectively preventing the flow of eddy currents in the assembled core4 ,the frame is cast iron and of the box type construction4 ,the frames of the smaller sizes are cast in one piece1 while frames of the larger sizes are split to facilitate installation4 ,large openings are provided in the box type frame1 in order to improve the ventilation4 ,the laminations are securely held in place in the frame by heavy end rings and by steel clamping fingers which are firmly bolted to the frame4 ,the outer circumference of the core is dovetailed to the frame1 and the inner circumference is slotted to receive the windings4 ,the alignment of the slots is insured by means of metal wedges1 and no filing is done on the slots1 so that each lamination is always insulated from the next one4 ,numerous ventilating ducts allow the free circulation of cool air through and around the coils4 ,the open slot construction is employed and the coils are fitted into insulating troughs which offer excellent mechanical and electric protection4 ,the coils are held in place by suitable wedges4 #h4 ,with respect to the shape of the coil ends1 as3 a4 ,single range2 b4 ,two range2 etc4 ,in addition to these several classes of winding1 there are a number of miscellaneous windings of which the following might be mentioned3 a4 ,chain or basket winding2 b4 ,skew coil winding2 c4 ,fed-in winding2 d4 ,imbricated winding2 e4 ,mummified winding2 f4 ,spiral winding2 g4 ,shuttle winding2 h4 ,creeping winding2 i4 ,turbine alternator winding4 ,illustration3 ,,fig4 #a1dhf4--,method of assembling form wound coils4 ,the picture shows a section of a ,general ,electric armature with part of the coils in place4 ,a layer of insulating material is first placed in the slots1 before inserting the coils as seen at the left4 ,when the coils are in place and surrounded by this layer of insulating material the retaining wedges are inserted in the notches1 thus closing the slots and protecting the coils from mechanical injury4 ,a few wedges are seen in position at the right4 ,ques4 ,define a revolving and a stationary winding4 ,ans4 ,the words are self-defining2 a winding is said to be revolving or stationary according as the armature forms the rotor or stator of the machine4 ,ques4 ,what is the significance of the terms lap and wave as applied to alternator windings8 ,ans4 ,they have the same meaning as they do when applied to dynamo windings4 ,illustration3 ,,fig4 #a1dhg4--,section of ,general ,electric stationary armature ventilating ducts and winding in position4 ,these are described in detail in ,chapter ,,xviii4 ,briefly a lap winding is one composed of lap coils2 a wave winding is one which roughly resembles in its diagram1 a section of waves4 ,half ,coil and ,whole ,coil ,windings4--,the distinction as to whether the adjacent sides of consecutive coils are placed together under one pole or whether they are separated a distance equal to the pole pitch1 gives rise to what is known as half coil and whole coil windings4 ,a half coil or hemitropic winding is one in which the coils in any phase are situated opposite every other pole1 that is1 a winding in which there is only one coil per phase per pair of poles1 as in fig4 #a1dhh4 ,a whole coil winding is one in which there is one coil per phase per pole1 as in fig4 #a1dhi1 the whole 7every one7 of the poles being subtended by coils4 ,illustration3 ,,figs4 #a1dhh and #a1dhi4--;,elementary bipolar alternators with half coil and whole coil windings4 ,in a half coil winding there is one coil per phase per pair of poles2 in a whole coil winding there is one coil per phase per pole4 ,concentrated or ,uni-,coil ,winding4--,fig4 #a1dib shows the simplest type of single phase winding4 ,it is a one slot winding and is sometimes called monotooth or uni-coil winding4 ,the surface of the armature is considered as divided into a series of large teeth1 one tooth to each pole1 and each tooth is wound with one coil1 of one or more turns per pole4 ,since all the turns of the coil are placed in single slots1 the winding is called concentrated4 ,illustration3 ,,fig4 #a1dij4--,multi-polar revolving armature alternator with half coil winding1 shown in radially developed diagram to clearly indicate the path of the winding4 ,a half coil or hemitropic winding has a slightly higher reactance than a winding in which two distinct coils are used in the same slot1 one going forward and the other backward4 ,the most usual three phase windings are of the half coil type as the three sets of coils are equispaced over a pair of poles4 ,illustration3 ,,fig4 #a1dia4--,multi-polar revolving armature alternator with whole coil winding shown in radially developed diagram to clearly indicate the path of the winding4 ,ques4 ,what are the features of concentrated windings8 ,ans4 ,cheap construction1 maximum voltage for a given number of inductors4 ,concentrated windings have greater armature reaction and inductance than other types hence the terminal voltage of an alternator with concentrated winding falls off more than with distributed winding when the current output is increased4 ,an alternator1 therefore1 does not have as good regulation with concentrated winding as with distributed winding4 ,illustration3 ,,figs4 #a1dib and #a1dic4--;,concentrated windings4 ,a concentrated winding is one in which the armature has only one tooth per phase per pole1 that is1 the number of teeth equals the number of poles4 ,a concentrated winding of the half coil type has only one side of a coil in each slot as in fig4 #a1dib4 ,in the whole coil variety1 each slot contains neighboring sides of adjacent coils1 as in fig4 #a1dic4 ,in construction1 wedges are generally used for retaining the half coils1 and with whole coils the teeth have projecting horns for this purpose4 ,ques4 ,what should be noted with respect to concentrated windings8 ,ans4 ,a concentrated winding1 though giving higher voltage than the distributed type with no load1 may give a lower voltage than the latter at full load4 ,illustration3 ,,fig4 #a1did4--,laminated core with two coils in position2 type of punchings used on some machines having concentrated whole coil windings4 ,the manner of assembling the coils is shown in fig4 #a1die4 ,ques4 ,what is the wave form with a concentrated winding8 ,ans4 ,the pressure curve rises suddenly in value as the armature slots pass under the pole pieces1 and falls suddenly as the armature slots recede from under the pole pieces4 ,illustration3 ,,fig4 #a1die4--,westinghouse single phase concentrated coil armature2 view showing method of placing coils4 ,the coils are machine wound on formers and after being taped1 varnished and baked1 are spread out slightly so as to pass over the teeth and are then forced into place in the deep slots by means of wooden wedges1 being securely held in place by retaining wedges1 as shown in fig4 #a1did4 ,distributed or ,multi-,coil ,windings4--,instead of winding an armature so it will occupy only one slot per phase per pole1 it may be spread out so as to fill several slots per phase per pole4 ,this arrangement is called a distributed winding4 ,to illustrate1 fig4 #a1dif represents a coil of say fifteen turns4 ,this could be placed on an armature just as it is1 in which case only one slot would be required for each side1 that is1 two in all4 ,in place of this thick coil1 the wire could be divided into several coils of a lesser number of turns each1 arranged as in fig4 #a1dig2 it is then said to be partially distributed1 or it could be arranged as in fig4 #a1dih1 when it is said to be fully distributed4 ,illustration3 ,,figs4 #a1dif to #a1dih4--;,alternator coils1 showing difference between the concentrated1 partially distributed1 and fully distributed forms4 ,fig4 #a1dif shows a concentrated coil in which all the wire is wound in one large coil2 in the partially distributed type fig4 #a1dig1 the wire of fig4 #a1dif1 is wound in