,,! ,,?\ght ,,is ,,9 ,,! ,,"q ,,! ,,in=mation ,,is ,,9 ,,! ,,answ] ,illu/ration3 ,,hawk9s ,,electrical ,,guide ,,numb] ,,five ,,que/ions ,,answ]s ,,illu/rations ,a ,,progressive ,,c\rse ,,( ,,/udy ,,= ,,eng9e]s1 ,,electricians1 ,,/ud5ts ,,& ,,^? ,,desir+ ,,to ,,acquire ,a ,,work+ ,,k ,,( ,,electricity ,,& ,,its ,,applications ,a ,,practical ,,treatise by ,,hawk9s ,,& ,,/aff ,illu/ration3 ,,!o4 ,,audel ,,co4 #gb ,,fif? ,,ave4 ,,new ,,york4 ,,copyright$1 #aiad1 ,,by ,,!o4 ,,audel ,,co41 ,,new ,,york4 ,pr9t$ 9 ! ,unit$ ,/ates4 ,,table ,,( ,,cont5ts ,,guide ,,no4 #e4 ,,alt]nat+ ,,curr5ts #iig to #a1jff ,! ^w alt]nat+--advantages ( alt]nat+ curr5t--direct curr5t app>atus2 alt]nat+ curr5t app>atus--disadvantages ( alt]nat+ curr5t--alt]nat+ curr5t pr9ciples--! s9e--application & con/ruction ( ! s9e curve--illu/rat$ def9itions3 cycle1 alt]nation1 amplitude1 p]iod1 p]iodicity1 frequ5cy--comm]cial frequ5cies--advantages ( l[ frequ5cy--phase--phase diff]5ce--phase displacem5t--syn*ronism--9 phase--curves illu/rat+ 9 phase & out ( phase--illu/rat$ def9itions3 9 phase2 9 quadrature1 curr5t lead+2 9 quadrature1 curr5t lagg+2 9 opposition--maximum volts & amp]es--av]age volts & amp]es--elem5t>y alt]nator develop+ "o av]age volt--virtual volts & amp]es--effective volts & amp]es--relation betwe5 %ape ( wave & =m factor--wave =m--oscillograph wave =m records--:at det]m9es wave =m--effect ( "o coil p] phase p] pole--s+le phase curr5t2 hydraulic analogy--two phase curr5t2 hydraulic analogy--two phase curr5t di/ribution--?ree phase curr5t2 hydraulic analogy2 di/ribution--inductance--! h5ry--inductive & non-inductive coils--hydraulic analogy ( inductance--inductance coil calculations--ohmic value ( inductance--capacity3 hydraulic analogy--! f>ad--specific inductive capacity--cond5s] connections--ohmic value ( capacity--lag & lead--me*anical analogy ( lag--lag measurem5t--/eam eng9e analogy ( curr5t fl[ at z]o pressure--reactance--examples--*ok+ coil--imp$ance curve--resonance--critical frequ5cy--sk9 effect4 ,,alt]nat+ ,,curr5t ,,diagrams #a1jfg to #a1ajj ,def9itions3 impress$ pressure1 active pressure1 self-induction pressure1 rev]se pressure ( self-induction--rate ( *ange 9 curr5t /r5g?--prop]ties ( "r angle triangles--equations ( ! "r triangle--repres5tation ( =ces by wires--p>allelogram ( =ces2 ! resultant--circuits conta9+ resi/ance & inductance--graphical me?od ( obta9+ ! impress$ pressure--equations = ohmic drop & reactance drop--examples--diagram = imp$ance1 angle ( lag1 etc4--circuits conta9+ resi/ance & capacity--capacity 9 s]ies1 & 9 p>allel--am\nt ( lead--action ( cond5s]--! cond5s] pressure--capacity pressure--equation = imp$ance--- examples & diagrams--circuits conta9+ resi/ance1 inductance1 & capacity--imp$ance equation--examples & diagrams--equation = impress$ pressure--examples & diagrams4 ,,! ,,p[] ,,factor #a1aja to #a1abd ,def9ition ( p[] factor--true watts--- app>5t watts--f]ry boat analogy ( p[] factor--limits ( p[] factor--effect ( lag or lead--h[ to obta9 ! p[] curve--nature ( ! p[] curve--syn*ronism ( curr5t & pressure2 p[] factor unity--case ( syn*ronism ( curr5t & pressure ) p[] factor less ?an unity--/eam eng9e analogy ( p[] factor--wattless curr5t2 p[] factor z]o--examples ( phase diff]5ce ne>ly #ij degrees--me*anical analogy ( wattless curr5t--:y ! p[] factor is equal to cos --graphical me?od ( obta9+ ! active compon5t--examples & diagrams--effect ( capacity--diagrams illu/rat+ :y ! p[] factor is unity :5 !re is no resultant reactance 9 ! circuit--usual value ( p[] factor--p[] factor te/--h[ alt]nators are rat$2 kva4--curves illu/rat+ p[] factor--h[ to keep ! p[] factor high--:y p[] factor is important 9 /ation op]ation--wattmet] me?od ( ?ree phase p[] measurem5t4 ,,alt]nators #a1abe to #a1ahf ,uses ( alt]nators--classes ( alt]nator--s+le phase alt]nators2 ess5tial features2 wid? ( armature coils--elem5t>y s+le phase alt]nator--polyphase alt]nators--uses = two & ?ree phase curr5t--elem5t>y ?ree phase alt]nator--/>t+ difficulty ) s+le phase motors--six & twelve phase w9d+s--belt or *a9 driv5 alt]nators--sub-base & rat*et device = tight5+ ! belt--horse p[] transmitt$ by belts--be/ spe$s = belts--advantages ( *a9 drive2 objections--direct connect$ alt]nator--direct connect$ & direct c\pl$ units--revolv+ armature alt]nators2 _! uses--revolv+ field alt]nators--m>9e view %[+ t motion is purely a relative matt]--ess5tial p>ts ( revolv+ field alt]nator--! t]ms /ator & rotor--inductor alt]nators3 classes1 use1 defects--hunt+ or surg+ 9 alt]nators--amortisseur w9d+s--monocyclic alt]nators--diagram ( connections--teas] coil--armature reaction--di/ortion ( field--/r5g!n+ & weak5+ effects--sup]positions ( fields--?ree phase reactions--magnetic leakage--field excitation ( alt]nators--self-excit$ alt]nator--direct connect$ excit]--ge> driv5 excit]s--sl[ spe$ alt]nators--fly :eel alt]nators--high spe$ alt]nators--wat] :eel alt]nators--con/ruction ( rotor--turb9e driv5 alt]nators--con/ruction--/ep be>+--alt]nators ( exceptional "*--asyn*ron\s alt]nators--image curr5t alt]nators--extra high frequ5cy alt]nators--self-excit+ image curr5t alt]nators4 ,,con/ruction ,,( ,,alt]nators #a1ahg to #a1bff ,ess5tial p>ts ( an alt]nator--field magnets--me?ods ( excitation3 self-excit$1 sep>ately excit$1 compositely excit$--magneto--con/ruction ( /ation>y magnets--revolv+ field--slip r+s--spid] = l>ge alt]nator--provision = %ift+ armature to give access to field--armatures--core con/ruction--advantages ( slott$ core armatures--armature w9d+s--classification3 revolv+ & /ation>y w9d+s--half coil & :ole coil w9d+s--conc5trat$ or uni-coil w9d+2 features2 wave=m--di/ribut$ or multi-coil w9d+s3 bread? ( coil1 p>tial & fully di/ribut$ coils--! ,kapp coeffici5t--g5]al equation = voltage--wire1 /rap1 & b> w9d+s--condition1 gov]n+ type ( inductor--coil cov]+--s+le & d\ble lay] multi-wire inductors & me?ods ( plac+ !m on ! core--insulation--core /amp+--s+le & multi-slot w9d+s--- arrangem5t 9 slot ( two lay] b> w9d+--table ( relative effectiv5ess ( w9d+s--s+le phase w9d+s--advantage ( half coil w9d+--two phase w9d+s--%ape ( coil ends--?ree phase w9d+s--%ape ( coil ends--k9d ( coil us$ ) ?ree phase w9d+s--gr\p+ ( phases--two phase /> connection--two phase me% connection--?ree phase /> connection--w9d+ diagrams ) /> & connections--?ree phase connection--?ree phase w9d+ ) %ort coils--?ree phase lap w9d+ /> connection--?ree phase wave w9d+ /> connection--output ( /> & delta connect$ alt]nators--gramme r+ armatures %[+ ?ree phase /> & me% connections ) direction ( curr5ts 9 ! coils--features ( /> connection--*>act]i/ics ( delta connection--prop] ends to connect to /> po9t--det]m9ation ( pa? & value ( curr5ts 9 delta connection--po9ts to be not$ ) ,y connection--diagram ( ,y connection ) return wire--*a9 or basket w9d+--skew w9d+--f$-9 w9d+--imbricat$ w9d+--spiral w9d+--mummifi$ w9d+--%uttle w9d+--creep+ w9d+--turb9e alt]nator w9d+3 h[ ! high voltage is obta9$ ) s few poles2 table ( frequ5cy & revolutions--turb9e alt]nator con/ruction--=m ( armature g5]ally us$--two pole radial slot field--p>allel slot field--difficulty exp]i5c$ ) revolv+ armatures--h[ ! field design is modifi$ to r$uce c5trifugal =ce--examples ( revolv+ fields4 ,,*apt] ,,xlvi ,,alt]nat+ ,,curr5ts ,! ^w alt]nat+ is us$ ) a l>ge numb] ( electrical & magnetic quantities to d5ote t _! magnitudes v>y cont9u\sly1 pass+ repeat$ly ?r\gh a def9ite cycle ( values 9 a def9ite int]val ( "t4 ,z appli$ to ! fl[ ( electricity1 an alt]nat+ curr5t may be def9$ z3 ,a curr5t :i* rev]ses its direction 9 a p]iodic mann]1 ris+ f z]o to maximum /r5g?1 return+ to z]o1 & !n go+ ?r\gh simil> v>iations 9 /r5g? 9 ! opposite direction2 ^! *anges comprise ! cycle :i* is repeat$ ) great rapidity4 ,! prop]ties ( alt]nat+ curr5ts are m complex ?an ^? ( cont9u\s curr5ts1 & _! behavior m difficult to pr$ict4 ,?is arises f ! fact t ! magnetic effects are ( f> m importance ?an ^? ( /eady curr5ts4 ,) ! latt] ! magnetic effect is con/ant1 & has no reactive influ5ce on ! curr5t :5 ! latt] is once e/abli%$4 ,! l9es ( =ce1 h[ev]1 produc$ by alt]nat+ curr5ts are *ang+ z rapidly z ! curr5t itself1 & !y ?us induce electric pressures 9 neighbor+ circuits1 & ev5 9 adjac5t p>ts ( ! same circuit4 ,?is inductive influ5ce 9 alt]nat+ curr5ts r5d]s _! action v diff]5t f t ( cont9u\s curr5t4 ,ques4 ,:at are ! advantages ( alt]nat+ curr5t ov] direct curr5t8 ,ans4 ,! r$uc$ co/ ( transmission by use ( high voltages & trans=m]s1 great] simplicity ( g5]ators & motors1 facility ( trans=m+ f "o voltage to ano!r 7ei!r high] or l[]7 = diff]5t purposes4 ,illu/ration3 ,,figs4 #a1bjf to #a1bab4--;,app>atus :i* op]ates successfully on a direct curr5t circuit4 ,! direct curr5t w op]ate inc&esc5t lamps1 arc lamps1 electric heat+ app>atus1 electro-plat+ & typ+ ba?1 direct curr5t motors2 *>ge /orage batt]ies1 produce electro-*emical action4 ,x w fl[ ?r\gh a /raight wire or j z freely ?r\gh ! same wire :5 w\nd ov] an iron b>4 ,illu/ration3 ,,figs4 #a1bac to #a1bag4--;,app>atus :i* op]ates successfully on an alt]nat+ circuit4 ,! alt]nat+ curr5t w op]ate inc&esc5t lamps1 arc lamps1 electric heat+ app>atus1 alt]nat+ curr5t motors4 ,x w fl[ ?r\gh a /raight wire ) slightly increas$ ret>d+ effect1 b if ! wire be w\nd on an iron b> its /r5g? is greatly r$uc$4 ,! size ( wire ne$$ to transmit a giv5 am\nt ( electrical en]gy 7watts7 ) a giv5 p]c5tage ( drop1 be+ inv]sely proportional to ! squ>e ( ! voltage employ$1 ! great sav+ 9 copp] by ! use ( alt]nat+ curr5t at high pressure mu/ be app>5t4 ,?is advantage c be realiz$ ei!r by a sav+ 9 ! weight ( wire requir$1 or by transmitt+ ! curr5t to a great] di/ance ) ! same weight ( copp]4 ,9 alt]nat+ curr5t electric light+1 ! prim>y voltage is usually at lea/ #a1jjj & (t5 #b1jjj to #aj1jjj volts4 ,ques4 ,:y is alt]nat+ curr5t us$ in/ead ( direct curr5t on con/ant pressure light+ circuits8 ,ans4 ,x is due to ! great] ease ) :i* ! curr5t c be trans=m$ f high] to l[] pressures4 ,ques4 ,h[ is ?is accompli%$8 ,ans4 ,by means ( simple trans=m]s1 consi/+ m]ely ( two or m coils ( wire w\nd ^u an iron core4 ,s9ce !re are no mov+ p>ts1 ! att5tion requir$ & ! likelihood ( ! app>atus gett+ out ( ord] are small4 ,! app>atus necess>y = direct curr5t consi/s ( a motor dynamo set :i* is consid]ably m co/ly ?an a trans=m] & n s effici5t4 ,ques4 ,:at are "s ( ! disadvantages ( alt]nat+ curr5t8 ,ans4 ,! high pressure at :i* x is us$ r5d]s x dang]\s1 & requires m effici5t insulation2 alt]nat+ curr5t _c be us$ = su* purposes z electro-plat+1 *>g+ /orage batt]ies1 etc4 ,illu/ration3 ,,fig4 #a1bah4--;,application & con/ruction ( ! s9e curve4 ,! s9e curve is a wavelike curve us$ to repres5t ! *anges 9 /r5g? & direction ( an alt]nat+ curr5t4 ,at ! left ( ! figure is %[n an elem5t>y alt]nator1 consi/+ ( a loop ( wire ,,abcd1 ^: ends are atta*$ to ! r+ ,f1 & %aft ,g1 be+ arrang$ to revolve 9 a uni=m magnetic field1 z indicat$ by ! v]tical arr[s repres5t+ magnetic l9es at equidi/ances4 ,! alt]nat+ curr5t induc$ 9 ! loop is c>ri$ to ! ext]nal circuit ?r\gh ! bru%es ,m & ,s4 ,! loop1 z %[n1 is 9 its horizontal position at "r angles to ! magnetic field4 ,! dott$ circle indicates ! circul> pa? describ$ by ,,ab or ,,cd dur+ ! revolution ( ! loop4 ,n[1 z ! loop rotates1 ! induc$ electric pressure w v>y 9 su* a mann] t its int5sity at any po9t ( ! rotation is proportional to ! s9e ( ! angle correspond+ to t po9t4 ,h5ce1 on ! horizontal l9e :i* passes ?r\gh ! c5t] ( ! dott$ circle1 take any l5g? z #jh1 & divide into any numb] ( equal p>ts repres5t+ fractions ( a revolution1 z #j1 #ij1 #ahj1 etc4 ,erect p]p5dicul>s at ^! po9ts1 & f ! correspond+ po9ts on ! dott$ circle project l9es 7p>allel to #jh7 to ! p]p5dicul>s2 ^! int]sections give po9ts1 on ! s9e curve1 = in/ance1 ?r\gh #b at ! #ij po9t ( ! revolution ( ! loop1 & project+ ov] to ! correspond+ p]p5dicul> gives #b'b1 ^: l5g? is proportional to ! electric pressure at t po9t4 ,9 l mann] o!r po9ts are obta9$1 & ! curv$ l9e ?r\gh !m w repres5t ! v>iation 9 ! electric pressure = all po9ts ( ! revolution4 ,at #ij ! pressure is at a maximum1 h5ce by us+ a pressure scale su* t ! l5g? ( ! p]p5dicul> #b'b = #ij w measure ! maximum pressure1 ! l5g? ( ! p]p5dicul> at any o!r po9t w repres5t ! actual pressure at t po9t4 ,! curve lies above ! horizontal axis dur+ ! fir/ half ( ! revolution & bel[ x dur+ ! second half1 :i* indicates t ! curr5t fl[s 9 "o direction = a half revolution1 & 9 ! opposite direction dur+ ! rema9d] ( ! revolution4 ,alt]nat+ ,curr5t ,pr9ciples4--,9 ! op]ation ( a direct curr5t g5]ator or dynamo1 z expla9$ 9 ,*apt] ,,xiii1 alt]nat+ curr5ts are g5]at$ 9 ! armature w9d+ & are *ang$ into direct curr5t by ! action ( ! commutator4 ,x 0 !re=e necess>y 9 t *apt]1 9 pres5t+ ! basic pr9ciples ( ! dynamo1 to expla9 ! g5]ation ( alt]nat+ curr5ts at l5g?1 & ! graphic me?od ( repres5t+ ! alt]nat+ curr5t cycle by ! s9e curve4 ,9 ord] to avoid unnecess>y repetition1 ! read] %\ld c>efully review ! above m5tion$ *apt] be=e cont9u+ fur!r4 ,! diagram fig4 #afh1 %[+ ! con/ruction & application ( ! s9e curve to ! alt]nat+ curr5t1 is h[ev] = conv5i5ce "h %[n enl>g$ 7fig4 #a1bah74 ,9 ! diagram ! v>i\s alt]nat+ curr5t t]ms are graphically def9$4 ,illu/ration3 ,,fig4 #a1bai--;,diagram illu/rat+ ! s9e ( an angle4 ,9 ord] to und]/& ! s9e curve1 x is necess>y to "k ! mean+ ( ! s9e ( an angle4 ,?is is def9$ z ! ratio ( ! p]p5dicul> let fall f any po9t 9 "o side ( ! angle to ! o!r side divid$ by ! hypot5use ( ! triangle ?us =m$4 ,= in/ance1 9 ! diagram1 let ,,ad & ,,ae be ! two sides ( ! angle 1 & ,,de a p]p5dicul> let fall f any po9t ,d ( ! side ,,ad to ! o!r side ,,ae4 ,!n1 ! s9e ( ! angle 7writt5 s9 7 ,,de ,,ad4 ,x is evid5t t if ! p]p5dicul> be let fall at a unit's di/ance f ! apex ,a1 z at ,b1 ,,bc ,,bc ,s9 -- -- ,,bc ,,ab #a ,?is l9e ,,bc is call$ ! natural s9e ( ! angle1 & its values = diff]5t angles are giv5 9 ! table on page #dea4 ,illu/ration3 ,,fig4 #a1bbj4--;,diagram illu/rat+ ! equation ( ! s9e curve3 y s9 4 y is any ord9ate1 & 1 ! angle :i* ! coil makes ) ! horizontal l9e1 correspond+ to ! p>ticul> value ( y tak54 ,! alt]nat+ curr5t1 z has be5 expla9$1 rises f z]o to a maximum1 falls to z]o1 rev]ses its direction1 atta9s a maximum 9 ! new direction1 & aga9 returns to z]o2 ?is comprises ! cycle4 ,?is s]ies ( *anges c be/ be repres5t$ by a curve1 ^: absciss repres5t "t1 or degrees ( armature rotation1 & ^: ord9ates1 ei!r curr5t or pressure4 ,! curve usually *os5 = ?is purpose is ! s9e curve1 z %[n 9 fig4 #a1bah1 because x closely agrees ) t giv5 by mo/ alt]nators4 ,! equation ( ! s9e curve is y s9 9 :i* y is any ord9ate1 & 1 ! angle ( ! correspond+ position ( ! coil 9 :i* ! curr5t is be+ g5]at$ z illu/rat$ 9 fig4 #a1bbj4 ,ques4 ,:at is an alt]nation8 ,ans4 ,! *anges :i* ! curr5t und]goes 9 ris+ f z]o to maximum pressure & return+ back to z]o2 t is1 a s+le positive or negative wave or half p]iod1 z %[n 9 fig4 #a1bba4 ,illu/ration3 ,,fig4 #a1bba4--;,diagram %[+ "o alt]nation ( ! curr5t 9 :i* ! latt] v>ies f z]o to maximum & back to z]o :ile ! g5]at+ loop ,,abcd makes "o half revolution4 ,ques4 ,:at is ! amplitude ( ! curr5t8 ,ans4 ,! greate/ value ( ! curr5t /r5g? atta9$ dur+ ! cycle4 ,! =ego+ def9itions are also illu/rat$ 9 fig4 #a1bah4 ,illu/ration3 ,,fig4 #a1bbb4--;,diagram illu/rat+ amplitude ( ! curr5t4 ,! curr5t rea*es its amplitude or maximum value 9 "o qu>t] p]iod f its po9t ( z]o value1 z1 = in/ance1 :ile ! g5]at+ loop moves f position ,,abcd to ,a',b',c',d'4 ,at ?ree-qu>t] revolution1 ! curr5t rea*es its maximum value 9 ! opposite direction4 ,ques4 ,def9e ! t]m p]iod4 ,ans4 ,?is is ! "t ( "o cycle ( ! alt]nat+ curr5t4 ,ques4 ,:at is p]iodicity8 ,ans4 ,a t]m sometimes us$ = frequ5cy4 ,frequ5cy4--,if a sl[ly v>y+ alt]nat+ curr5t be pass$ ?r\gh an inc&esc5t lamp1 ! filam5t w be se5 to v>y 9 brightness1 foll[+ ! *ange ( curr5t /r5g?4 ,if1 h[ev]1 ! alt]nations take place m rapidly ?an ab\t #ej to #fj p] second1 ! eye _c foll[ ! v>iations & ! lamp appe>s to burn /eadily4 ,h5ce x is important to consid] ! rate at :i* ! alt]nations take place1 or z x is call$1 ! frequ5cy1 :i* is def9$ z3 ! numb] ( cycles p] second4 ,illu/ration3 ,,fig4 #a1bbc4--;,diagram ( alt]nator & eng9e1 illu/rat+ frequ5cy4 ,! frequ5cy or cycles p] second is equal to ! revolution ( armature p] second multipli$ by "o-half ! numb] ( poles p] phase4 ,9 ! figure ! armature makes #f revolutions to "o ( ! eng9e2 "o-half ! numb] ( poles #h #b #d1 h5ce frequ5cy 7#aej #d #f7 #fj #fj4 ,! expression 9 ! p>5!sis gives ! cycles p] m9ute1 & divid+ by #fj1 ! cycles p] second4 ,9 a two pole ma*9e1 ! frequ5cy is ! same z ! numb] ( revolutions p] second1 b 9 multipol> ma*9es1 x is great] 9 proportion to ! numb] ( pairs ( poles p] phase4 ,?us1 9 an #h pole ma*9e1 !re w be f\r cycles p] revolution4 ,if ! spe$ be #ijj revolutions p] m9ute1 ! frequ5cy is #h #ijj - --- #fj #b #fj ,! symbol is read cycles p] second4 ,ques4 ,:at frequ5cies are us$ 9 comm]cial ma*9es8 ,ans4 ,! two /&>d frequ5cies are #be & #fj cycles4 ,illu/ration3 ,,fig4 #a1bbd--;,diagram answ]+ ! "q3 ,:y are alt]nators always built multipol>8 ,!y are made multipol> because x is desirable t ! frequ5cy be high4 ,x is evid5t f ! figure t to obta9 high frequ5cy w\ld require too _m revolutions ( ! armature ( a bipol> ma*9e = me*anical safety--especially 9 l>ge alt]nators4 ,moreov] a d\ble r$uction ge> 9 mo/ cases w\ld be necess>y1 add+ complication to ! drive4 ,comp>+ ! above illu/ration ) fig4 #a1bbc1 %[s pla9ly ! reason = multipol> con/ruction4 ,ques4 ,= :at s]vice are ^! frequ5cies adapt$8 ,ans4 ,! #be cycle frequ5cy is us$ = conv]sion to direct curr5t1 = alt]nat+ curr5t railways1 & = ma*9es ( l>ge size2 ! #fj cycle frequ5cy is us$ = g5]al di/ribution = light+ & p[]4 ,! frequ5cy ( #dj cycles1 :i* once 0 introduc$ z a compromise betwe5 #be & #fj has be5 f\nd n desirable1 z x is some:at l[ = g5]al di/ribution1 & high] ?an desirable = conv]sion to direct curr5t4 ,illu/ration3 ,,fig4 #a1bbe4--;,diagram illu/rat+ phase4 ,9 wave1 vibratory1 & simple h>monic motion1 phase may be def9$ z3 ! portion ( "o complete vibration1 measur$ ei!r 9 angle or 9 "t1 t any mov+ po9t has execut$4 ,ques4 ,:at are ! advantages ( l[ frequ5cy8 ,ans4 ,! numb] ( revolutions ( ! rotor is correspond+ly l[2 arc lamps c be m readily op]at$2 bett] pressure regulation2 small motors su* z fan motors c be op]at$ m easily f ! circuit4 ,phase4--,z appli$ to an alt]nat+ curr5t1 phase d5otes ! angle turn$ ?r\gh by ! g5]at+ elem5t reckon$ f a giv5 in/ant4 ,phase is usually measur$ 9 degrees f ! initial position ( z]o g5]ation4 ,if 9 ! diagram fig4 #a1bbe1 ! elem5t>y armature or loop be ! g5]at+ elem5t1 & ! curve at ! "r be ! s9e curve repres5t+ ! curr5t1 !n ! phase ( any po9t p w be ! angle or angle mov$ ?r\gh f ! horizontal l9e1 ! />t+ po9t4 ,ques4 ,:at is phase diff]5ce8 ,ans4 ,! angle betwe5 ! phases ( two or m alt]nat+ curr5t quantities z measur$ 9 degrees4 ,ques4 ,:at is phase displacem5t8 ,ans4 ,a *ange ( phase ( an alt]nat+ pressure or curr5t4 ,illu/ration3 ,,figs4 #a1bbf & #a1bbg4--;,diagram & s9e curves illu/rat+ syn*ronism4 ,if two alt]nators1 ) coils 9 p>allel planes1 be made to rotate at ! same spe$ by connect+ !m ) *a9 drive or equival5t means1 !y w !n be 9 syn*ronism t is1 ! alt]nat+ pressure or curr5t 9 "o w v>y 9 /ep ) t 9 ! o!r4 ,9 o!r words1 ! cycles ( "o take place ) ! same frequ5cy & at ! same "t z ! cycles ( ! o!r z indicat$ by ! curves1 fig4 #a1bbf4 ,x %\ld be not$ t ! maximum values are n necess>ily ! same b ! maximum & z]o values mu/ occur at ! same "t 9 bo? ma*9es1 & ! maximum value mu/ be ( ! same sign4 ,if ! waves be di/ort$ ! maximum values may n occur simultane\sly4 ,see fig4 #a1cdh4 ,syn*ronism4--,?is t]m may be def9$ z3 ! simultane\s occurr5ce ( any two ev5ts4 ,?us two alt]nat+ curr5ts or pressures are said to be 9 syn*ronism :5 !y h ! same frequ5cy & are 9 phase4 ,ques4 ,:at does ! expression 9 phase mean8 ,ans4 ,two alt]nat+ quantities are said to be 9 phase1 :5 !re is no phase diff]5ce betwe52 t is :5 ! angle ( phase diff]5ce equals z]o4 ,?us ! curr5t is said to be 9 phase ) ! pressure :5 x nei!r lags nor leads1 z 9 fig4 #a1bbh4 ,a rotat+ cyl9d]1 or ! movem5t ( an index or trail+ arm is br\ght into syn*ronism ) ano!r rotat+ cyl9d] or ano!r index or trail+ arm1 n only :5 ! two are mov+ ) exactly ! same spe$1 b :5 9 addition !y are simultane\sly mov+ ov] simil> portions ( _! respective pa?s4 ,illu/ration3 ,,fig4 #a1bbh--,pressure & curr5t curves illu/rat+ ! t]m 9 phase4 ,! curr5t is said to be 9 phase ) ! pressure :5 x nei!r lags nor leads4 ,:5 !re is phase diff]5ce1 z betwe5 curr5t & pressure1 !y are said to be out ( phase ! phase diff]5ce be+ measur$ z 9 fig4 #a1bbi by ! angle 4 ,illu/ration3 ,,fig4 #a1bbi--,pressure & curr5t curves illu/rat+ ! t]m out ( phase4 ,! curr5t is said to be out ( phase ) ! pressure :5 x ei!r lags or leads1 t is :5 ! curr5t is n 9 syn*ronism ) ! pressure4 ,9 practice ! curr5t & pressure are ne>ly always out ( phase4 ,:5 ! phase diff]5ce is #ij z 9 fig4 #a1bca or #a1bcb1 ! two alt]nat+ quantities are said to be 9 quadrature2 :5 x is #ahj1 z 9 fig4 #a1bcc1 !y are said to be 9 opposition4 ,:5 !y are 9 quadrature1 "o is at a maximum :5 ! o!r is at z]o2 :5 !y are 9 opposition1 "o rea*es a positive maximum :5 ! o!r rea*es a negative m9imum1 be+ at ea* in/ant opposite 9 sign4 ,ques4 ,:at is a dep>ture f syn*ronism call$8 ,ans4 ,loss ( syn*ronism4 ,illu/ration3 ,,figs4 #a1bcj to #a1bcc4--;,curves %[+ "s phase relations betwe5 curr5t & pressure4 ,fig4 #a1bcj1 syn*ronism ( curr5t & pressure1 express$ by ! t]m 9 phase1 mean+ simultane\s z]o values1 & simultane\s maximum values ( ! same sign2 fig4 #a1bca1 9 quadrature1 curr5t lead+ #ij2 fig4 #a1bcb 9 quadrature1 curr5t lagg+ #ij2 fig4 #a1bcc1 9 opposition1 mean+ t ! phase diff]5t betwe5 curr5t & pressure is #ahj4 ,maximum ,volts & ,amp]es4--,9 ! op]ation ( an alt]nator1 ! pressure & /r5g? ( ! curr5t are cont9ually ris+1 fall+ & rev]s+4 ,dur+ ea* cycle !re are two po9ts at :i* ! pressure or curr5t rea*es its greate/ value1 be+ kn[n z ! maximum value4 ,?is maximum value is n us$ to any great ext5t1 b x %[s ! maximum to :i* ! pressure rises1 & h5ce1 ! greate/ /ra9 to :i* ! insulation ( ! alt]nator is subject$4 ,illu/ration3 ,,fig4 #a1bcd4--;,elem5t>y alt]nator develop+ "o av]age volt4 ,if ! loop make "o revolution p] second1 & ! maximum numb] ( l9es ( =ce embrac$ by ! loop 9 ! position %[n 7! z]o position7 be d5ot$ by ,n1 !n ea* limb w cut #b,n l9es p] second1 because x cuts e l9e dur+ ! "r sweep & aga9 dur+ ! left sweep4 ,h5ce ea* limb develops an av]age pressure ( #b,n units 7,c4,g4,s4 units71 & z bo? limbs are connect$ 9 s]ies1 ! total pressure is #d,n units p] revolution4 ,n[1 if ! loop make f revolutions p] second in/ead ( only "o1 !n f times z _m l9es w be cut p] second1 & ! av]age pressure w be #d,n f units4 ,s9ce ! ,c4,g4,s4 unit ( pressure is s extremely small1 a mu* great] practical unit call$ ! volt is us$1 :i* is equal to #ajj1jjj1jjj1 or #aj ,c4,g4,s4 units is employ$4 ,h5ce av]age voltage #d,nf #aj4 ,! value ( ,n 9 actual ma*9es is v high1 be+ sev]al million l9es ( =ce4 ,! illu/ration %[s "o set ( conditions necess>y to g5]ate "o av]age volt4 ,! maximum pressure develop$ is #a 4#fcg #a4eg volts2 virtual pressure #a4eg 4#gjg #a4aa volts4 ,av]age ,volts & ,amp]es4--,s9ce ! s9e curve is us$ to repres5t ! alt]nat+ curr5t1 ! av]age value may be def9$ z3 ! av]age ( all ! ord9ates ( ! curve = "o-half ( a cycle4 ,ques4 ,( :at use is ! av]age value8 ,ans4 ,x is us$ 9 "s calculations b1 l ! maximum value1 n v (t54 ,! relation betwe5 ! av]age & virtual value is ( importance z x gives ! =m factor4 ,virtual ,volts & ,amp]es4--,! virtual#a value ( an alt]nat+ pressure or curr5t is equival5t to t ( a direct pressure or curr5t :i* w\ld produce ! same effect2 ^? effects ( ! pressure & curr5t are tak5 :i* are n affect$ by rapid *anges 9 direction & /r5g?1--9 ! case ( pressure1 ! read+ ( an electro/atic voltmet]1 & 9 ! case ( curr5t1 ! heat+ effect4 #a ,,note4--,i adh]e to ! t]m virtual1 z x 0 9 use be=e ! t]m efficace :i* 0 recomm5d$ 9 #ahhi by ! ,p>is ,congress to d5ote ! squ>e root ( mean squ>e value4 ,! correspond+ ,engli% adjective is efficaci\s2 b "s eng9e]s mi/ranslate x ) ! ^w effective4 ,i adh]e to ! t]m virtual ma9ly because ! adjective effective is requir$ 9 its usual mean+ 9 k9ematics to repres5t ! resolv$ "p ( a =ce :i* acts obliquely to ! l9e ( motion1 ! effective =ce be+ ! :ole =ce multipli$ by ! cos9e ( ! angle at :i* x acts ) respect to ! direction ( motion4 ,"s au?ors use ! expression ',r4,m4,s4 value' 7mean+ 'root mean squ>e'7 to d5ote ! virtual or quadratic mean value4--,s4 ,p4 ,?ompson4 ,illu/ration3 ,,fig4 #a1bce4--,maximum & av]age values ( ! s9e curve4 ,! av]age value ( ! s9e curve is repres5t$ by an ord9ate ,,ms ( su* l5g? t :5 multipli$ by ! base l9e ,,fg1 w give a rectangle ,,mfsg ^: area is equal to t includ$ betwe5 ! curve & base l9e ,,fdgs4 ,illu/ration3 ,,fig4 #a1bcf4--;,diagram illu/rat+ virtual volts & amp]es4 ,! ^w virtual is def9$ z3 ,be+ 9 ess5ce or effect1 n 9 fact2 n actual1 b equival5t1 s f> z effect is conc]n$4 ,z appli$ to ! alt]nat+ curr5t1 x d5otes an imag9>y direct curr5t ( su* value z w produce an effect equival5t to t ( ! alt]nat+ curr5t4 ,?us1 a virtual pressure ( #a1jjj volts is "o t w\ld produce ! same deflection 9 an electro/atic voltmet] z a direct pressure ( #a1jjj volts3 a virtual curr5t ( #aj amp]es is t curr5t :i* w\ld produce ! same heat+ effect z a direct curr5t ( #aj amp]es4 ,bo? pressure & curr5t v>y cont9ually above & bel[ ! virtual values 9 alt]nat+ curr5t circuits4 ,di/9ction %\ld be made betwe5 ! virtual & effective values ( an alt]nat+ curr5t4 ,see fig4 #a1bcg4 ,! ^w effective is commonly us$ errone\sly = virtual4 ,see note page #a1jaa4 ,! attraction 7or repulsion7 9 electro/atic voltmet]s is proportional to ! squ>e ( ! volts4 ,! read+s :i* ^! in/rum5ts give1 if fir/ calibrat$ by us+ /eady curr5ts1 are n true means1 b are ! squ>e roots ( ! means ( ! squ>es4 ,n[ ! mean ( ! squ>es ( ! s9e 7tak5 ov] ei!r "o quadrant or a :ole circle7 is 2 h5ce ! squ>e root ( mean squ>e value ( ! s9e functions is obta9$ by multiply+ _! maximum value by #a #b1 or by #j4gjg4 ,! ari?metical mean ( ! values ( ! s9e1 h[ev]1 is #j4fcg4 ,h5ce an alt]nat+ curr5t1 if x obey ! s9e law1 w produce a heat+ effect great] ?an t ( a /eady curr5t ( ! same av]age /r5g?1 by ! ratio ( #j4gjg to #j4fcg2 t is1 ab\t #a4aa times great]4 ,if a ,c>dew voltmet] be plac$ on an alt]nat+ circuit 9 :i* ! volts are oscillat+ betwe5 maxima ( #ajj & -#ajj volts1 x w read #gj4g volts1 ?\gh ! ari?metical mean is really only #fc4g2 & #gj4g /eady volts w\ld be requir$ to produce an equal read+4 ,illu/ration3 ,,fig4 #a1bcg4--;,diagram illu/rat+ virtual & effective pressure4 ,if ! coil be %ort circuit$ by ! swit* & a con/ant virtual pressure be impress$ on ! circuit1 ! :ole ( ! impress$ pressure w be effective 9 caus+ curr5t to fl[ ar\nd ! circuit4 ,9 ?is case ! virtual & effective pressures w be equal4 ,if ! coil be swit*$ into circuit1 ! rev]se pressure due to self induction w oppose ! virtual pressure2 h5ce1 ! effective pressure 7:i* is ! diff]5ce betwe5 ! virtual & rev]se pressures7 w be r$uc$1 ! virtual or impress$ pressure rema9+ con/ant all ! "t4 ,a virtual curr5t is t indicat$ by an ammet] reg>dless ( ! phase relation betwe5 curr5t & pressure4 ,an effective curr5t is t indicat$ by an ammet] :5 ! curr5t is 9 phase ) ! pressure4 ,9 practice1 ! curr5t is h>dly ev] 9 phase ) ! pressure1 usually lagg+1 ?\gh sometimes lead+ 9 phase4 ,n[ ! great] ?is phase diff]5ce1 ei!r way1 ! less is ! p[] ( a giv5 virtual curr5t to d "w4 ,) respect to ?is feature1 effective curr5t may be def9$ z3 t proportion ( a giv5 virtual curr5t :i* c d useful "w4 ,if !re be no phase diff]5ce1 !n effective curr5t is equal to virtual curr5t4 ,! matt] may be look$ at 9 a diff]5t way4 ,if an alt]nat+ curr5t is to produce 9 a giv5 wire ! same am\nt ( effect z a cont9u\s curr5t ( #ajj amp]es1 s9ce ! alt]nat+ curr5t goes d[n to z]o twice 9 ea* p]iod1 x is cle> t x mu/ at "s po9t 9 ! p]iod rise to a maximum great] ?an #ajj amp]es4 ,h[ mu* great] mu/ ! maximum be8 ,! answ] is t1 if x undulate up & d[n ) a pure wave =m1 its maximum mu/ be #b times z great z ! virtual mean2 or conv]sely ! virtual amp]es w be equal to ! maximum divid$ by #b4 ,9 fact1 to produce equal effect1 ! equival5t direct curr5t w be a k9d ( mean betwe5 ! maximum & ! z]o value ( ! alt]nat+ curr5t2 b x mu/ n be ! ari?metical mean1 nor ! geometrical mean1 nor ! h>monic mean1 b ! quadratic mean2 t is1 x w be ! squ>e root ( ! mean ( ! squ>es ( all ! in/antane\s values betwe5 z]o & maximum4 ,effective ,volts & ,amp]es4--,virtual pressure1 al?\gh already expla9$1 may be fur!r def9$ z ! pressure impress$ on a circuit4 ,n[1 9 ne>ly all circuits ! impress$ or virtual pressure meets ) an oppos+ pressure due to inductance & h5ce ! effective pressure is some?+ less ?an ! virtual1 be+ def9$ z t pressure :i* is available = driv+ electricity ar\nd ! circuit1 or = do+ "w4 ,! diff]5ce betwe5 virtual & effective pressure is illu/rat$ 9 fig4 #a1bcg4 ,ques4 ,does a giv5 alt]nat+ voltage affect ! insulation ( ! circuit diff]5tly ?an a direct pressure ( ! same value8 ,ans4 ,x puts m /ra9 on ! insulation 9 ! same proportion z ! maximum pressure exce$s ! virtual pressure4 ,illu/ration3 ,,fig4 #a1bch4--;,curr5t or pressure curve illu/rat+ =m factor4 ,x is simply ! virtual value divid$ by ! av]age value4 ,= a s9e wave ! virtual value is #a _/ #b times ! maximum1 & ! av]age is #b _/ times ! maximum1 s t ! =m factor is _/ #bb or #a4aa4 ,! induction wave :i* g5]ates an alt]nat+ pressure wave has a maximum value proportional to ! area1 t is1 to ! av]age value ( ! pressure wave4 ,h5ce ! induction values correspond+ to two pressure waves ^: virtual values are equal1 w be inv]sely proportional to _! =m factors4 ,?is is illu/rat$ by ! fact t a peak$ wave causes less hy/]esis loss 9 a trans=m] core ?an a flat topp$ wave1 ow+ to ! high] =m factor ( ! peak$ wave4 ,see wave =ms1 figs4 #a1bde to #a1bdh4 ,=m ,factor4--,?is t]m 0 introduc$ by ,flem+1 & d5otes ! ratio ( ! virtual value ( an alt]nat+ wave to ! av]age value4 ,t is virtual value 4#gjg =m factor ------------- ---- #a4aa av]age value 4#fcg ,ques4 ,:at does ?is indicate8 ,ans4 ,x gives ! relative heat+ effects ( alt]nat+ & direct curr5ts1 z illu/rat$ 9 figs4 #a1bci & #a1bdj4 ,t is1 ! alt]nat+ curr5t w h ab\t #aa p] c5t4 m heat+ p[] ?an ! direct curr5t :i* is ( ! same av]age /r5g?4 ,if an alt]nat+ curr5t voltmet] be plac$ ^u a circuit 9 :i* ! volts range f #ajj to -#ajj1 x w read #gj4g volts1 al?