two or more coils or sections connected as shown1 leaving some space inside not taken up by the subdivisions4 ,in fig4 #a1dih the wire of fig4 #a1dif is fully distributed1 being wound in a series of coils1 so that all the interior space is taken up by the wire1 that is to say1 the spaces not occupied by the wire 7the teeth when placed on the armature7 are of equal size4 ,a partially distributed winding1 then1 is one1 as in fig4 #a1dii1 in which the coil slots do not occupy all the circumference of the armature2 that is1 the core teeth are not continuous4 ,a fully distributed winding is one in which the entire surface of the core is taken up with slots1 as in fig4 #a1ejj4 ,ques4 ,in a distributed coil what is understood by the breadth of the coil8 ,ans4 ,the distance between the two outer sides1 as ,b in figs4 #a1dig and #a1dih4 ,illustration3 ,,fig4 #a1dii4--,partially distributed winding4 ,each coil unit is here divided into two concentric coils of different dimensions and connected in series1 as shown in detail in fig4 #a1dig4 ,this being a whole coil winding the several units are so connected that the winding of adjacent units proceeds in opposite directions1 that is1 one coil is wound clockwise1 and the next counter clockwise1 etc41 so that the induced currents flow in a common direction as indicated by the arrows for the position shown4 ,illustration3 ,,fig4 #a1ejj4--;,fully distributed winding4 ,in this type of winding each coil consists of so many sub-coils that the winding occupies the entire surface of the armature core2 that is1 there are no extensive spaces unoccupied1 the spacing being uniform as shown4 ,ques4 ,how far is it advisable to spread distributed coils of a single phase alternator8 ,ans4 ,there is not much advantage in reducing the interior breadth much below that of the breadth of the pole faces1 nor is there much advantage in making the exterior breadth greater than the pole pitch4 ,undue spreading of distributed coils lowers the value of the ,kapp coefficient 7later explained7 by reducing the breadth coefficient and makes necessary a larger number of inductors to obtain the same voltage4 ,the increase in the number of inductors causes more armature self-induction4 ,from this point of view1 it would be preferable to concentrate the winding in fewer slots that were closer together4 ,this1 however1 would accentuate the distorting and demagnetizing reactions of the armature4 ,accordingly1 between these two disadvantages a compromise is made1 as to the extent of distributing the coils and spacing of the teeth1 the proportions assigned being those which experience shows best suited to the conditions of operation for which the machine is designed4 ,illustration3 ,,fig4 #a1eja4--;,developed diagram of single phase concentrated whole coil winding in two slot stamping for six pole alternator4 ,if the sides of adjacent whole coils be slightly separated by placing the winding in a two slot stamping the electrical result will not differ materially from the monotooth whole coil winding1 but if the winding be hemitropic1 as in fig4 #a1ejb1 and has coils of two sizes as shown1 it will be suitable for high voltages4 ,the ,kapp ,coefficient4--,a volt or unit of electric pressure is defined as the pressure induced by the cutting of #ajj1jjj1jjj or #aj lines of force per second4 ,in the operation of an alternator the maximum pressure generated may be expressed by the following equation3 f,,zn ,e ------ 7#a7 #aj in which f frequency2 ,z number of inductors in series in any one magnetic circuit2 ,n magnetic flux1 or total number of magnetic lines in one pole or in one magnetic circuit4 ,the maximum value of the pressure1 as expressed in equation 7#a71 occurs when #ij4 ,illustration3 ,,fig4 #a1ejb4--;,developed diagram of single phase partially distributed half coil winding for six pole alternator in two slot stamping1 same as in fig4 #a1eja4 ,in this arrangement the direction of rotation is not reversed4 ,it is a question as to how far the coils of a single-phase armature may be spread with advantage4 ,there is not much advantage in reducing the interior breadth of the coils below that of the pole face1 nor in widening the exterior breadth beyond that of the pole pitch4 ,the virtual value of the volts is equal to the maximum value divided by #b1 or multiplied by #b1 hence1 #b f,,zn #b4bb;f,,zn ,e -------------- --------- 7#b7 #aj #aj ,this is usually taken as the fundamental equation in designing alternators4 ,it is1 however1 deduced on the assumptions that the distribution of the magnetic flux follows a sine law1 and that the whole of the loops of active inductors in the armature circuit acts simultaneously1 that is to say1 the winding is concentrated4 ,illustration3 ,,fig4 #a1ejc4--;,developed diagram of single phase winding with fully distributed coils4 ,as explained1 excessive spreading lowers the value of the ,kapp coefficient1 and consequently the voltage2 also the use of a larger number of inductors to obtain the same voltage results in an increase of armature self-induction4 ,on the other hand1 if the winding were concentrated in fewer slots and these slots were closer together1 the result will be an increase in distorting and demagnetizing reactions of the armature4 ,therefore1 a compromise between these two disadvantages must be made4 ,the common practice is to wind in two or three slots per pole per phase4 ,illustration3 ,,fig4 #a1ejd4--;,allis-,chalmers lap wound coils forming a three slot distributed coil unit4 ,in construction1 after the coils have been covered with insulating materials and treated with insulating compound1 the parts that lie in the slots are pressed to exact size in steam-heated moulds4 ,this runs the insulating material into all the small spaces in the coil1 excluding moisture and rendering the insulation firm and solid4 ,the ends of the coils1 where they project beyond the slots1 are heavily taped4 ,illustration3 ,,fig4 #aeje4--;,allis-,chalmers armature construction2 view showing section of frame and two layer winding4 ,in practice1 the coils are often more or less distributed1 that is1 they do not always subtend an exact pole pitch2 moreover1 the flux distribution1 which depends on the shaping and breadth of the poles1 is often quite different from a sine distribution4 ,hence1 the coefficient #b4bb in equation 7#b7 is often departed from1 and in the general case equation 7#b7 may be written kf,,zn ,e ------- 7#c7 #aj where k is a number which may have different values1 according to the construction of the alternator4 ,this number k is called the ,kapp coefficient because its significance was first pointed out by ,prof4 ,gisbert ,kapp4 ,illustration3 ,,figs4 #a1ejf and #a1ejg4--;,effect of breadth of coils in distributed windings4 ,in the section of the alternator shown in fig4 #a1ejf the directions of the pressures induced as the armature rotates clockwise are represented by dots for those which act towards the reader1 and by crosses for those which act from the reader 7the dots and crosses representing respectively the heads and tails of arrows74 ,since the field is not uniform but maximum at the center and gradually weakening towards the extremities1 it is obvious that the maximum pressure is induced in any inductor as it passes the center of the pole1 this variation being indicated by the heavier dots and crosses toward the center4 ,now if a number of these inductors be connected up to form a distributed coil as in fig4 #a1ejg1 the pressures induced in each will be added1 but all the maximum pressure will not be induced in all at the same time1 hence the total pressure induced in the distributed coil is less than it would be if the coil were concentrated as in fig4 #a1eji4 ,illustration3 ,,fig4 #a1ejh4--;,diagram of distributed coil whose inner breadth is less than the breadth of the pole face1 showing the disadvantage of such arrangement4 ,the pressures induced in the inner windings of such a coil are opposing each other at the instant depicted1 that is1 while the inductors are under the pole face1 such action of course being objectionable4 ,the value of k is further influenced by a breadth coefficient or winding factor4 ,the effect of breadth in distributed windings is illustrated in figs4 #a1ejf to #a1ejh4 ,wire1 ,strap1 and ,bar ,windings4--,in the construction of alternators1 the windings may be of either wire1 strap1 or bar1 according to which is best suited for the conditions to be met4 ,ques4 ,what conditions principally govern the type of inductor8 ,ans4 ,it depends chiefly upon the current to be carried and the space in which the inductor is to be placed4 ,illustration3 ,,fig4 #a1eji4--,simple form of alternator coil1 consisting of numerous turns of insulated wire wound around a form1 then covered with a tape winding1 varnished and baked4 ,ques4 ,what kind of inductors are used on machines intended for high voltage and moderate current8 ,ans4 ,the winding is composed of what is called magnet wire1 with double or triple cotton insulation4 ,ques4 ,where considerable cross section is required how is a wire inductor arranged8 ,ans4 ,in order that the coil may be flexible several small wires in multiple are used instead of a single large wire4 ,ques4 ,how is the insulation arranged on inductors of this kind8 ,ans4 ,bare wire is used for the wires in parallel1 insulation being wrapped around them as in fig4 #a1eaj4 ,this construction reduces the space occupied by the wires1 and the insulation serves to hold them in place4 ,illustration3 ,,figs4 #a1eaj and #a1eaa4--,multi-wire inductors4 ,when the cross section of inductor necessary to carry the current is large1 the use of a single wire would present difficulties in winding on account of its stiffness4 ,accordingly two or more smaller wires are used in parallel to secure the required cross section4 ,bare wire is used and the several sections encased in insulation as shown1 the combination being more flexible than an equivalent single wire4 ,illustration3 ,,fig4 #a1eab4--,two coil slot for whole coil winding4 ,the slot has two recesses ,a and ,b for the reception of separate coils4 ,in assembling the winding1 the inner wedge is first placed in position and then the slot line with the insulating material4 ,this usually consists of alternate layers of mica and pressboard4 ,the coils composed of several turns of wire or copper strip are wound in place1 and after covering with a layer of insulation1 the outer wedge is pushed in place to retain the inductors in position4 ,ques4 ,what precaution is taken in insulating a wire wound coil containing a large number of turns8 ,ans4 ,on account of the considerable difference of pressure between layers1 it is necessary to insulate each layer of turns as well as the outside of the coil1 as shown in fig4 #a1eac4 ,illustration3 ,,fig4 #a1eac4--,method of winding a coil containing a large number of turns1 when there is considerable difference of pressure between the layers4 ,in such cases to guard against short circuits or breakdown of the insulation1 each layer of turns is insulated from the next layer by the insulating strips ,a1 ,b1 ,c1 in addition to the regular insulation around each wire4 ,after the coil is made up it is wound with insulating tape1 varnished and baked4 ,ques4 ,do distributed coils require insulation between the separate layers8 ,ans4 ,since they are subdivided into several coils insulation between layers is usually not necessary4 ,ques4 ,how is a coil covered8 ,ans4 ,it is wound with a more or less heavy wrapping of tape depending upon the voltage4 ,illustration3 ,,figs4 #a1ead and #a1eae4--,single and double layer multi-wire inductors and methods of placing them on the core4 ,here the term layer means unit1 in fact each unit is made up of several layers of wires4 ,in fig4 #a1ead1 where so many wires are bunched together in one unit1 each layer of turns is separated from those adjacent by insulating strips on account of the considerable difference of pressure between layers4 ,this insulation is not necessary in fig4 #a1eae where there are two units or so called layers4 ,in both cases the inductors are held in place by wedges driven into dovetail grooves4 ,linen tape of good quality1 treated with linseed oil1 forms a desirable covering4 ,where extra high insulation is required the tape may be interleaved with sheet mica4 ,ques4 ,is the insulation placed around the coils all that is necessary8 ,ans4 ,the slots into which the coils are placed1 are also insulated4 ,illustration3 ,,fig4 #a1eaf4--;,copper strap or ribbon with insulation4 ,these are generally from _/ to _/ inch thick with rounded edges as shown to avoid cutting the insulation4 ,illustration3 ,,fig4 #a1eag4--;,bar inductor4 ,its shape enables putting the maximum cross section of copper into the slot and is used to advantage on machines which generate large currents4 ,illustration3 ,,fig4 #a1eah4--,style of armature core stamping used with bar wound machines4 ,this construction1 since there are no indentations in the teeth for wedges1 makes it necessary to provide bands to hold the bars in place4 ,ques4 ,how are bar windings sometimes arranged8 ,ans4 ,in two layers1 as in fig4 #a1ebc4 ,single and ,multi-,slot ,windings4--,these classifications correspond to concentrated and distributed windings1 previously described4 ,in usual modern practice1 only two-thirds of the total number of slots 7assuming the spacing to be uniform7 ,illustration3 ,,figs4 #a1eai and #a1ebj4--;,bent bar inductor and method of connection with soldered joint4 ,fig4 #a1eai shows one bar and shape of bent ends4 ,the portion from ,c to ,d is placed in the slot2 ,b to ,c and ,d to ,e1 bent or connector sections2 ,a to ,b and ,e to ,f1 ends bent parallel to slot for soldering4 ,fig4 #a1ebj shows two bar inductors connected4 ,illustration3 ,,figs4 #a1eba and #a1ebb4--,method of avoiding a soldered joint at one end of a bar inductor by using a bar of twice the length shown in fig4 #a1eai1 and bending it into a long ,u form1 as in fig4 #a1eba1 after which it is spread out forming two inductors1 as in fig4 #a1ebb4 of a single phase armature are wound with coils4 ,the reason for this may be explained by aid of fig4 #a1ebd1 which shows an armature with six slots per pole1 four of which are wound4 ,owing to the different positions of1 say1 coils ,a and ,b1 there will be a difference in phase between the pressure generated in them and consequently the resultant pressure of the two coils joined in series will be less than the sum of the pressure in each coil4 ,illustration3 ,,fig4 #a1ebc4--;,arrangement in slot of two layer bar winding4 ,with bar inductors1 as must be evident from the illustration1 the maximum cross section of copper can be placed in a slot of given dimension1 hence a bar winding is used to advantage for alternators designed to carry a large current4 ,bar inductors1 on account of the shape of their ends1 must be placed in the slots from the top1 because the bent ends do not admit of pushing them in4 ,straight slots are therefore necessary1 the inductors being held in place by wooden strips and tie bands as shown4 ,fig4 #a1ebe shows the pressure plotted out as vector quantities1 and the table which follows gives the relative effectiveness of windings with various numbers of slots wound in series4 ,the figures in the last column of the table show that a large increase in the weight of active material is required if the inductors in a single phase machine are to be distributed over more than two-thirds the pole pitch4 ,again1 if much less than two-thirds of the surface be wound1 it is more difficult to provide a sine wave of pressure4 ,illustration3 ,,fig4 #a1ebd4--;,diagram of single phase multi-coil or distributed winding to show characteristic differences in action and construction from