\gh ! ari?metical av]age1 irrespective ( or-sign1 is only #fc4g volts4 ,if ! voltmet] be connect$ to a direct curr5t circuit1 ! pressure necess>y to give ! same read+ w\ld be #gj4g volts4 ,illu/ration3 ,,figs4 #a1bci & #a1bdj4--,relative heat+ effects ( alt]nat+ & direct curr5ts4 ,if x takes say five m9utes to produce a c]ta9 heat+ effect ) alt]nat+ curr5t at say #fc4g av]age volts1 x w take #cc seconds long] ) direct curr5t at ! same pressure1 t is1 ! alt]nat+ curr5t has ab\t #aa p] c5t4 m heat+ p[] ?an ! direct curr5t ( ! same av]age pressure4 ,! read] %\ld be c>eful n to get a wrong conception ( ! above2 x does n mean t !re is a sav+ by us+ alt]nat+ curr5t4 ,:5 bo? voltmet]s read ! same1 t is1 :5 ! virtual pressure ( ! alt]nat+ curr5t is ! same z ! direct curr5t pressure1 ! heat+ effect is ( c\rse ! same4 ,ques4 ,:at is ! relation betwe5 ! %ape ( ! wave curve & ! =m factor8 ,ans4 ,! m peak$ ! wave1 ! great] ! value ( its =m factor4 ,a =m factor ( units w\ld correspond to a rectangul> wave2 ?is is ! lea/ possible value ( ! =m factor1 & "o :i* is n realiz$ 9 comm]cial ma*9es4 ,illu/ration3 ,,figs4 #a1bda to #a1bdd4--,v>i\s =ms ( pressure or curr5t waves4 ,figs4 #a1bda to #a1bdc %[ ! g5]al %ape ( ! waves produc$ by "s alt]nators us$ l>gely = light+ "w & hav+ too!d armatures4 ,! effect ( ! slots & %ape ( pole pieces is "h v m>k$4 ,fig4 #a1bdd %[s a wave *>act]i/ic ( l>ge alt]nators design$ = p[] transmission & hav+ multi-slot or di/ribut$ w9d+s4 ,wave ,=m4--,!re is always m or less irregul>ity 9 ! %ape ( ! curr5t waves z met 9 practice1 dep5d+ ^u ! con/ruction ( ! alt]nator4 ,! ideal wave curve is ! s call$ true s9e wave1 & is obta9$ ) a rate ( cutt+ ( l9es ( =ce1 by ! armature coils1 equival5t to ! sw+ ( a p5dulum1 :i* increases 9 spe$ f ! end to ! middle ( ! sw+1 decreas+ at ! same rate aft] pass+ ! c5t]4 ,?is sw+ is express$ 9 physics1 z simple h>monic motion4 ,illu/ration3 ,,figs4 #a1bde & #a1bdf4--,resolution ( complex curves into s9e curves4 ,! heavy curve c be resolv$ into ! simpl] curves ,a & ,b %[n 9 ,no4 #a1 ! compon5t curves ,a & ,b h 9 ! ratio ( ?ree to "o2 t is1 curve ,b has ?ree times z _m p]iods p] second z curve ,a4 ,all ! curves1 h[ev]1 cross ! z]o l9e at ! same "t1 & ! resultant curve1 ?\gh curi\sly unlike ei!r ( !m1 has a c]ta9 symmetry4 ,9 ,no4 #b ! compon5t curves1 besides hav+ p]iods 9 ! ratio ( ?ree to "o1 cross ! z]o l9e at diff]5t po9ts4 ,! resultant curve produc$ is /ill less simil> to its compon5ts1 & is curi\sly & unsymmetrically hump$4 ,at fir/ sight x is difficult to believe t su* a curi\s curve c\ld be resolv$ into two su* simple & symmetrical ones4 ,9 bo? figures ! compon5t curves are s9e curves1 & z ! curves = s9e & cos9e functions are exactly simil> 9 =m1 ! simple/ supposition t c be made = ! v>iation ( pressure or ( curr5t is t bo? foll[ a s9e law4 ,illu/ration3 ,,fig4 #a1bdg4--,reproduction ( oscillograph record ( wave =m ( alt]nator ) "o coil p] phase p] pole4 ,"h ! s-call$ sup]-impos$ h>monic is cle>ly indicat$4 ,illu/ration3 ,,fig4 #a1bdh4--,reproduction ( oscillograph record ( ,wagn] alt]nator hav+ ?ree coils p] phase p] pole4 ,! losses 9 all second>y app>atus are slightly l[] ) ! s call$ peak$ =m ( wave4 ,= ! same virtual voltage1 h[ev]1 ! top ( ! peak w be mu* high]1 !reby submitt+ ! insulation to t mu* great] /ra94 ,by reason ( ! fact t ! losses are less "u su* wave =ms1 _m manufactur]s 9 submitt+ p]=mance data on trans=m]s recite t ! figures are = s9e wave conditions1 /at+ fur!r t if ! trans=m]s are to be op]at$ 9 a circuit m peak$ ?an ! s9e wave1 ! losses w be less ?an %[n4 ,! slight sav+ 9 ! losses ( second>y app>atus1 obta9$ ) a peak$ wave1 by no means comp5sates = ! increas$ insulation /ra9s & an alt]nator hav+ a true s9e wave is pref]r$4 ,ques4 ,:at det]m9es ! =m ( ! wave8 ,ans4 #a4 ,! numb] ( coils p] phase p] pole1 #b1 %ape ( pole faces1 #c1 eddy curr5ts 9 ! pole pieces1 & #d1 ! air gap4 ,ques4 ,:at are ! requirem5ts = prop] rate ( cutt+ ( ! l9es ( =ce8 ,ans4 ,x is necess>y to h1 z a m9imum1 two coils p] phase p] pole 9 ?ree phase "w4 ,ques4 ,:at is ! effect ( only "o coil p] phase p] pole8 ,ans4 ,! wave =m w be di/ort$ z %[n 9 fig4 #a1bdg4 ,ques4 ,:at is ! lea/ numb] ( coils p] phase p] pole t %\ld be us$ = two & ?ree phase alt]nators8 ,ans4 ,= ?ree phase1 two coils1 & = two phase1 ?ree coils1 p] phase p] pole4 ,s+le or ,monophase ,curr5t4--,?is k9d ( alt]nat+ curr5t is g5]at$ by an alt]nator hav+ a s+le w9d+ on its armature4 ,two wires1 a lead & return1 are us$ z 9 direct curr5t4 ,an elem5t>y diagram %[+ ! work+ pr9ciples is illu/rat$ 9 fig4 #a1bdi1 a simil> hydraulic cycle be+ %[n 9 figs4 #a1bej to #a1beb4 ,illu/ration3 ,,fig4 #a1bdi4--;,elem5t>y "o loop alt]nator & s9e curve illu/rat+ s+le phase alt]nat+ curr5t4 ,!re are ?ree po9ts dur+ ! revolution at :i* !re is no curr5t3 at #j ! position %[n1 #ahj1 & #cfj2 9 o!r words1 at ! beg9n+1 middle po9t & end ( ! cycle4 ,! curr5t rea*es a maximum at #ij1 rev]ses at #ahj1 & rea*es a maximum 9 ! rev]se direction at #bgj4 ,two ,phase ,curr5t4--,9 mo/ cases two phase curr5t actually consi/s ( two di/9ct s+le phase curr5ts fl[+ 9 sep>ate circuits4 ,!re is (t5 no electrical connection betwe5 !m2 !y are ( equal p]iod & equal amplitude1 b diff] 9 phase by "o qu>t] ( a p]iod4 ,) ?is phase relation "o ( !m w be at a maximum :5 ! o!r is at z]o4 ,two phase curr5t is illu/rat$ by s9e curves 9 fig4 #a1bec1 & by hydraulic analogy 9 figs4 #a1bed & #a1bee4 ,illu/ration3 ,,figs4 #a1bej to #a1beb4--;,hydraulic analogy illu/rat+ ! diff]5ce betwe5 direct 7cont9u\s7 & alt]nat+ curr5t4 ,9 fig4 #a1bej a c5trifugal pump ,c =ces wat] to ! upp] pipe1 f :i* x falls by gravity to ! l[] pipe ,b & re-ent]s ! pump4 ,! curr5t is cont9u\s1 always fl[+ 9 "o direction1 t is1 x does n rev]se its direction4 ,simil>ly a direct electric curr5t is con/ant 9 direction 7does n rev]se72 ?\gh n necess>ily con/ant 9 value4 ,a direct curr5t1 con/ant 9 bo? value & direction z a result ( con/ant pressure1 is call$ cont9u\s curr5t4 ,simil>ly 9 ! figure ! fl[ is con/ant1 & a gauge ,d plac$ at any po9t w regi/] a con/ant pressure1 h5ce ! curr5t may be call$1 9 ! electrical s5se1 cont9u\s4 ,! conditions 9 fig4 #a1bea are q diff]5t4 ,! illu/ration repres5ts a d\ble act+ cyl9d] ) ! ends connect$ by a pipe ,a1 & ! pi/on driv5 by crank & ,scot* yoke z %[n4 ,9 op]ation1 if ! cyl9d] & pipe be full ( wat]1 a curr5t ( wat] w beg9 to fl[ ?r\gh ! pipe 9 ! direction indicat$ z ! pi/on beg9s its /roke1 increas+ to maximum velocity at "o-qu>t] revolution ( ! crank1 decreas+ & com+ to re/ at "o-half revolution1 !n rev]s+ & rea*+ maximum velocity 9 ! rev]se direction at ?ree-qu>t] revolution1 & com+ to re/ aga9 at ! end ( ! return /roke4 ,a pressure gauge at ,g w regi/] a pressure :i* v>ies ) ! curr5t4 ,s9ce ! alt]nat+ electric curr5t und]goes simil> *anges1 ! s9e curve w apply equally z well to ! pump cycle z to ! alt]nat+ curr5t cycle4 ,illu/ration3 ,,fig4 #a1bec4--;,elem5t>y two loop alt]nator & s9e curves1 illu/rat+ two phase alt]nat+ curr5t4 ,if ! loops be plac$ on ! alt]nator armature at #ij magnetic degrees1 a s+le phase curr5t w be g5]at$ 9 ea* ( ! w9d+s1 ! curr5t 9 "o w9d+ be+ at its maximum value :5 ! o!r is at z]o4 ,9 ?is case f\r transmission conductors are g5]ally us$1 two = ea* sep>ate circuit1 & ! motors to :i* ! curr5t is l$ h a d\ble w9d+ correspond+ to t on ! alt]nator armature4 ,if two id5tical simple alt]nators h _! armature %afts c\pl$ 9 su* a mann]1 t :5 a giv5 armature coil on "o is directly "u a field pole1 ! correspond+ coil on ! o!r is midway betwe5 two poles ( its field1 ! two curr5ts g5]at$ w diff] 9 phase by a half alt]nation1 & w be two phase curr5t4 ,ques4 ,h[ mu/ an alt]nator be con/ruct$ to g5]ate two phase curr5t8 ,ans4 ,x mu/ h two indep5d5t w9d+s1 & ^! mu/ be s spac$ out t :5 ! volts g5]at$ 9 "o ( ! two phases are at a maximum1 ^? g5]at$ 9 ! o!r are at z]o4 ,9 o!r words1 ! w9d+s1 :i* mu/ be alike1 ( an equal numb] ( turns1 mu/ be displac$ along ! armature by an angle correspond+ to "o-qu>t] ( a p]iod1 t is1 to half ! pole pit*4 ,illu/ration3 ,,figs4 #a1bed & #a1bee4--;,hydraulic analogy illu/rat+ two phase alt]nat+ curr5t4 ,9 ! figure two cyl9d]s1 simil> to ! "o 9 fig4 #a1bea1 are %[n1 op]at$ f "o %aft by crank & ,scot* yoke drive4 ,! cranks are at #ij z %[n1 & ! cyl9d]s & connect+ pipes full ( wat]4 ,9 op]ation1 ! same cycle ( wat] fl[ takes place z 9 fig4 #a1bea4 ,s9ce ! cranks are at #ij1 ! second pi/on is "o-half /roke beh9d ! fir/2 ! fl[ ( wat] 9 ,no4 #a 7phase ,a7 is at a maximum :5 ! fl[ 9 ,no4 #b 7phase ,b7 comes to re/1 ! curr5t conditions 9 bo? pipes = ! entire cycle be+ repres5t$ by ! two s9e curves ^: phase diff]5ce is #ij4 ,comp>+ ^! curves ) fig4 #a1bec1 x w be se5 t ! wat] & electric curr5t act 9 a simil> mann]4 ,! w9d+s ( ! two phases mu/1 ( c\rse1 be kept sep>ate1 h5ce ! armature w h f\r t]m9als1 or if x be a revolv+ armature x w h f\r collector r+s4 ,z mu/ be evid5t ! phase diff]5ce may be ( any value betwe5 #j & #cfj1 b 9 practice x is almo/ always made #ij4 ,ques4 ,9 :at o!r way may two phase curr5t be g5]at$8 ,ans4 ,by two s+le phase alt]nators c\pl$ to "o %aft4 ,ques4 ,h[ _m wires are requir$ = two phase di/ribution8 ,ans4 ,a two phase sy/em requires f\r l9es = its di/ribution2 two l9es = ea* phase z 9 fig4 #a1bec4 ,x is possible1 b n advisable1 to r$uce ! numb] to #c1 by employ+ "o r ?ick] l9e z a common return = ea* ( ! phases z 9 fig4 #a1bef4 ,illu/ration3 ,,fig4 #a1bef4--;,diagram ( ?ree wire two phase curr5t di/ribution4 ,9 ord] to save "o wire x is possible to use a common return conductor = bo? circuits1 z %[n1 ! dott$ portion ( "o wire #d be+ elim9at$ by connect+ across to #a at ,m & ,s4 ,= long l9es ?is is economical1 b ! int]connection ( ! circuits increases ! *ance ( tr\ble f gr\nds or %ort circuits4 ,! curr5t 9 ! conductor w be ! resultant ( ! two curr5ts1 diff]+ by #ij 9 phase4 ,if ?is be done1 ! voltage betwe5 ! ,a l9e & ! ,b l9e w be equal to #b times ! voltage 9 ei!r phase1 & ! curr5t 9 ! l9e us$ z common return w be #b times z great z ! curr5t 9 ei!r l9e1 assum+ ! two curr5ts 9 ! two phases to be equal4 ,ques4 ,9 :at o!r way may two phase curr5t be di/ribut$8 ,ans4 ,! mid po9t ( ! w9d+s ( ! two phases may be unit$ 9 ! alt]nator at a common junction4 ,illu/ration3 ,,figs4 #a1beg to #a1bei4--,v>i\s two phase armature connections4 ,fig4 #a1beg1 two sep>ate circuit f\r collector r+ arrangem5t2 fig4 #a1beh1 common middle connection1 f\r collector r+s2 fig4 #a1bei1 circuit connect$ 9 armature = ?ree collector r+s4 ,9 ! figures ! black w9d+ repres5ts phase ,a1 & ! light w9d+1 phase ,b4 ,?is is equival5t to mak+ ! ma*9e into a f\r phase alt]nator ) half ! voltage 9 ea* ( ! f\r phases1 :i* w !n be 9 successive quadrature ) ea* o!r4 ,ques4 ,h[ are two phase alt]nator armatures