single coil or concentrated winding4 ,illustration3 ,,fig4 #a1ebe4--,vector diagram of pressures induced in the single phase multi-coil or distributed winding shown in diagram in fig4 #a1ebd4 ,,table ,,of ,,relative ,,effectiveness ,,of ,,windings ---------------------------------------- ------------------------ ,slots wound ,pressure across ,winding ,quantity of in series coils coefficient copper to produce same pressure ---------------------------------------- --------------------- #a #a #a #a #b #a4ic 4#ig #a4jc #c #b4gc 4#ia #a4aj #d #c4cd 4#hd #a4ai #e #c4gb 4#gd #a4ce #f #c4hf 4#fd #a4ef ---------------------------------------- --------------------- ,ques4 ,what other advantage besides obtaining a sine wave is secured by distributing a coil8 ,ans4 ,there is less heating because of the better ventilation4 ,illustration3 ,,fig4 #a1ebf4--;,developed diagram of a single phase monotooth or one slot bar winding2 it is suitable only for operation at low voltage4 ,single ,phase ,windings4--,there are various kinds of single phase winding1 such as1 concentrated1 distributed1 hemitropic1 etc4 ,fig4 #a1ebg shows the simple type of single phase winding4 ,it is a one slot winding1 that is1 concentrated coils are used4 ,the armature has the same number of teeth as there are poles1 the concentrated coils being arranged as shown4 ,in designing such a winding1 the machine1 for example1 may be required to generate1 say1 #c1jjj volts1 frequency #de1 revolutions #ijj per minute4 ,these conditions require #gbj inductors in series in the armature circuit1 and as the armature is divided into six slots corresponding to the six poles1 there will be #abj inductors per slot1 and the coil surrounding each of the six teeth on the surface of the armature will consist of #fj turns4 ,the connections must be such as to give alternate clockwise and counter-clockwise winding proceeding around the armature4 ,illustration3 ,,fig4 #a1ebg4--;,diagram of six pole single phase revolving armature alternator1 with monotooth or concentrated whole coil winding4 ,for #c1jjj volts at #ijj revolutions per minute1 #abj inductors are required4 ,and in the case of a concentrated or monotooth winding they may be arranged in whole coils as above or in half coils 7hemitropic7 as in fig4 #a1ebh4 ,ques4 ,in what other way could the inductors be arranged in concentrated coils8 ,ans4 ,they could be grouped in three coils of #abj turns each1 as shown in fig4 #a1ebh4 ,when thus grouped the arrangement is called a hemitropic winding1 as previously explained4 ,illustration3 ,,fig4 #a1ebh4--;,diagram of six pole single phase alternator with concentrated half coil or hemitropic winding of same capacity as in fig4 #a1ebg4 ,there are an equal number of inductors1 but in this case arranged in three instead of six coils4 ,in this winding the direction of winding is alternately reversed so that the induced pressures do not oppose one another4 ,ques4 ,what is the advantage1 if any1 of a half coil winding8 ,ans4 ,in single phase machines a half coil winding is equivalent1 electrically1 to a monotooth winding1 and1 therefore1 is not of any particular advantage2 but in three phase machines1 it has a decided advantage1 as in such1 a concentrated winding yields a higher pressure than a distributed winding4 ,illustration3 ,,fig4 #a1ebi4--,two phase concentrated whole coil winding4 ,in this style winding the total number of slots is twice the number of poles1 or one slot per pole per phase4 ,it comprises two windings identical with fig4 #a1ebg1 being spaced #ij polar degrees as shown4 ,the two circuits are independent1 the windings terminating at the four collector rings4 ,illustration3 ,,fig4 #a1ecj4--,two phase winding in two slots per pole per phase4 ,this stamping distributes the coils of each phase into two sections1 as ,a and ,b4 ,the coils are of the whole type and with six poles the total number of slots is #d #f #bd1 uniformly spaced as shown4 ,two ,phase ,armature ,windings4--,this type of winding can be made from any single phase winding by providing another set of slots displaced along the surface of the armature to the extent of one-half the pole pitch1 placing therein a duplicate winding4 ,illustration3 ,,figs4 #a1eca and #a1ecb4--;,developed diagram of the single phase monotooth windings shown in figs4 #a1ebg and #a1ebh4 ,for instance3 ,if the six pole monotooth1 single phase winding1 shown in fig4 #a1ebg1 be thus duplicated1 the result will be the one slot two-phase winding shown in fig4 #a1ebi1 which will have twelve slots1 and will require four slip rings1 or two rings for each phase4 ,by connecting up the two windings in series1 the machines could be used as a single phase1 with an increase of voltage in the ratio of #a4da to #a4 ,illustration3 ,,fig4 #a1ecc4--,two phase winding in three slots per pole per phase4 ,the coils of each phase are of the partially distributed type1 each coil being made up of three sections as shown4 ,the direction of winding is alternately reversed4 ,illustration3 ,,fig4 #a1ecd4--,section of two phase winding showing shaping of the coil ends4 ,every other coil is flat1 while the alternates have their ends bent down as shown4 ,with respect to the shaping of the coil ends1 it is called a two range winding4 ,ques4 ,how must the coils be constructed for two phase windings8 ,ans4 ,they must be made of two different shapes1 one bent up out of the way of the other1 as in fig4 #a1ecd4 ,there are numerous kinds of two phase windings2 the coils may be concentrated or distributed1 half coil or whole coil1 etc4 ,fig4 #a1ecj shows a two phase winding with four slots per pole1 and fig4 #a1ecc one with six slots per pole4 ,illustration3 ,,fig4 #a1ece4--,section of ,triumph armature showing method of arranging the three phase winding4 ,three ,phase ,armature ,windings4--,on the same general principle applicable to two phase windings1 a three phase winding can be made from any single phase winding1 by placing three identical single phase windings spaced out successively along the surface of the armature at intervals equal to one-third and two-thirds1 respectively1 of the double pole pitch1 the unit in terms of which the spacing is expressed1 being that pitch1 which corresponds to one whole period4 ,illustration3 ,,fig4 #a1ecf4--,three phase winding with distributed coils--wound in four slots per pole per phase2 diagram showing placement of the coils4 ,illustration3 ,,fig4 #a1ecg4--,treatment of coil ends in two phase1 two range windings4 ,in this arrangement straight out 7,b7 and bent up 7,a7 coils are used which are placed on the armature as is clearly shown in the illustration4 ,illustration3 ,,fig4 #a1ech4--,three phase1 #aj pole1 #cj slot winding in two ranges4 ,in this winding perfect symmetry occurs after every four poles4 ,accordingly in the case of an odd number of pairs of pole1 one of the coils must necessarily be askew going from the inner to the outer range as at ,m4 ,each of the three individual windings must be concentrated into narrow belts so as to leave sufficient space for the other windings between them4 ,this limits the breadth or space occupied by the winding of any one phase to one-third of the pole pitch4 ,illustration3 ,,fig4 #a1eci4--,three phase #aj pole #cj slot winding in three ranges4 ,the coils of each phase are alike1 those of the ,a phase being all in the straight out range1 those in the ,b phase1 in a bent up range1 and those in the ,c phase in a bent down range4 ,this arrangement has the disadvantage1 that by reason of the third range1 the field magnet cannot be withdrawn4 ,this treatment of the coil ends is more clearly shown in fig4 #a1edj4 ,ques4 ,how are three phase coil ends treated8 ,ans4 ,they may be arranged in two ranges1 as in fig4 #a1ech1 or in three ranges1 as in fig4 #a1eci4 ,ques4 ,what kind of coil must be used for three phase windings in order that the ends may be arranged in