w\nd8 ,ans4 ,! two circuits may be sep>ate1 ea* hav+ two collector r+s1 z %[n 9 fig4 #a1beg1 or ! two circuits may be c\pl$ at a common middle z 9 fig4 #a1beh1 or ! two circuits may be c\pl$ 9 ! armature s t only ?ree collector r+s are requir$ z %[n 9 fig4 #a1bei4 ,illu/ration3 ,,fig4 #a1bfj4--;,elem5t>y ?ree loop alt]nator & s9e curves1 illu/rat+ ?ree phase alt]nat+ curr5t4 ,if ! loops be plac$ on ! alt]nator armature at #abj magnetic degrees f "o ano!r1 ! curr5t 9 ea* w atta9 its maximum at a po9t "o-?ird ( a cycle di/ant f ! o!r two4 ,! arrangem5t "h %[n gives ?ree indep5d5t s+le phase curr5ts & requires six wires = _! transmission4 ,a bett] arrangem5t & ! "o g5]ally us$ is %[n 9 fig4 #a1bfa4 ,illu/ration3 ,,fig4 #a1bfa4--;,elem5t>y ?ree wire ?ree phase alt]nator4 ,= ! transmission ( ?ree phase curr5t1 x is n cu/om>y to use six wires1 z 9 fig4 #a1bfj1 in/ead1 ?ree ends 7"o end ( ea* ( ! loops7 are br\ght toge!r to a common connection z %[n1 & ! o!r ends1 connect$ to ! collector r+s1 giv+ only ?ree wires = ! transmission ( ! curr5t4 ,?ree ,phase ,curr5t4--,a ?ree phase curr5t consi/s ( ?ree alt]nat+ curr5ts ( equal frequ5cy & amplitude1 b diff]+ 9 phase f ea* o!r by "o-?ird ( a p]iod4 ,?ree phase curr5t z repres5t$ by s9e curves is %[n 9 fig4 #a1bfj1 & by hydraulic analogy 9 fig4 #a1bfb4 ,inspection ( ! figures w %[ t :5 any "o ( ! curr5ts is at its maximum1 ! o!r two are ( half _! maximum value1 & are fl[+ 9 ! opposite direction4 ,illu/ration3 ,,figs4 #a1bfb & #a1bfc4--;,hydraulic analogy illu/rat+ ?ree phase alt]nat+ curr5t4 ,?ree cyl9d]s are "h %[n ) pi/ons connect$ ?r\gh ,scot* yokes to cranks plac$ #abj ap>t4 ,! same action takes place 9 ea* cyl9d] z 9 ! prec$+ cases1 ! only diff]5ce be+ ! additional cyl9d]1 & diff]5ce 9 phase relation4 ,ques4 ,h[ is ?ree phase curr5t g5]at$8 ,ans4 ,x requires ?ree equal w9d+s on ! alt]nator armature1 & !y mu/ be spac$ out ov] its surface s z to be successively & ( ! p]iod 7t is1 ( ! d\ble pole pit*7 ap>t f "o ano!r4 ,ques4 ,h[ _m wires are us$ = ?ree phase di/ribution8 ,ans4 ,ei!r six wires or ?ree wires4 ,six wires1 z 9 fig4 #a1bfj1 might be us$ :]e x is desir$ to supply entirely indep5d5t circuits1 or z is m usual only ?ree wires are us$ z %[n 9 fig4 #a1bfa4 ,9 ?is case x %\ld be obs]v$ t if ! voltage g5]at$ 9 ea* "o ( ! ?ree phases sep>ately ,e 7virtual7 volts1 ! voltage g5]at$ betwe5 any two ( ! t]m9als w be equal to #c ,e4 ,?us1 if ea* ( ! ?ree phases g5]ate #ajj volts1 ! voltage f ! t]m9al ( ! ,a phase to t ( ! ,b phase w be #agc volts4 ,illu/ration3 ,,fig4 #a1bfd4--;,exp]im5t illu/rat+ self-induction 9 an alt]nat+ curr5t circuit4 ,if an inc&esc5t lamp be connect$ 9 s]ies ) a coil made ( "o p\nd ( ,no4 #bj magnet wire1 & connect$ to ! circuit1 ! curr5t ?r\gh ! lamp w be decreas$ due to ! self-induction ( ! coil4 ,if n[ an iron core be gradually pu%$ into ! coil1 ! self-induction w be greatly increas$ & ! lamp w g out1 ?us %[+ ! great importance :i* self-induction plays 9 alt]nat+ curr5t "w4 ,inductance4--,ea* "t a direct curr5t is />t$1 /opp$ or v>i$ 9 /r5g?1 ! magnetism *anges1 & induces or t5ds to induce a pressure 9 ! wire :i* always has a direction oppos+ ! pressure :i* orig9ally produc$ ! curr5t4 ,?is self-induc$ pressure t5ds to weak5 ! ma9 curr5t at ! />t & prolong x :5 ! circuit is op5$4 ,! expression inductance is frequ5tly us$ 9 ! same s5se z coeffici5t ( self-induction1 :i* is a quantity p]ta9+ to an electric circuit dep5d+ on its geometrical =m & ! nature ( ! surr\nd+ m$ium4 ,if ! direct curr5t ma9ta9s ! same /r5g? & fl[ /eadily1 !re w be no v>iations 9 ! magnetic field surr\nd+ ! wire & no self-induction1 consequ5tly ! only ret>d+ effect ( ! curr5t w be ! ohmic resi/ance ( ! wire4 ,if an alt]nat+ curr5t be s5t ?r\gh a circuit1 !re w be two ret>d+ effects3 #a4 ,! ohmic resi/ance2 #b4 ,! spuri\s resi/ance4 ,illu/ration3 ,,fig4 #a1bfe4--,non-inductive & inductive resi/ances4 ,two curr5ts are %[n jo9$ 9 p>allel1 "o conta9+ a lamp & non-inductive resi/ance1 & ! o!r a lamp & inductive resi/ance4 ,! two resi/ances be+ ! same1 a suffici5t direct pressure appli$ at ,t1 ,t' w cause ! lamps to light up equally4 ,if1 h[ev]1 an alt]nat+ pressure be appli$1 ,m w burn brightly1 :ile ,s w give v little or no light because ( ! effect ( ! inductance ( ! inductive resi/ance4 ,ques4 ,^u :at does ! ohmic resi/ance dep5d8 ,ans4 ,^u ! l5g?1 cross sectional area & mat]ial ( ! wire4 ,ques4 ,^u :at does ! spuri\s resi/ance dep5d8 ,ans4 ,^u ! frequ5cy ( ! alt]nat+ curr5t1 ! %ape ( ! conductor1 & nature ( ! surr\nd+ m$ium4 ,illu/ration3 ,,fig4 #a1bff4--;,inductance te/1 illu/rat+ ! self-induction ( a coil :i* is gradually increas$ by mov+ an iron wire core in* by in* into ! coil4 ,! curr5t is kept con/ant ) ! adju/able resi/ance ?r\gh\t ! te/ & read+s tak51 fir/ )\t ! iron core1 & aga9 :5 ! core is put 9 ! coil & mov$ to ! #a1 #b1 #c1 #d1 etc41 in* m>ks4 ,by plott+ ! voltmet] read+s & ! position ( ! iron core on section pap]1 a curve is obta9$ %[+ graphically ! effect ( ! self-induction4 ,a curve ( ?is k9d is %[n 9 fig4 #a1cjb4 ,ques4 ,def9e inductance4 ,ans4 ,x is ! total magnetic flux ?read+ ! circuit p] unit curr5t :i* fl[s 9 ! circuit1 & :i* produces ! flux4 ,9 ?is x mu/ be und]/ood t if any portion ( ! flux ?read ! circuit m ?an once1 ?is portion mu/ be add$ 9 z _m times z x makes l9kage4 ,inductance1 or ! coeffici5t ( self-induction is ! capacity :i* an electric circuit has ( produc+ induction )9 itself4 ,inductance is consid]$ z ! ratio betwe5 ! total induction ?r\gh a circuit to ! curr5t produc+ x4 ,ques4 ,:at is ! unit ( inductance8 ,ans4 ,! h5ry4 ,ques4 ,def9e ! h5ry4 ,ans4 ,a coil has an inductance ( "o h5ry :5 ! product ( ! numb] ( l9es enclos$ by ! coil multipli$ by ! numb] ( turns 9 ! coil1 :5 a curr5t ( "o amp]e is fl[+ 9 ! coil1 is equal to #ajj1jjj1jjj or #aj4 ,an inductance ( "o h5ry exi/s 9 a circuit :5 a curr5t *ang+ at ! rate ( "o amp]e p] second induces a pressure ( "o volt 9 ! circuit4 ,ques4 ,:at is ! h5ry call$8 ,ans4 ,! coeffici5t ( self-induction4 ,illu/ration3 ,,fig4 #a1bfg4--;,diagram illu/rat+ ! h5ry4 ,by def9ition3 ,a circuit has an inductance ( "o h5ry :5 a rate ( *ange ( curr5t ( "o amp]e p] second induces a pressure ( "o volt4 ,9 ! diagram x is assum$ t ! int]nal resi/ance ( ! cell & resi/ance ( ! connect+ wires are z]o4 ,! h5ry is ! coeffici5t by :i* ! "t rate ( *ange ( ! curr5t 9 ! circuit mu/ be multipli$1 9 ord] to give ! pressure ( self-induction 9 ! circuit4 ,! =mula = ! h5ry is z foll[s3 magnetic flux turns h5rys --------------------- curr5t #ajj1jjj1jjj or ,n ,t ,l ----- 7#a7 #aj :]e ,l coeffici5t ( self induction 9 h5rys2 ,n total numb] ( l9es ( =ce ?read+ a coil :5 ! curr5t is "o amp]e2 ,t numb] ( turns ( coil4 ,if a coil _h a coeffici5t ( self-induction ( "o h5ry1 x w\ld mean t if ! coil _h "o turn1 "o amp]e w\ld set up #ajj1jjj1jjj1 or #aj1 l9es ?r\gh x4 ,illu/ration3 ,,figs4 #a1bfh to #a1bgj4--,v>i\s coils4 ,! inductance effect1 ?\gh p]ceptible 9 an air core coil1 fig4 #a1bfh1 may be greatly int5sifi$ by ins]t+ a core made ( num]\s pieces ( iron wire1 z 9 fig4 #a1bfi4 ,fig4 #a1bgj %[s a non-inductive coil4 ,:5 w\nd 9 ?is mann]1 a coil w h little or no inductance because ea* half ( ! coil neutralizes ! magnetic effect ( ! o!r4 ,?is coil1 ?\gh non-inductive1 w h capacity4 ,x w\ld be useless = sol5oids or electromagnets1 z x w\ld h no magnetic field4 ,! h5ry#b is too l>ge a unit = use 9 practical computations1 :i* involves t ! millih5ry1 or _/? h5ry1 is ! accept$ unit4 ,9 pole susp5d$ l9es ! inductance v>ies z ! metallic resi/ance1 ! di/ance betwe5 ! wires on ! cross arm & ! numb] ( cycles p] second1 z indicat$ by accept$ tables4 ,?us1 = "o mile ( ,no4 #h ,b4 ,s4 copp] wire1 ) a resi/ance ( #c1djf ohms1 ! coeffici5t ( self-induction ) #f in*es betwe5 c5t]s is 4#jjaec1 &1 ) #ab in*es1 4#jjage4 #b ,,note4--,! ,am]ican physici/1 ,joseph ,h5ry1 0 born 9 #agih & di$ #ahgh4 ,he 0 not$ = 8 rese>*es 9 electromagnetism4 ,he develop$ ! electromagnet1 :i* _h be5 inv5t$ by ,/urgeon 9 ,engl&1 s t x became an in/rum5t ( f> great] p[] ?an be=e4 ,9 #ahca1 he employ$ a mile ( f9e copp] wire ) an electromagnet1 caus+ ! curr5t to attract ! armature & /rike a bell1 !reby e/abli%+ ! pr9ciple employ$ 9 mod]n telegraph practice4 ,he 0 made a pr(essor at ,pr9ceton 9 #ahcb1 & :ile exp]im5t+ at t "t1 he devis$ an arrangem5t ( batt]ies & electromagnets embody+ ! pr9ciple ( ! telegraph relay :i* made possible long di/ance transmission4 ,he 0 ! fir/ to obs]ve magnetic self-induction1 & p]=m$ important inve/igations 9 oscillat+ electric dis*>ges 7#ahdb71 & o!r electrical ph5om5a4 ,9 #ahdf he 0 *os5 secret>y ( ! ,smi?sonian ,in/itution at ,wa%+ton1 an (fice :i* he held until 8 dea?4 ,z *airman ( ! ,u4 ,s4 ,ligh?\se ,bo>d1 he made important te/s 9 m>9e signals & lights4 ,9 meteorology1 t]re/rial magnetism1 & ac\/ics1 he c>ri$ on important rese>*es4 ,h5ry enjoy$ an int]national reputation1 & is ackn[l$g$ to be "o ( ,am]ica's greate/ sci5ti/s4 ,illu/ration3 ,,fig4 #a1bga4--;,hydraulic-me*anical analogy illu/rat+ inductance 9 an alt]nat+ curr5t circuit4 ,! two cyl9d]s are connect$ at _! ends by ! v]tical pipes1 ea* be+ provid$ ) a pi/on & ! sy/em fill$ ) wat]4 ,reciprocat+ motion is imp>t$ to ! l[] pulley by ,scot* yoke connection ) ! drive pulley4 ,! upp] pi/on is connect$ by rack & p9ion ge> ) a fly :eel4 ,9 op]ation1 ! to & fro movem5t ( ! l[] pi/on produces an alt]nat+ fl[ ( wat] 9 ! upp] cyl9d] :i* causes ! upp] pi/on to move back & =?4 ,! rack & p9ion connection ) ! fly :eel causes ! latt] to revolve fir/ 9 "o direction1 !n 9 ! o!r1 9 /ep ) ! upp] pi/on4 ,! in]tia ( ! fly :eel causes x to resi/ any *ange 9 its /ate1 :e!r x be at re/ or 9 motion1 :i* is transmitt$ to ! upp] pi/on1 caus+ x to (f] resi/ance to any *ange 9 its rate or direction ( motion4 ,inductance 9 ! alt]nat+ curr5t circuit has precisely ! same effect1 t is1 x opposes any *ange 9 ! /r5g? or direction ( ! curr5t4 ,ques4 ,h[ does ! inductance ( a coil v>y ) respect to ! core8 ,ans4 ,x is lea/ ) an air core2 ) an iron core1 x is great] 9 proportion to ! p]meability#c ( ! iron4 #c ,,note4--,! p]meability ( iron v>ies f #ejj to #a1jjj or m4 ,! p]meability ( a giv5 sample ( iron is n con/ant1 b decreases 9 value z ! magnetiz+ =ce increases4 ,!re=e ! inductance ( a coil hav+ an iron core is n a con/ant quantity z is ! inductance ( an air