only two ranges8 ,ans4 ,hemitropic or half coils2 that is1 the number of coil per phase must be equal to one-half the number of pole4 ,illustration3 ,,figs4 #a1edj and #a1eda4--,treatment of coil ends in three phase1 three range windings4 ,fig4 #a1edj1 inadmissible arrangement in which the field magnet cannot be withdrawn2 fig4 #a1eda1 admissible arrangement in which the armature segments can be divided4 ,this enables the top half of armature to be removed by disconnection without unwinding any coil4 ,grouping of ,phases4--,in the preceding diagrams1 the general arrangement of the coils on the armature surface are shown for the numerous classes of winding4 ,in polyphase alternators the separate windings of the various phases may be grouped in two ways3 #a4 ,star connection2 #b4 ,mesh connection4 ,illustration3 ,,fig4 #a1edb4--,three phase winding with half coils4 ,the advantage of employing half coils is that the ends may be arranged in two ranges as shown4 ,there is one slot per phase per pole1 that is1 total number of slots #c number of poles4 ,illustration3 ,,fig4 #a1edc4--,three phase winding with whole coils4 ,two sides of adjacent coils come in one slot4 ,number of coils per phase number of poles per phase4 ,total number of slots #c multiplied by number of poles per phase4 ,whole coils require the ends arranged in three ranges as indicated4 ,the coils are concentrated4 ,ques4 ,describe the two phase star connection4 ,ans4 ,in this method of grouping1 the middle points of each of the two phases are united to a common junction ,m1 and the four ends are brought out to four terminals a1 a'1 b1 b'1 as shown in fig4 #a1edd1 or in the case of revolving armatures1 to four slip rings4 ,illustration3 ,,fig4 #a1edd4--;,diagram of two phase star grouping4 ,ques4 ,what does this arrangement give8 ,ans4 ,it is practically equivalent to a four phase system4 ,illustration3 ,,fig4 #a1ede4--;,diagram of two phase mesh grouping4 ,ques4 ,how is the two phase mesh connection arranged8 ,ans4 ,in this style of grouping1 the two phases are divided into two parts1 and the four parts are connected up in cyclic order1 the end of one to the beginning of the next1 so as to form a square1 the four corners of which are connected to the four terminals a1 b1 a'1 b'1 as shown in fig4 #a1ede1 or in the case of revolving armatures1 to four slip rings4 ,ques4 ,describe a three phase star connection8 ,ans4 ,in three phase star grouping1 one end of each of the three circuits is brought to a common junction ,m1 usually insulated1 and the three other ends are connected to three terminals a1 b1 c1 as shown in fig4 #a1edf1 or in the case of revolving armatures to three slip rings4 ,illustration3 ,,fig4 #a1edf4--;,diagram of three phase star grouping1 commonly called ,y grouping owing to its resemblance of the letter ,y4 ,the current in each main is obviously equal to the current in each phase winding1 but the terminal pressure is the vector sum of the pressures in the component phase windings1 that is1 #c multiplied by the pressure in one phase4 ,ques4 ,what other name is given to this connection1 and why8 ,ans4 ,it is commonly called a ,y connection or grouping owing to the resemblance of its diagrammatic representation to the letter ,y4 ,illustration3 ,,fig4 #a1edg4--,radial diagram of three phase1 one slot winding with ,y connection4 ,illustration3 ,,fig4 #a1edh4--,radial diagram of three phase one slot winding with delta connection4 ,ques4 ,how is a three phase mesh connection arranged8 ,ans4 ,the three circuits are connected up together in the form of a triangle1 the three corners are connected to the three terminals1 a1 b1 c1 as shown in fig4 #a1edi1 or in the case of revolving armatures to three slip rings4 ,illustration3 ,,fig4 #a1edi4--;,diagram of three phase mesh grouping1 commonly called delta grouping owing to its resemblance to the ,greek letter 4 ,the voltage at the terminals is equal to the voltage in one phase1 and the current in each line is equal to the vector sum of the currents in two phases1 that is1 it is equal to #c multiplied by the current in one phase4 ,ques4 ,what other name is given to this style of connection1 and why8 ,ans4 ,it is commonly called a delta grouping on account of the resemblance of its diagrammatic representation to the ,greek letter 4 ,illustration3 ,,fig4 #a1eej4--,three phase winding with short coils4 ,the use of short coils as here shown1 in which the coil breadth pole pitch1 avoids the necessity of overlapping4 ,in polyphase working1 it is evident that by the use of four equal independent windings on the armature1 connected to eight terminals or slip rings1 a two phase alternator can be built to supply currents of equal voltage to four independent circuits4 ,likewise1 by the use of three equal independent windings1 connected to six terminals or slip rings1 a three phase alternator can be made to supply three independent circuits4 ,this is not the usual method employed in either case1 however1 as the star grouping or mesh grouping methods of connection not only gives the same results1 but also1 in star grouping1 a greater plurality of voltages for the same machine1 and a higher voltage between its main terminals4 ,radial diagrams of the arrangement and connections of ,y grouping of lap windings and wave windings for three phase alternators are shown by figs4 #a1eea and #a1eeb4 ,illustration3 ,,fig4 #a1eea4--,radial diagram of three phase lap winding with star connection4 ,ques4 ,in three phase star grouping1 what is the point where the phases join1 called8 ,ans4 ,the star point4 ,ques4 ,in a three phase star connected alternator what is the voltage between any two collector rings8 ,ans4 ,it is equal to the voltage generated per phase multiplied by #c or #a4gcb4 ,illustration3 ,,fig4 #a1eeb4--,radial diagram of three phase wave winding with star connection4 ,ques4 ,in a three phase star connected alternator what is the value of the current in each line8 ,ans4 ,the same as the current in each phase winding4 ,illustration3 ,,figs4 #a1eec and #a1eed4--;,gramme ring armatures showing three phase star and mesh connections1 respectively1 with direction of currents in the coils4 ,in the figures1 the coils ,a1 ,b1 ,c1 are spaced at equidistant positions on the ring core4 ,the arrow heads represent the directions of the induced pressures or currents for the position shown1 the rotation being clockwise4 ,in coil ,a the pressure is increasing1 in coil ,b it is diminishing1 but is in the same direction as in ,a1 whereas in coil ,c it is also diminishing1 but is in the opposite direction to what it is in coils ,a and ,b4 ,as the rings rotate the three coils have similar alternations of pressure induced in them1 but differ in phase4 ,if a1 b and c be joined to collector rings three phase currents can be supplied to the outer circuits4 ,in fig4 #a1eec at the instant represented a and b are giving their current to their lines1 while c is receiving from its line a current equal to the sum of a and b4 ,in fig4 #a1eed1 at the instant represented1 the currents sent out from a will be equal to the sum of the currents in x and y1 and intermediate between them in phase4 ,the current from b will be equal to the difference of the currents in z and y1 and of intermediate phase1 while similarly the current received by c will be equal to the sum of the currents in x and z4 ,ques4 ,what is the value of the total output in watts of a star connected alternator8 ,ans4 ,it is equal to the sum of the outputs of each of the three phases4 ,when working on a non-inductive load1 the total output of a star connected alternator is equal to #c multiplied by the product of the line current and line voltage4 ,ques4 ,what is the value of the line voltage in a three phase delta connected alternator8 ,ans4 ,it is equal to the voltage generated in each phase4 ,ques4 ,what is the value of the line current in a three phase delta connected alternator8 ,ans4 ,it is equal to the current in each phase multiplied by #c4 ,ques4 ,what is the total output of a three phase delta connected alternator working on a non-inductive load8 ,ans4 ,the total watts is equal to #c multiplied by the product of the line current and the line voltage4 ,illustration3 ,,figs4 #a1eee to #a1eeg4--,separate coils1 and section of ,allis-,chalmers alternator with coils in place4 ,numerous openings are provided in the frame through which air currents1 set up by the revolving field1 can pass freely and carry off heat4 ,shields are provided to protect the armature coils where they project beyond the core4 ,in assembling the core spacing segments are placed at intervals to form ventilating ducts4 ,after the coils have been covered with insulating materials and treated with insulating compound1 the parts that are to lie in the slots are pressed to exact size in steam heated moulds4 ,this runs the insulating material into all the small spaces in the coil so as to exclude moisture1 it also makes the coil structure firm and solid4 ,the projecting ends of the coils are heavily taped1 suitable supports being provided for the coil connections so that they cannot become displaced on account of stresses due to short circuits or other causes4 ,on high pressure machines the armature terminals are arranged so that it is impossible for an attendant to make accidental contact with them4 ,ques4 ,what are the features of the star connection8 ,ans4 ,it gives a higher line voltage than the delta connection for the same pressure generated per phase1 hence it is suited for machines of high voltage and moderate current4 ,the delta connection gives a lower line voltage than the star#e connection for the pressure generated per phase1 and cuts down the current in the inductors2 since the inductors1 on this account1 may be reduced in size1 the delta connection is adapted to machines of large current output4 #e ,,note4--,in the star connected armature the proper ends to connect to the common terminal or star point are determined as follows3 ,assume that the inductor opposite the middle of a pole is carrying the maximum current1 and mark its direction by an arrow4 ,then the current in the inductors on either side of and adjacent to it will be in the same direction4 ,as the maximum current must be coming from the common terminal1 the end toward which the arrow points must be connected to one of the rings1 while the other end is connected to the common terminal4 ,the current in the two adjacent inductors evidently must be flowing into the common terminal1 hence the ends toward which the arrows point must be connected to the common terminal1 while their other ends are connected to the remaining two rings4 ,illustration3 ,,fig4 #a1eeh4--;,diagram of ,westinghouse two phase composite wound alternator1 showing connections between two phase armature and a single phase rectified and composite field winding4 ,the arrangement makes use of a series transformer1 mounted on the spokes of the armature4 ,by means of this series transformer the voltage delivered to the rectifying commutator and the fields is much less than that generated by the machine4 ,the armature of this machine is of the closed coil single winding type1 all the armature inductors being connected with each other to form a closed circuit which resembles to a certain extent the ordinary drum winding of a multipolar direct current machine4 ,this winding is tapped out at two points per pole just as is the continuous winding of a two phase rotary converter1 these taps running to collector rings through which the currents are delivered to the outside circuits4 ,on account of this connection of both phases to one winding there is a definite voltage set up between the inductors of phase ,a1 and of phase ,b1 this voltage being shown by the figures given in the diagram4 ,the arrangement is adapted for two phase work by fitting the series transformer for the auxiliary field excitation with two primaries connected respectively in one leg of each of the two phases2 thus the transformer is excited by two currents normally period out of phase with each other4 ,the result upon the secondary is a combination of the effects of the two primary currents1 the voltage delivered by the secondary being intermediate in phase between those pressures which would be separately set up by the two primaries4 ,this combination effect is shown in the small diagram in the upper right hand corner of the illustration4 ,if ,,oa be the effect set up in the secondary of the series transformer by the primary current of phase ,a1 and ,,ob be the effect set up by the primary current of phase ,b1 ,,oc represents in magnitude and phase relation the resultant effect upon the secondary4 ,it is readily seen that this resultant is not equal to the arithmetical sum of the two components since1 to a certain extent1 they work at cross purposes4 ,however1 if either one of them increase the resultant effect increases1 although not in exact proportion4 ,if the load remain balanced1 the two components remaining equal to each other1 the resultant ,,oc varies in exact proportion to any changes in the components4 ,if the load become unbalanced1 the resultant swings around more nearly into phase with the larger load2 thus if ,,ob become greater1 ,,oa remaining the same1 ,,oc swings around1 becoming more nearly horizontal4 ,this requires a readjustment of the position of the brushes on the commutator to set them properly for minimum sparking1 an adjustment exactly similar to that required when the power factor of the load changes4 ,illustration3 ,,fig4 #a1eei4--;,diagram of ,westinghouse three phase composite wound alternator4 ,the armature inductors are of the closed coil or delta connected type1 but are tapped at three points per pair or poles to the three collector rings4 ,all three connections between the armature coils and the collector rings run through primary circuits of the series transformer within the armature1 these three primaries each giving their own effect upon the secondary4 ,since the resultant of three equal alternating electromotive forces #abj apart is zero1 so that some special arrangement must be adopted to make these electromotive forces act with instead of against each other4 ,the arrangement is a reversal of the connections of one of the primaries of the series transformer4 ,this is shown in the case of the lowest primary indicated in the diagram4 ,the combination of the effects of the three primaries is again indicated in the small vector diagram in the upper right hand corner4 ,here ,,oa is the effect of one primary1 ,,ob that of another of a period displaced from the former in phase1 and ,,oc that which the third would exert were it not reversed1 but the reversal brings the effect of this third coil into the phase relation ,,od1 so that the three are only #fj apart4 ,the combination of ,,oa and ,,ob is equal to ,,oc1 which combined again with ,,od gives a resultant effect1 ,,oe4 ,in this case1 as in the other1 the effect upon the series field does not remain exactly proportional to the load unless the latter is balanced2 in fact1 an increased current through the one leg represented by ,,od1 affects the series field as much as an equal increase in each of the other legs put together4 ,practically1 however1 any increase of the load--distributed as it must be in two legs at least--increases the field excitation so that proper regulation is secured4 ,ques4 ,how is the path and value of currents in a delta connected armature determined8 ,ans4 ,starting with the inductors of one phase opposite the middle of the poles1 assume the maximum current to be induced at this moment2 then but one-half of the same value of current will be induced at the same moment in the other two phases1 and its path and value will best be shown by aid of fig4 #a1efj1 in which ,x