core coil4 ,! coeffici5t ,l = a giv5 coil is a con/ant quantity s long z ! magnetic p]meability ( ! mat]ial surr\nd+ ! coil does n *ange4 ,?is is ! case :]e ! coil is surr\nd$ by air4 ,:5 iron is pres5t1 ! coeffici5t ,l is practically con/ant1 provid$ ! magnetism is n =c$ too high4 ,9 mo/ cases aris+ 9 practice1 ! coeffici5t ,l may be consid]$ to be a con/ant quantity1 j z ! resi/ance ,r is usually consid]$ con/ant4 ,! coeffici5t ,l ( a coil or circuit is (t5 spok5 ( z its inductance4 ,illu/ration3 ,,fig4 #a1bgb4--;,exp]im5t %[+ effect ( inductive & non-inductive coils 9 alt]nat+ curr5t circuit4 ,! app>atus is connect$ up z %[n2 by means ( ! swit*1 ! lamp may be plac$ 9 p>allel ) ei!r ! inductive or non-inductive coil4 ,^! coils %\ld h ! same resi/ance4 ,pass an alt]nat+ curr5t ?r\gh ! lamp & non-inductive coil1 ( su* /r5g? t ! lamp w be dimly light$4 ,n[ turn ! swit* s z to put ! lamp & inductive coil 9 p>allel & ! lamp w burn ) increas$ brilliancy4 ,! reason = ?is is because ( ! opposition (f]$ by ! inductive coil to ! curr5t1 less curr5t is %unt$ f ! lamp :5 ! inductive coil is 9 ! circuit ?an :5 ! non-inductive coil is 9 ! circuit4 ,t is1 ea* coil has ! same ohmic resi/ance1 b ! inductive coil has 9 addition ! spuri\s resi/ance due to inductance1 h5ce x %unts less curr5t f ! lamp ?an does ! non-inductive coil4 ,ques4 ,:y is ! iron core ( an inductive coil made ) a numb] ( small wires in/ead ( "o l>ge rod8 ,ans4 ,x is lam9at$ 9 ord] to r$uce eddy curr5ts & consequ5t loss ( en]gy1 & to prev5t excessive heat+ ( ! core4 ,ques4 ,h[ does ! numb] ( turns ( a coil affect ! inductance8 ,ans4 ,! inductance v>ies z ! squ>e ( ! turns4 ,t is1 if ! turns be d\bl$1 ! inductance becomes f\r times z great4 ,! inductance ( a coil is easily calculat$ f ! foll[+ =mul3 ,l #drn 7l #aj7 7#a7 = a ?9 coil ) air core1 & ,l #drn 7l #aj7 7#b7 = a coil hav+ an iron core4 ,9 ! above =mul3 ,l inductance 9 h5rys2 #c4adaf2 r av]age radius ( coil 9 c5timet]s2 n numb] ( turns ( wire 9 coil2 p]meability ( iron core2 l l5g? ( coil 9 c5timet]s4 ,,example4--,an air core coil has an av]age radius ( #aj c5timet]s & is #bj c5timet]s long1 !re be+ #ejj turns1 :at is ! inductance8 ,sub/itut+ ^! values 9 =mula 7#a7 ,l #d 7#c4adaf7 #aj #ejj 7#bj #aj7 4#jjdid h5ry ,ques4 ,is ! answ] 9 ! above example 9 ! cu/om>y =m8 ,ans4 ,no2 ! h5ry be+ a v l>ge unit1 x is usual to express inductance 9 ?\s&?s ( a h5ry1 t is1 9 milli-h5rys4 ,! answ] !n w\ld be 4#jdice #a1jjj #di4ce milli-h5rys4 ,illu/ration3 ,,figs4 #a1bgc to #a1bge4--;,g5]al ,electric *oke coils4 ,fig4 #a1bgc1 h\r glass coil1 #ce1jjj volts2 fig4 #a1bgd1 #d1fjj volt coil2 fig4 #a1bge1 #f1fjj volt coil4 ,a *oke coil is a coil ) l>ge inductance & small resi/ance1 us$ to imp$e alt]nat+ curr5ts4 ,! *oke coil is us$ ext5sively z an auxili>y to ! lightn+ arre/]4 ,9 ?is connection ! prim>y objects ( ! *oke coil %\ld be3 #a1 to hold back ! lightn+ di/urbance f ! trans=m] or g5]ator until ! lightn+ arre/] dis*>ges to e>?4 ,if !re be no lightn+ arre/] ! *oke coil evid5tly _c p]=m ?is function4 #b1 to l[] ! frequ5cy ( ! oscillation s t :atev] *>ge gets ?r\gh ! *oke coil w be ( a frequ5cy too l[ to cause a s]i\s drop ( pressure ar\nd ! fir/ turns ( ! end coil 9 ei!r g5]ator or trans=m]4 ,ano!r way ( express+ ?is is f ! /&po9t ( wave front3 a /eep wave front piles up ! pressure :5 x meets an inductance4 ,! second function ( ! *oke coil is1 !n1 to smoo? out ! wave front ( ! surge4 ,! pr9cipal electrical condition to be avoid$ is t ( resonance4 ,! coil %\ld be s arrang$ t if cont9ual surges be set up 9 ! circuit1 a resonant voltage due to ! pres5ce ( ! *oke coil _c build up at ! trans=m] or g5]ator t]m9als4 ,9 ! types %[n above1 ! h\r glass coil has ! foll[+ advantages on high voltages3 #a1 %\ld !re be any arc+ betwe5 adjac5t turns ! coils w re-insulate !mselves1 #b1 !y are me*anically /rong1 & sagg+ is prev5t$ by tap]+ ! coils t[>d ! c5t] turns1 #c1 ! insulat+ supports c be be/ design$ = ! /ra9s :i* !y h to )/&4 ,*oke coils %\ld n be us$ 9 connection ) cable sy/ems4 ,,example4--,an air core coil has an inductance ( #ej milli-h5rys2 if an iron core1 hav+ a p]meability ( #fjj be ins]t$1 :at is ! inductance8 ,! inductance ( ! air core coil w be multipli$ by ! p]meability ( ! iron2 ! inductance !n is increas$ to #ej #fjj #cj1jjj milli-h5rys1 or #cj h5rys4 ,ohmic ,value ( ,inductance4--,! rate ( *ange ( an alt]nat+ curr5t at any po9t express$ 9 degrees is equal to ! product ( #b multipli$ by ! frequ5cy1 ! maximum curr5t1 & ! cos9e ( ! angle ( position 2 t is 7us+ symbols7 rate ( *ange #b;f,icos 4 ,! num]ical value ( ! rate ( *ange is indep5d5t ( its positive or negative sign1 s t ! sign ( ! cos is disreg>d$4 ,illu/ration3 ,,fig4 #a1bgf4--;,inductance exp]im5t ) int]mitt5t direct curr5t4 ,a lamp ,s is connect$ 9 p>allel ) a coil ( fairly f9e wire hav+ a removable iron core1 & ! t]m9als ,t1 ,t' connect$ to a s\rce ( direct curr5t1 a swit* ,m be+ provid$ to int]rupt ! curr5t4 ,! voltage ( ! curr5t & resi/ance ( ! coil are ( su* values t :5 a /eady curr5t is fl[+1 ! lamp filam5t is j p]ceptibly r$4 ,at ! in/ant ( mak+ ! circuit1 ! lamp w mom5t>ily gl[ m brightly ?an :5 ! curr5t is /eady2 on break+ ! circuit ! lamp w mom5t>ily fla% ) great brightness4 ,9 ! fir/ case1 ! rev]se pressure1 due to inductance1 z indicat$ by arr[ b1 w mom5t>ily oppose ! normal pressure 9 ! coil1 s t ! voltage at ! lamp w be mom5t>ily increas$1 & w consequ5tly s5d a mom5t>ily /rong] curr5t ?r\gh ! lamp4 ,on break+ ! ma9 circuit at ,m1 ! field ( ! coil w collapse1 g5]at+ a mom5t>y mu* great] voltage ?an 9 ! fir/ in/ance1 9 ! direction ( arr[ a1 ! lamp w fla% up brightly 9 consequ5ce4 ,! p]iod ( greate/ rate ( *ange is t at :i* cos has ! greate/ value1 & ! maximum value ( a cos9e is :5 ! arc has a value ( z]o degrees or ( #ahj degrees1 its value correspond+1 be+ #a4 7,see fig4 #a1jcg1 page #a1jfh47 ,! pressure due to inductance is equal to ! product ( ! rate ( *ange by ! inductance2 t is1 call+ ! inductance ,l1 ! pressure due to x at ! po9t ( maximum value or ,e #b;f,i ,l 7#a7 ,n[ by ,ohm's law ,e ,,ri 7#b7 = a curr5t ,i1 h5ce sub/itut+ equation 7#b7 9 equation 7#a7 ,,ri #b;f,i ,l f :i*1 divid+ bo? sides by ,i1 & us+ ,x = ,r ,x #b;f,l 7#c7 :i* is ! ohmic equival5t ( inductance4 ,illu/ration3 ,,fig4 #a1bgg4--;,diagram %[+ alt]nat+ circuit conta9+ inductance4 ,=mula = calculat+ ! ohmic value ( inductance or inductance reactance1 is ,x #b;f,l 9 :i* ,x inductance reactance2 #c4adaf2 f frequ5cy2 ,l inductance 9 h5rys 7n milli-h5rys74 ,l #ae milli-h5rys #ae #ajjj 4#jae h5rys4 ,sub/itut+1 ,x #b #c4adaf #ajj 4#jae #i4db ohms4 ,! frequ5cy ( a curr5t be+ ! numb] ( p]iods or waves p] second1 !n1 if ,t ! "t ( a p]iod1 ! frequ5cy ( a curr5t may be obta9$ by divid+ #a second by ! "t ( a p]iod2 t is "o second #a frequ5cy ------------------ --- 7#d7 "t ( "o p]iod ,t sub/itut+ #a _/ ,t = f 9 equation 7#c7 ,l ,x #b - ,t ,illu/ration3 ,,fig4 #a1bgh4--- ,diagram illu/rat+ effect ( capacity 9 an alt]nat+ circuit4 ,consid]+ its action dur+ "o cycle ( ! curr5t1 ! alt]nator fir/ pumps1 say f ,m to ,s2 electricity w be heap$ up1 s to speak1 on ,s1 & a deficit left on ,m1 t is1 ,s w be & ,m-4 ,if ! alt]nator be n[ sudd5ly /opp$1 !re w\ld be a mom5t>y return fl[ ( electricity f ,s to ,m ?r\gh ! alt]nator4 ,if ! alt]nator g on work+1 h[ev]1 x is obvi\s t ! electricity heap$ up on ,s helps or increases ! fl[ :5 ! alt]nator beg9s to pump f ,s to ,m 9 ! second half ( ! cycle1 & :5 ! alt]nator aga9 rev]ses its pressure1 ! *>ge on ,m fl[s r\nd to ,s1 & helps ! ord9>y curr5t4 ,! above circuit is n /rictly analog\s to ! insulat$ plates ( a cond5s]1 b1 z is v]ifi$ 9 practice1 t ) a rapidly alt]nat+ pressure1 ! cond5s] action is n p]ceptibly affect$ if ! cables be connect$ across by "s non-inductive resi/ance z = in/ance inc&esc5t lamps4 ,capacity4--,:5 an electric pressure is appli$ to a cond5s]1 ! curr5t plays 9 & out1 *>g+ ! cond5s] 9 alt]nate directions4 ,z ! curr5t runs 9 at "o side & out at ! o!r1 ! dielectric becomes *>g$1 & tries to dis*>ge itself by sett+ up an oppos+ electric pressure4 ,?is oppos+ pressure rises j z ! *>ge increases4 ,a me*anical analogue is af=d$ by ! b5d+ ( a spr+1 z 9 fig4 #a1bgi1 :i*1 z x is be+ b5t1 ex]ts an oppos+ =ce equal to t appli$1 provid$ ! latt] d n exce$ ! capacity ( ! spr+4 ,ques4 ,:at is ! effect ( capacity 9 an alt]nat+ circuit8 ,ans4 ,x is exactly opposite to t ( inductance1 t is1 x assi/s ! curr5t to rise to its maximum value soon] ?an x w\ld o!rwise4 ,illu/ration3 ,,fig4 #a1bgi4--,me*anical analogy illu/rat+ effect ( capacity 9 an alt]nat+ circuit4 ,if an alt]nat+ twi/+ =ce be appli$ to ! top ,r ( ! spr+ ,s1 ! action ( ! latt] may be tak5 to repres5t capacity1 & ! rotation ( ! :eel ,w1 alt]nat+ curr5t4 ,! twi/+ =ce 7impress$ pressure7 mu/ fir/ be appli$ be=e ! rotation ( ,w 7curr5t7 w beg94 ,! resili5cy or reb\nd+ effect ( ! spr+ w1 9 "t1 cause ! :eel ,w to move 7amp]es7 9 advance ( ! twi/+ =ce 7voltage7 ?us repres5t+ ! curr5t lead+ 9 phase4 ,ques4 ,is x necess>y to h a cont9u\s metallic circuit = an alt]nat+ curr5t8 ,ans4 ,no1 x is possible = an alt]nat+ curr5t to fl[ ?r\gh a circuit :i* is divid$ at "s po9t by insulat+ mat]ial4 ,ques4 ,h[ c ! curr5t fl[ "u su* condition8 ,ans4 ,its fl[ dep5ds on ! capacity ( ! circuit & accord+ly a cond5s] may be ins]t$ 9 ! circuit z 9 fig4 #a1bhf1 ?us int]pos+ an insulat$ gap1 yet p]mitt+ an alt]nat+ fl[ 9 ! metallic portion ( ! circuit4 ,illu/ration3 ,,fig4 #a1bhj4--;,hydraulic analogy illu/rat+ capacity 9 an alt]nat+ curr5t circuit4 ,a *amb] conta9+ a rubb] diaphragm is connect$ to a d\ble act+ cyl9d] & ! sy/em fill$ ) wat]4 ,9 op]ation1 z ! pi/on moves1 say to ! left f ! c5t]1 ! diaphragm is displac$ f its neutral position ,n1 & /ret*$ to "s position ,m1 9 s do+ (f]+ increas+ resi/ance to ! fl[ ( wat]4 ,on ! return /roke ! fl[ is rev]s$ & is assi/$ by ! diaphragm dur+ ! fir/ half ( ! /roke1 & oppos$ dur+ ! second half4 ,! diaphragm ?us acts ) ! fl[ ( wat] "o-half ( ! "t & 9 opposition to x "o-half ( ! "t4 ,?is corresponds to ! electrical pressure at ! t]m9als ( a cond5s] connect$ 9 an alt]nat+ curr5t circuit1 & x has a maximum value :5 ! curr5t is z]o & a z]o value :5 ! curr5t is a maximum4 ,ques4 ,"n ! unit ( capacity & def9e x4 ,ans4 ,! unit ( capacity is call$ ! f>ad & its symbol is ,c4 ,a cond5s] is said to h a capacity ( "o f>ad if "o c\lomb 7t is1 "o amp]e fl[+ "o second71 :5 /or$ on ! plates ( ! cond5s] w cause a pressure ( "o volt across its t]m9als4 ,! f>ad be+ a v l>ge unit1 ! capacities ord9>ily enc\nt]$ 9 practice are express$ 9 million?s ( a f>ad1 t is1 9 micr(>ads--a capacity equal to ab\t ?ree miles ( an ,atlantic cable4 ,x %\ld be not$ t ! micr(>ad is us$ only = conv5i5ce1 & t 9 work+ out problems1 capacity %\ld always be express$ 9 f>ads be=e sub/itut+ 9 =mul1 because ! f>ad is *os5 ) respect to ! volt & amp]e1 z above def9$1 & h5ce mu/ be us$ 9 =mul along ) ^! units4 ,illu/ration3 ,,fig4 #a1bha--;,diagram illu/rat+ a f>ad4 ,a cond5s] is said to h a capacity ( "o f>ad if x w absorb "o c\lomb ( electricity :5 subject$ to a pressure ( "o volt4 ,! f>ad is a v l>ge unit1 & accord+ly ! micr(>ad or "o million? ( a f>ad is (t5 us$1 ?