may be taken as the middle collector ring1 and the maximum current to be flowing from ,x toward ,z4 ,it will be seen that no current is coming in through the line ,y1 but part of the current at ,z will have been induced in the branches b and c4 ,illustration3 ,,fig4 #a1efj4--;,diagram showing determination of path and value of current flowing in delta connected armature4 ,ques4 ,since most three phase windings can be connected either ,y or delta1 what should be noted as to the effects produced8 ,ans4 ,with the same winding1 the delta connection will stand #a4gcb as much current as the ,y connection1 but will give only #a #a4gcb or 4#egg as much voltage4 ,illustration3 ,,fig4 #a1efa4--,triumph brushes and brush holder4 ,the holder is of the box type provided with an adjustable tension spring1 making the brushes self-feeding4 ,each holder is carried on insulated studs attached to a cast iron yoke which is mounted on the bearing4 ,illustration3 ,,fig4 #a1efb4--;,diagram of ,y connection with a common return wire4 ,when the three lines leading from a1 b and c are equal in resistance and reactance1 or in other words when the system is balanced1 the currents of the three phases are equal and are #abj apart in phase 7each current lagging behind its pressure by the same amount as the others7 and their sum is at each instant equal to zero4 ,in this case the resultant current being equal to zero there is no need of a common return wire4 ,however1 in some cases1 where power is distributed from transformers or three wire systems1 the different branches are liable to become unbalanced4 ,under such circumstances the common return wire is sometimes used1 being made large enough to take care of the maximum unbalancing that may occur in operation4 ,the return wire is used sometimes on alternators that furnish current mostly for lighting work4 ,chain or ,basket ,winding4--,one disadvantage in ordinary two-range windings is that two or three separate shapes of coil are required4 ,the cost of making1 winding1 and supplying spares would be less if one shape of coil could be made to do for all phases4 ,one way of accomplishing this is by the method of chain winding1 in which the two sides of each coil are made of different lengths1 as shown in fig4 #a1efc1 and bent so that they can lie behind one another4 ,illustration3 ,,fig4 #a1efc4--;,diagram showing chain winding4 ,in this method of winding the coils are all similar with long and short sides4 ,it obviates the extra cost of making coils of several different shapes4 ,the diagram represents a winding for one slot per pole per phase4 ,illustration3 ,,fig4 #a1efd4--;,general ,electric terminal board showing cables leading to three phase winding4 ,in the case of open slots the coils may be former wound and afterwards wedged into their places4 ,in chain winding the adjacent coils link one another as in a chain 7hence1 the name72 the winding is similar to a skew coil winding4 ,this plan of winding is supposed to have some advantage in keeping coils of different phases further separated than the two range plan4 ,illustration3 ,,fig4 #a1efe4--,section of armature winding of ,allis-,chalmers #ejj kw4 three phase water wheel alternator4 ,the coils are of the concentrated half type4 ,each coil is completely insulated before being placed on the core and no insulation is placed in the slot itself4 ,the ends of the coils where they project beyond the slots are heavily taped4 ,where necessary suitable supports are provided for the coil connections so that they cannot become displaced on account of stresses due to short circuits or other causes4 ,the winding is of the chain type4 ,this is shown by the way the coils are connected together at the right4 ,the armature terminals are either provided with insulated connectors or are led to a marble terminal board on which the terminals are so mounted and protected that it is impossible for an attendant to make accidental contact with them4 ,the position of the illustration would indicate a horizontal alternator but the machine is of the vertical type2 the lug on the right shows this1 being used for adjusting the alternator on the foundation4 ,skew ,coil ,winding4--,in this type of winding the object is to shape the coils so that all may be of one pattern4 ,this is accomplished by making the ends skew shape as shown in figs4 #a1eff to #a1efh4 ,illustration3 ,,figs4 #a1eff to #a1efh4--,views of a section of skew coil winding2 so called on account of the skew shape given to the coil ends in order that all the coils may be of one shape4 ,fed-in ,winding4--,this name is given to a type of winding possible with open or only partially closed slots1 in which coils previously formed are introduced1 only a few inductors at a time if necessary4 ,they are inserted into the slots from the top1 the slot being provided with a lining of horn fibre or other suitable material1 which is finally closed over and secured in place by means of a wedge1 or by some other suitable means4 ,an example of a fed-in winding is shown in figs4 #a1eff and #a1efh4 ,imbricated ,winding4--,this is a species of spiral coil winding in which the end connections are built up one above the other1 either in a radial1 or in a horizontal direction4 ,the winding is used especially on the armatures of turbine alternators and dynamos4 ,spiral ,winding4--,this is a winding in which spiral coils1 as shown in fig4 #a1efi1 are used4 ,the spiral form of coil is very extensively used for armature windings of alternators4 ,illustration3 ,,fig4 #a1efi4--;,diagram showing a spiral coil4 ,this type of coil is one in which each successive turn lies entirely within the previous turn1 starting with the outermost turn of the coil4 ,the successive turns of a spiral coil are thus not of the same size1 and are not overlapping as in a lap coil4 ,mummified ,winding4--,the word mummified as applied to a winding is used to express the treatment the coils of the winding receive in the making2 that is1 when a winding1 after being covered with tape or other absorbent material1 is saturated in an insulating compound and baked until the whole is solidified1 it is said to be mummified4 ,shuttle ,winding4--,this type of winding consists of a single coil having a large number of turns1 wound in two slots spaced #ahj apart4 ,it was originally used on ,siemens' armature and is now used on magnetos1 as shown in figs4 #a1dei to #a1dfa4 ,illustration3 ,,fig4 #a1egj4--;,frame and armature winding of ,westinghouse pedestal bearing alternator4 ,armature frames are of cast iron and ventilated4 ,interior transverse ribs strengthen the frame and support the core laminations4 ,the armature core is built up of annealed and japanned punched laminations4 ,armature slots are open4 ,armature coils are form wound1 impregnated1 and interchangeable2 they are held in place with fiber wedges4 ,ventilating spaces are provided at intervals in the armature core and also between all coil ends4 ,creeping ,winding4--,another species of winding1 known as a creeping winding is applicable to particular cases4 ,if three adjacent coils1 each having a pitch of #abj electrical degrees1 be set side by side1 they will occupy the same breadth as #d poles1 and1 by repetition1 will serve for any machine having a multiple of #d poles1 but cannot be used for machines with #f1 #aj or #ad poles4 ,fig4 #a1ega shows this example4 ,illustration3 ,,figs4 #a1ega and #a1egb4--;,diagram of creeping windings4 ,fig4 #a1ega1 three coils subtending four poles2 fig4 #a1egb1 nine coils subtending eight poles4 ,in the same way #i coils1 each of #afj electrical degrees1 will occupy the same angular breadth as #h poles4 ,further1 #i coils of #bjj electrical degrees will occupy the same angular breadth as #aj poles4 ,now of these #i coils1 any three contiguous ones are nearly in phase1 if wound alternately clockwise and counter-clockwise4 ,for the #h pole machine1 the phase difference between adjacent coils is #bj degrees4 ,for the #aj pole machine1 the phase difference is also #bj degrees4 ,the cosine of #bj degrees is 4#icig1 consequently1 if #c adjacent coils be united in series1 their joint pressure will be #b4hig multiplied by that of the middle one of the three4 ,the #i coils may therefore be joined up in three groups of #c adjacent coils1 for the three phases4 ,by repetition1 the same grouping will suit for any machine having a multiple of #h or of #aj poles4 ,these two cases are illustrated in figs4 #a1egb and #a1egc4 ,in the figures1 the coils are represented as occupying two slots each1 but they might be further distributed4 ,illustration3 ,,fig4 #a1egc4--;,developed diagram of creeping winding3 nine coils subtending ten poles4 ,illustration3 ,,fig4 #a1egd4--,triumph pedestal and brush rigging for large revolving field alternators4 ,carbon brushes are used1 carried in box type brush holders4 ,the stand or pedestal here shown is the kind used with the engine and fly wheel types of alternator4 ,the brush studs are mounted on the stand in such a manner that the brushes are easily accessible4 ,the latter carry only the low voltage direct current necessary for exciting the field4 ,turbine ,alternator ,winding4--,for the reason that steam turbines run at so much higher speed than steam engines1 the construction of armatures and windings for alternators intended to be direct connected to turbines must be quite different from those driven by steam engines4 ,accordingly1 in order that the frequency be not too high1 turbine driven alternators must have very few poles--usually two or four1 but rarely six4 ,illustration3 ,,figs4 #a1ege and #a1egf4--,westinghouse turbine alternator armature construction4 ,fig4 #a1ege4 ,view showing dovetail grooves in armature casting2 fig4 #a1egf1 lamin assembled in dovetail grooves of armature casting4 ,the following table will show the relation between the revolutions and frequencies for the numbers of poles just designated4 ,,table ,,of ,,frequency ,,and ,,revolutions -------------------------------------- ,,revolutions ,frequency -------------------------- #b pole #d pole #f pole ----------------------------------- #be #a1ejj #gej #ejj #fj #c1fjj #a1hjj #a1bjj #ajj #f1jjj #c1jjj #b1jjj ----------------------------------- ,illustration3 ,,fig4 #a1egg4--;,armature of ,westinghouse turbine alternator with end bells removed showing method of bracing the coil ends4 ,illustration3 ,,fig4 #a1egh4--,stationary armature of ,westinghouse turbine alternator with part of the winding in place4 ,because of the small number of coils in a turbine alternator as compared with a slow speed machine of the same kva4 rating1 each coil carries a great amount of power on large load1 particularly at times of short circuits or grounds on the external circuit4 ,the throw of the coils is large1 leaving a considerable part of the winding in the end turns unsupported by the armature core4 ,for these reasons great stresses1 which are dangerous1 if effective means be not adopted to withstand them1 may exist between the coils4 ,the inductors are of such cross section that they can be made rigid and insulated satisfactorily4 ,the end turns are given a fan like form as shown1 affording ventilation and effective bracing as shown in fig4 #a1egg4 ,cord lashings are1 except in the smallest frames1 used only for holding in the small spacing blocks between the coils4 ,they are not depended on to support the coils4 ,malleable iron braces1 hard maple blocks1 and brass or steel bolts with brass washers are used to withstand the mechanical stresses imposed on the armature coils by external short circuits4 ,from the table1 it is evident that a large number of poles is not permissible1 considering the high speed at which the turbine must be run4 ,illustration3 ,,fig4 #a1egi4--,two pole radial slot field4 ,radial slot fields are used on very small and very large alternators4 ,the field diameters are so small that the end turns of the winding can be effectively bound into place1 such binding being necessary with a radial slot machine4 ,the shaft and disc are a one piece forging of steel4 ,ques4 ,how is the high voltage obtained with so few poles8 ,ans4 ,there must be either numerous inductors per slot or numerous slots per pole4 ,illustration3 ,,figs4 #a1ehj to #a1ehb4--,westinghouse two pole parallel slot field with ends removed showing construction4 ,the parallel slot design of field construction is used in ,westinghouse machines up to #aj1jjj kva4 capacity4 ,in fig4 #a1eha1 the large holes at the end near the circumference of the cylinder are for the accommodation of the bolts that hold the bronze end discs and stub shafts4 ,in winding1 the cylinder is mounted on a horizontal turntable that rotates in a horizontal plane4 ,the copper strap field coil winding is wound turn by turn under pressure and strip insulation is wound in between4 ,when completed the turns are held rigidly in position with heavy brass wedges4 ,an end disc made of bronze holds the stub shaft and is bolted to each end of the steel center4 ,when the leads are attached to the collector rings the field is complete4 ,ques4 ,what form of armature is generally used8 ,ans4 ,a stationary armature4 ,ques4 ,what difficulty is experienced with revolving armatures8 ,ans4 ,the centrifugal force being considerable on account of the high speed1 requires specially strong construction to resist it1 consequently closed or nearly closed slots must be used4 ,ques4 ,how is the design of the rotor modified so as to reduce the centrifugal force8 ,ans4 ,it is made long and of small diameter4 ,some examples of revolving fields are shown in figs4 #a1egi to #a1ehd4 ,figs4 #a1egg and #a1egh show some construction details of a stationary armature of turbine alternator4 ,illustration3 ,,fig4 #a1ehc4--,westinghouse two pole parallel slot turbine alternator field4 ,illustration3 ,,fig4 #a1ehd4--,westinghouse four pole parallel slot turbine alternator field4 ,,hawkins ,,practical ,,library ,,of ,,electricity ,,in ,,handy ,,pocket ,,form ,,price #a ,,each 99 99 99 99 99 ,they are not only the best1 but the cheapest work published on ,electricity4 ,each number being complete in itself4 ,separate numbers sent postpaid to any address on receipt of price4 ,they are guaranteed in every way or your money will be returned4 ,complete catalog of series will be mailed free on request4 ,,electrical ,,guide1 ,,no4 #a ,containing the principles of ,elementary ,electricity1 ,magnetism1 ,induction1 ,experiments1 ,dynamos1 ,electric ,machinery4 ,,electrical ,,guide1 ,,no4 #b ,the construction of ,dynamos1 ,motors1 ,armatures1 ,armature ,windings1 ,installing of ,dynamos4 ,,electrical ,,guide1 ,,no4 #c ,electrical ,instruments1 ,testing1 ,practical ,management of ,dynamos and ,motors4 ,,electrical ,,guide1 ,,no4 #d ,distribution ,systems1 ,wiring1 ,wiring ,diagrams1 ,sign ,flashers1 ,storage ,batteries4 ,,electrical ,,guide1 ,,no4 #e ,principles of ,alternating ,currents and ,alternators4 ,,electrical ,,guide1 ,,no4 #f ,alternating ,current ,motors1 ,transformers1 ,converters1 ,rectifiers4 ,,electrical ,,guide1 ,,no4 #g ,alternating ,current ,systems1 ,circuit ,breakers1 ,measuring ,instruments4 ,,electrical ,,guide1 ,,no4 #h ,alternating ,current ,switch ,boards1 ,wiring1 ,power ,stations1 ,installation and ,operation4 ,,electrical ,,guide1 ,,no4 #i ,telephone1 ,telegraph1 ,wireless1 ,bells1 ,lighting1 ,railways4 ,,electrical ,,guide1 ,,no4 #aj ,modern ,practical ,applications of ,electricity and ,ready ,reference ,index of the #aj ,numbers4 ,theo4 ,audel ,co41 ,publishers4 #gb ,,fifth ,,avenue1 ,,new ,,york ,,transcriber',s ,,notes ,silently corrected simple spelling1 grammar1 and typographical errors4 ,retained anachronistic and non-standard spellings as printed4 ,enclosed italics markup in underscores4 ,enclosed bold markup in tildes4