\gh ?is mu/ be r$uc$ to f>ads be=e sub/itut+ 9 =mul4 ,= in/ance1 a capacity ( #h micr(>ads z giv5 9 a problem w\ld be sub/itut$ 9 a =mula z 4#jjjjjh ( a f>ad4 ,! *>ge ,q =c$ into a cond5s] by a /eady electric pressure ,e is ,q ,,ec 9 :i* ,q *>ge 9 c\lombs2 ,e electric pressure 9 volts2 ,c capacity ( cond5s] 9 f>ads4 ,ques4 ,:at is ! mat]ial betwe5 ! plates ( a cond5s] call$8 ,ans4 ,! dielectric4 ,ques4 ,^u :at does ! capacity ( a cond5s] dep5d8 ,ans4 ,x is proportional to ! area ( ! plates1 & inv]sely proportional to ! ?ickness ( ! dielectric betwe5 ! plates1 a correction be+ requir$ unless ! ?ickness ( dielectric be v small z comp>$ ) ! dim5sions ( ! plates4 ,! capacity ( a cond5s] is also proportional to ! specific inductive capacity ( ! dielectric betwe5 ! plates ( ! cond5s]4 ,illu/ration3 ,,fig4 #a1bhb4--;,cond5s] ( "o micr(>ad capacity4 ,x is subdivid$ into five sections ( 4#e1 4#b1 4#b1 4#je & 4#je micr(>ad4 ,! plates are m\nt$ betwe5 & c>ri$ by lat]al brass b>s :i* are fa/5$ to a h>d rubb] top4 ,ea* pair ( cond5s] t]m9als is fa/5$ to small b9d+ po/s m\nt$ on h>d rubb] insulat$ po/s4 ,specific ,inductive ,capacity4--,f>aday discov]$ t diff]5t sub/ances h diff]5t p[]s ( c>ry+ l9es ( electric =ce4 ,?us ! *>ge ( two conductors hav+ a giv5 diff]5ce ( pressure betwe5 !m dep5ds on ! m$ium betwe5 !m z well z on _! size & %ape4 ,! numb] indicat+ ! magnitude ( ?is prop]ty ( ! m$ium is call$ its specific inductive capacity1 or dielectric con/ant4 ,! specific inductive capacity ( air1 :i* is ne>ly ! same z t ( a vacuum1 is tak5 z unity4 ,9 t]ms ( ?is unit ! foll[+ are "s typical values ( ! dielectric con/ant3 wat] #hj1 glass #f to #aj1 mica #f4g1 gutta-p]*a #c1 ,india rubb] #b4e1 p>aff9 wax #b1 ebonite #b4e1 ca/or oil #d4h4 ,9 und]gr\nd cables = v high pressures1 ! insulation1 if homog5e\s ?r\gh\t1 w\ld h to be ( v great ?ickness 9 ord] to h suffici5t dielectric /r5g?4 ,by employ+ mat]ial ( high specific inductive capacity close to ! conductor1 & mat]ial ( l[] specific inductive capacity t[>d ! outside1 t is1 by grad+ ! insulation1 a consid]ably less total ?ickness af=ds equally high dielectric /r5g?4 ,illu/ration3 ,,fig4 #a1bhc4--,p>allel connection ( cond5s]s4 ,l t]m9als are jo9$ toge!r4 ,! jo9t capacity ( su* arrangem5t is equal to ! sum ( ! respective capacities1 t is ,c c c' c4 ,ques4 ,h[ are capacity te/s usually made8 ,ans4 ,by ! aid ( /&>d cond5s]s4 ,ques4 ,h[ are cond5s]s connect$8 ,ans4 ,!y may be connect$ 9 p>allel z 9 fig4 #a1bhc1 or 9 s]ies 7cascade7 z 9 fig4 #a1bhd4 ,cond5s]s are n[ con/ruct$ s t ! two me?ods ( arrang+ ! plates may conv5i5tly be comb9$ 9 "o cond5s]1 !reby obta9+ a wid] range ( capacity4 ,ques4 ,h[ may ! capacity ( a cond5s]1 wire1 or cable be te/$8 ,ans4 ,?is may be done by ! aid ( a /&>d cond5s]1 trigg] key1 & an a/atic or balli/ic galvanomet]4 ,9 mak+ ! te/1 fir/ obta9 a con/ant by not+ ! deflection d1 due to ! dis*>ge ( ! /&>d cond5s] aft] a *>ge (1 say1 #aj seconds f a giv5 voltage4 ,!n dis*>ge ! o!r cond5s]1 wire1 or cable ?r\gh ! galvanomet] aft] #aj seconds *>ge1 & note ! deflection d'4 ,! capacity ,c' ( ! latt] is !n d' ,c' ,c ---- d 9 :i* ,c is ! capacity ( ! /&>d cond5s]4 ,illu/ration3 ,,fig4 #a1bhd4--,s]ies or cascade connection ( cond5s]s4 ,unlike t]m9als are jo9$ toge!r z %[n4 ,! total capacity ( su* connection is equal to ! reciprocal ( ! sum ( ! reciprocals ( ! sev]al capacities1 t is1 ,c #a 7#a _/ c #a _/ c' #a _/ c7 ,ohmic ,value ( ,capacity4--,! capacity ( an alt]nat+ curr5t circuit is ! measure ( ! am\nt ( electricity held by x :5 its t]m9als are at unit diff]5ce ( pressure4 ,e su* circuit acts z a cond5s]4 ,if an alt]nat+ circuit1 hav+ no capacity1 be op5$1 no curr5t c be produc$ 9 x1 b if !re be capacity at ! break1 curr5t may be produc$ z 9 fig4 #a1bhf4 ,! action ( capacity ref]r$ to ! curr5t wave is z foll[s3 ,z ! wave />ts f z]o value & rises to its maximum value1 ! curr5t is due to ! dis*>ge ( ! capacity1 :i* w\ld be repres5t$ by a cond5s]4 ,9 ! case ( a s9e curr5t1 ! p]iod requir$ = ! curr5t to pass f z]o value to maximum is "o-qu>t] ( a cycle4 ,illu/ration3 ,,figs4 #a1bhe & #a1bhf4--;,diagrams %[+ effect ( cond5s] 9 direct & alt]nat+ curr5t circuits4 ,ea* circuit conta9s an inc&esc5t lamp & a cond5s]1 "o circuit connect$ to a dynamo & ! o!r to an alt]nator4 ,s9ce ! cond5s] int]poses a gap 9 ! circuit1 evid5tly 9 fig4 #a1bhe no curr5t w fl[4 ,9 ! case ( alt]nat+ curr5t1 fig4 #a1bhf1 ! cond5s] gap does n h9d] ! fl[ ( curr5t 9 ! metallic portion ( ! circuit4 ,9 fact ! alt]nator produces a cont9ual surg+ ( electricity backw>ds & =w>ds f ! plates ( ! cond5s] ar\nd ! metallic portion ( ! circuit1 simil> to ! surg+ ( waves aga9/ a bulkhead :i* projects into ! ocean4 ,x %\ld be und]/ood t ! electric curr5t ceases at ! cond5s]1 !re be+ no fl[ betwe5 ! plates4 ,at ! beg9n+ ( ! cycle1 ! cond5s] is *>g$ to ! maximum am\nt x receives 9 ! op]ation ( ! circuit4 ,at ! end ( ! qu>t] cycle :5 ! curr5t is ( maximum value1 ! cond5s] is completely dis*>g$4 ,! cond5s] n[ beg9s to receive a *>ge1 & cont9ues to receive x dur+ ! next qu>t] ( a cycle1 ! *>ge atta9+ its maximum value :5 ! curr5t is ( z]o int5sity4 ,h5ce1 ! maximum *>ge ( a cond5s] 9 an alt]nat+ circuit is equal to ! av]age value ( ! curr5t multipli$ by ! "t ( *>ge1 :i* is "o-qu>t] ( a p]iod1 t is maximum *>ge av]age curr5t p]iod 7#a7 ,illu/ration3 ,,fig4 #a1bhg4--;,diagram %[+ alt]nat+ circuit conta9+ capacity4 ,=mula = calculat+ ! ohmic value ( capacity or capacity reactance is ,xc #a #b;f,c1 9 :i* ,xc capacity reactance2 #c4adaf2 f frequ5cy2 ,c capacity 9 f>ads 7n micr(>ads74 #bb micr(>ads #bb #a1jjj1jjj 4#jjjjbb f>ad4 ,sub/itut+1 ,xc #a 7#b #c4adaf #ajj 4#jjjjbb7 #gb4d ohms4 ,s9ce ! "t ( a p]iod #a frequ5cy1 ! "t ( "o-qu>t] ( a p]iod is 7#a frequ5cy71 or p]iod f 7#b7 f1 be+ ! symbol = frequ5cy4 ,sub/itut+ 7#b7 9 7#a7 maximum *>ge ,i f 7#c7 ,! pressure ( a cond5s] is equal to ! quoti5t ( ! *>ge divid$ by ! capacity1 t is *>ge cond5s] pressure -------- 7#d7 capacity ,sub/itut+ 7#c7 9 7#d7 #a ,i cond5s] pressure 7,i ----7 ,c ----- 7#e7 #d;f #d;f,c ,b1 ,i ,i #b _/ 1 & sub/itut+ ?is value ( ,i 9 equation 7#e7 gives ,i #b _/ ,i cond5s] pressure ----------- ------ 7#f7 #d;f,c #b;f,c ,?is la/ equation 7#f7 repres5ts ! cond5s] pressure due to capacity at ! po9t ( maximum value1 :i* pressure is oppos$ to ! impress$ pressure1 t is1 x is ! maximum rev]se pressure due to capacity4 ,n[1 s9ce by ,ohm's law ,e ,i ---1 or ,e ,i ,r ,r & z ,i #a ------ ,i ------ #b;f,c #b;f,c x foll[s t #a _/ 7#b;f,c7 is ! ohmic value ( capacity1 t is x expresses ! resi/ance equival5t ( capacity2 us+ ! symbol ,xc = capacity reactance #a ,xc ------- 7#g7 #b;f,c ,,example4--,:at is ! resi/ance equival5t ( a #ej micr(>ad cond5s] to an alt]nat+ curr5t hav+ a frequ5cy ( #ajj8 ,sub/itut+ ! giv5 values 9 ! expression = ohmic value #a #a #a ,xc ------ -------------------------- ------- #ca4h ohms4 #b;f,c #b #c4adaf #ajj 4#jjjjej 4#jcadaf ,if ! pressure ( ! supply be1 say #ajj volts1 ! curr5t w\ld be #ajj #ca4h #c4ad amp]es4 ,illu/ration3 ,,fig4 #a1bhh4--,pressure & curr5t curves1 illu/rat+ lag4 ,! effect ( inductance 9 a circuit is to ret>d ! curr5t cycle1 t is to say1 if ! curr5t & pressure be 9 phase1 ! introduction ( inductance w cause a phase diff]5ce1 ! curr5t wave lagg+ beh9d ! pressure wave z %[n4 ,9 o!r words1 inductance causes ! curr5t wave1 indicat$ 9 ! diagram by ! solid curve1 to lag beh9d ! pressure wave1 indicat$ by ! dott$ curve4 ,foll[+ ! curves />t+ f ! left end ( ! horizontal l9e1 x w be not$ t ! curr5t />ts aft] ! pressure />ts & rev]ses aft] ! pressure rev]ses2 t is1 ! curr5t lags 9 phase beh9d ! pressure1 al?\gh ! frequ5cy ( bo? is ! same4 ,lag & ,lead4--,alt]nat+ curr5ts d n always keep 9 /ep ) ! alt]nat+ volts impress$ ^u ! circuit4 ,if !re be inductance 9 ! circuit1 ! curr5t w lag2 if !re be capacity1 ! curr5t w lead 9 phase4 ,= example1 fig4 #a1bhh1 illu/rates ! lag due to inductance & fig4 #a1bhi1 ! lead due to capacity4 ,ques4 ,:at is lag8 ,ans4 ,lag d5otes ! condition :]e ! phase ( "o alt]nat+ curr5t quantity lags beh9d t ( ano!r4 ,! t]m is g5]ally us$ 9 connection ) ! effect ( inductance 9 caus+ ! curr5t to lag beh9d ! impress$ pressure4 ,illu/ration3 ,,fig4 #a1bhi4--,pressure & curr5t curves illu/rat+ lead4 ,! effect ( capacity 9 a circuit is to cause ! curr5t to rise to its maximum value soon] ?an x w\ld o!rwise d2 capacity produces an effect exactly ! opposite ( inductance4 ,! phase relation betwe5 curr5t & pressure ) curr5t lead+ is %[n graphically by ! two armature positions 9 full & dott$ l9es1 correspond+ respectively to curr5t & pressure at ! beg9n+ ( ! cycle4 ,ques4 ,h[ does inductance cause ! curr5t to lag beh9d ! pressure8 ,ans4 ,x t5ds to prev5t *anges 9 ! /r5g? ( ! curr5t4 ,:5 two p>ts ( a circuit are ne> ea* o!r1 s t "o is 9 ! magnetic field ( ! o!r1 any *ange 9 ! /r5g? ( ! curr5t causes a correspond+ *ange 9 ! magnetic field & sets up a rev]se pressure 9 ! o!r wire4 ,?is induc$ pressure causes ! curr5t to rea* its maximum value a little lat] ?an ! pressure1 & also t5ds to prev5t ! curr5t dim9i%+ 9 /ep ) ! pressure4 ,ques4 ,:at gov]ns ! am\nt ( lag 9 an alt]nat+ curr5t8 ,ans4 ,x dep5ds on ! relative values ( ! v>i\s pressures 9 ! circuit1 t is1 ^u ! am\nt ( resi/ance & inductance :i* t5ds to cause lag1 & ! am\nt ( capacity 9 ! circuit :i* t5ds to r$uce lag & cause lead4 ,ques4 ,h[ is lag measur$8 ,ans4 ,9 degrees4 ,illu/ration3 ,,fig4 #a1bij4--,me*anical analogy ( lag4 ,if at "o end =ce be appli$ to turn a v long %aft1 hav+ a load$ pulley at ! o!r1 ! torsion ?us produc$ 9 ! %aft w cause x to twi/ an appreciable am\nt :i* w cause ! movem5t ( ! pulley to lag beh9d t ( ! crank4 ,?is may be indicat$ by a rod atta*$ to ! pulley & t]m9at+ 9 a po9t] at ! crank end1 ! rod be+ s plac$ t ! po9t] regi/]s ) ! crank :5 !re is no torsion 9 ! %aft4 ,! angle made by ! po9t] & crank :5 ! load is ?r[n on1 indicates ! am\nt ( lag :i* is measur$ 9 degrees4 ,?us1 9 fig4 #a1bhh1 ! lag is indicat$ by ! di/ance betwe5 ! beg9n+ ( ! pressure curve & ! beg9n+ ( ! curr5t curve1 & is 9 ?is case #de4 ,ques4 ,:at is ! physical mean+ ( ?is8 ,ans4 ,9 an actual alt]nator1 ( :i* fig4 #a1bhh is an elem5t>y diagram %[+ "o coil1 if ! curr5t lag1 say #de beh9d ! pressure1 x means t ! coil rotates #de f its position ( z]o induction be=e ! curr5t />ts1 z 9 fig4 #a1bhh4 ,,example ,i4--,a circuit ?r\gh :i* an alt]nat+ curr5t is pass+ has an inductance ( #f ohms & a resi/ance ( #b4e ohms4 ,:at is ! angle ( lag8 ,illu/ration3 ,,fig4 #a1bia4--;,diagram ( circuit = example ,i4 ,sub/itut+ ^! values 9 equation 7#a71 page #a1jec1 #f tan --- #b4d #b4e ,ref]r+ to ! table ( natural s9es & tang5ts on page #dea ! correspond+ angle is approximately #fg4 ,,example ,,ii4--,a circuit has a resi/ance ( #b4c ohms & an inductance ( 4#jjcd h5ry4 ,if an alt]nat+ curr5t hav+ a frequ5cy ( #abe pass ?r\gh x1 :at is ! angle ( lag8 ,illu/ration3 ,,fig4 #a1bib4--;,diagram ( circuit = example ,,ii4 ,"h ! inductance is giv5 z a fraction ( a h5ry2 ?is mu/ be r$uc$ to ohms by sub/itut+ 9 equation 7#c71 page #a1jch1 :i* gives ! ohmic value ( ! inductance2 accord+ly1 sub/itut+ ! above giv5 value 9 ?is equation inductance 9 ohms or ,x #b #abe 4#jjcd #b4fg ,sub/itut+ ?is result & ! giv5 resi/ance 9 equation 7#a71 page #a1jec1 #b4fg tan ---- #a4af #b4c ! ne>e/ angle f table 7page #dea7 is #di4 ,ques4 ,h[ great may ! angle ( lag be8 ,ans4 ,any?+ up to #ij4 ,! angle ( lag1 indicat$ by ! ,greek lett] 7phi71 is ! angle ^: tang5t is equal to ! quoti5t ( ! inductance express$ 9 ohms or spuri\s resi/ance divid$ by ! ohmic resi/ance1 t is reactance #b;f,l tan ---------- ------ 7#a7 resi/ance ,r ,illu/ration3 ,,fig4 #a1bic4--,/eam eng9e analogy ( curr5t fl[ at z]o pressure 7see que/ions bel[74 ,:5 ! eng9e has rea*$ ! dead c5t] po9t ! full /eam pressure is act+ on ! pi/on1 ! valve hav+ op5$ an am\nt equal to its lead4 ,! =ce appli$ at ?is in/ant1 indicat$ by ! arr[ is p]p5dicul> to ! crank p9 circle1 t is1 ! tang5tial or turn+ compon5t is equal to z]o1 h5ce !re is no pressure t5d+ to turn ! crank4 ,! latt] cont9ues 9 motion pa/ ! dead c5t] because ( ! mom5tum previ\sly acquir$4 ,simil>ly1 ! electric curr5t1 :i* is "h analog\s to ! mov+ crank1 cont9ues 9 motion1 ?\gh ! pressure at "s in/ants be z]o1 because x acts z ?\gh x _h weight1 t is1 x _c be /opp$ or />t$ in/antly4 ,ques4 ,:5 an alt]nat+ curr5t lags beh9d ! pressure1 is !re n a consid]able curr5t at times :5 ! pressure is z]o8 ,ans4 ,yes2 su* effect is illu/rat$ by analogy 9 fig4 #a1bic4 ,ques4 ,:at is ! significance ( ?is8 ,ans4 ,x does n mean t curr5t c\ld be obta9$ f a circuit t %[$ no pressure :5 te/$ ) a suitable voltmet]1 = no curr5t w\ld fl[ "u su* conditions4 ,h[ev]1 9 ! fl[ ( an alt]nat+ curr5t1 ! pressure v>ies f z]o to maximum values _m times ea* second1 & ! in/ants ( no pressure may be comp>$ to ! dead c5t]s ( an eng9e at :i* po9ts !re is no pressure to cause rotation ( ! crank1 ! crank be+ c>ri$ pa/ ^! po9ts by ! mom5tum ( ! fly :eel4 ,simil>ly ! electric curr5t does n /op at ! in/ant ( no pressure because ( ! mom5tum acquir$ at o!r p>ts ( ! cycle4 ,ques4 ,on long l9es hav+ consid]able inductance1 h[ may ! lag be r$uc$8 ,ans4 ,by introduc+ capacity into ! circuit4 ,9 fact1 ! curr5t may be advanc$ s x w be 9 phase ) ! pressure or ev5 lead ! latt]1 dep5d+ on ! am\nt ( capacity introduc$4 ,!re has be5 "s objection to ! t]m lead z us$ 9 describ+ ! effect ( capacity 9 an alt]nat+ circuit1 pr9cipally on ! gr\nd t su* expressions z lead ( curr5t1 lead 9 phase1 etc41 t5d to convey ! idea t ! effect prec$es ! cause1 t is1 ! curr5t is 9 advance ( ! pressure produc+ x4 ,!re c1 ( c\rse1 be no curr5t until pressure has be5 appli$1 b if ! circuit has capacity1 x w lead ! pressure1 & ?is peculi> behavior is be/ illu/rat$ by a me*anical analogy z has already be5 giv54 ,ques4 ,:at effect has lag or lead on ! value ( ! effective curr5t8 ,ans4 ,z ! angle ( lag or lead increases1 ! value ( ! effective z comp>$ ) ! virtual curr5t dim9i%es4 ,reactance4--,! t]m reactance means simply reaction4 ,x is us$ to express c]ta9 effects ( ! alt]nat+ curr5t o!r ?an t due to ! ohmic resi/ance ( ! circuit4 ,?us1 inductance reactance means ! reaction due to ! spuri\s resi/ance ( inductance express$ 9 ohms2 simil>ly1 capacity reactance1 means ! reaction due to capacity1 express$ 9 ohms4 ,x %\ld be not$ t ! t]m reactance1 alone1 t is1 unqualifi$1 is g5]ally und]/ood to mean inductance reactance1 ?\gh ill advis$ly s4 ,! resi/ance (f]$ by a wire to ! fl[ ( a direct curr5t is express$ 9 ohms2 ?is resi/ance rema9s con/ant :e!r ! wire be /raight or coil$4 ,if an alt]nat+ curr5t fl[ ?r\gh ! wire1 !re is 9 addition to ! ord9>y or ohmic resi/ance ( ! wire1 a spuri\s resi/ance aris+ f ! developm5t ( a rev]se pressure due to induction1 :i* is m or less 9 value accord+ z ! wire be coil$ or /raight4 ,?is spuri\s resi/ance z di/+ui%$ f ! ohmic resi/ance is call$ ! reactance1 & is express$ 9 ohms4 ,reactance1 may !n be def9$ ) respect to its usual significance1 t is1 inductance reactance1 z ! compon5t ( ! imp$ance :i* :5 multipli$ into ! curr5t1 gives ! wattless compon5t ( ! pressure4 ,reactance is simply inductance measur$ 9 ohms4 ,illu/ration3 ,,fig4 #a1bid4--;,diagram ( ! circuit = example ,i4 ,"h ! resi/ance is tak5 at z]o1 b ?is w\ld n be possible 9 practice1 z all circuits conta9 m or less resi/ance ?\gh x may be1 9 "s cases1 negligibly small4 ,,example ,i4--,an alt]nat+ curr5t hav+ a frequ5cy ( #fj is pass$ ?r\gh a coil ^: inductance is 4#e h5ry4 ,:at is ! reactance8 ,"h f #fj & ,l 4#e2 sub/itut+ ^! 9 =mula = inductive reactance1 ,x #b;f,l #b #c4adaf #fj 4#e #ahh4e ohms ,! quantity #b;f,l or reactance be+ ( ! same nature z a resi/ance is us$ 9 ! same way z a resi/ance4 ,accord+ly1 s9ce1 by ,ohm's law ,e ,,ri 7#a7 an expression may be obta9$ = ! volts necess>y to ov]come reactance by sub/itut+ 9 equation 7#a7 ! value ( reactance giv5 above1 ?us ,e #b;f,,li 7#b7 ,illu/ration3 ,,fig4 #a1bie4--;,diagram ( circuit = example ,,ii4 ,z 9 example ,i1 resi/ance is disreg>d$4 ,,example ,,ii4--,h[ _m volts are necess>y to =ce a curr5t ( #c amp]es ) frequ5cy #fj ?r\gh a coil ^: inductance is 4#e h5ry8 ,sub/itut+ 9 equation 7#b7 ! values "h giv5 ,e #b;f,,li #b #fj 4#e #c #efe volts4 ,! =ego+ example may s]ve to illu/rate ! diff]5ce 9 behavi\r ( direct & alt]nat+ curr5ts4 ,z calculat$1 x requires #efe volts to pass only #c amp]es ( alt]nat+ curr5t ?r\gh ! coil on acc\nt ( ! consid]able spuri\s resi/ance4 ,! ohmic resi/ance ( a coil is v small1 z comp>$ ) ! spuri\s resi/ance1 say #b ohms4 ,!n by ,ohm's law ,i ,e ,r #efe #b #bhb4e amp]es4 ,in/ances ( ?is effect are commonly met ) 9 connection ) trans=m]s4 ,s9ce ! prim>y coil ( a trans=m] has a high reactance1 v little curr5t w fl[ :5 an alt]nat+ pressure is appli$4 ,if ! same trans=m] 7 plac$ 9 a direct curr5t circuit & ! curr5t turn$ on x w\ld at once burn out1 z v little resi/ance w\ld be (f]$ & a l>ge curr5t w\ld pass ?r\gh ! w9d+4 ,illu/ration3 ,,fig4 #a1bif4--;,diagram ( circuit = example ,,iii4 ,,example ,,iii4--,9 a circuit conta9+ only capacity1 :at is ! reactance :5 curr5t is suppli$ at a frequ5cy ( #ajj1 & ! capacity is #ej micr(>ads8 #a #ej micr(>ads #ej --------- 4#jjjje f>ad #a1jjj1jjj capacity reactance1 or #a #a ,xc ------ ------------------------- #ca4hd ohms #b;f,c #b #c4adaf #ajj 4#jjjje ,imp$ance4--,?is t]m1 /rictly speak+1 means ! ratio ( any impress$ pressure to ! curr5t :i* x produces 9 a conductor4 ,x may be fur!r def9$ z ! total opposition 9 an electric circuit to ! fl[ ( an alt]nat+ curr5t4 ,all p[] circuits = alt]nat+ curr5t are calculat$ ) ref]5ce to imp$ance4 ,! imp$ance may be call$ ! comb9ation (3 #a4 ,ohmic resi/ance2 #b4 ,inductance reactance2 #c4 ,capacity reactance4 ,! imp$ance ( an inductive circuit :i* does n conta9 capacity is equal to ! squ>e root ( ! sum ( ! squ>es ( ! resi/ance & reactance1 t is imp$ance 7resi/ance reactance7 7#a7 ,illu/ration3 ,,fig4 #a1big4--;,diagram %[+ alt]nat+ circuit conta9+ resi/ance1 inductance1 & capacity4 ,=mula = calculat+ ! imp$ance ( ?is circuit is ,z 7,r 7,x - ,xc77 9 :i*1 ,z imp$ance2 ,r resi/ance2 ,x inductance reactance2 ,xc capacity reactance4 ,example3 ,:at is ! imp$ance :5 ,r #d1 ,x #id4b1 & ,xc #gb4d8 ,sub/itut+ ,z 7#d 7#id4b - #gb4d77 #bb4b ohms4 ,:]e ! ohmic values ( inductance & capacity are giv5 z 9 ?is example1 ! calculation ( imp$ance is v simple1 b :5 inductance & capacity are giv5 9 milli-h5rys & micr(>ads respectively1 x is necess>y to fir/ calculate _! ohmic values z 9 figs4 #a1bie & #a1bif4 ,,example ,i4--,if an alt]nat+ pressure ( #ajj volts be impress$ on a coil ( wire hav+ a resi/ance ( #f ohms & inductance ( #h ohms1 :at is ! imp$ance ( ! circuit & h[ _m amp]es w fl[ ?r\gh ! coil8 ,9 ! example "h giv51 #f ohms is ! resi/ance & #h ohms ! reactance4 ,sub/itut+ ^! 9 equation 7#a7 ,imp$ance 7#f #h7 7#ajj7 #aj ohms4 ,! curr5t 9 amp]es :i* w fl[ ?r\gh ! coil is1 by ,ohm's law us+ imp$ance 9 ! same way z resi/ance4 volts #ajj volts curr5t --------- --------- #aj amp]es4 imp$ance #aj ohms ,! reactance is n always giv5 b in/ead 9 "s problems ! frequ5cy ( ! curr5t & inductance ( ! circuit4 ,an expression to fit su* cases is obta9$ by sub/itut+ #b;f,l = ! reactance z foll[s3 7us+ symbols = imp$ance & resi/ance7 ,z 7,r 7#b;f,l77 7#b7 ,illu/ration3 ,,fig4 #a1bih4--;,diagram ( circuit = example ,,ii4 ,,example ,,ii4--,if an alt]nat+ curr5t1 hav+ a frequ5cy ( #fj1 be impress$ on a coil ^: inductance is 4#je h5ry & ^: resi/ance is #f ohms1 :at is ! imp$ance8 ,"h ,r #f2 f #fj1 & ,l 4#je2 sub/itut+ ^! values 9 7#b7 ,z 7#f 7#b #fj 4#je77 7#cic7 #ai4h ohms4 ,illu/ration3 ,,fig4 #a1bii4--;,diagram ( circuit = example ,,iii4 ,,example ,,iii4--,if an alt]nat+ curr5t1 hav+ a frequ5cy ( #fj1 be impress$ on a circuit ^: inductance is 4#je h5ry1 & ^: capacity reactance is #aj ohms1 :at is ! imp$ance8 ,x #b;f,l #b #c4adaf #fj 4#je #ah4he ohms ,z ,x - ,xc #ah4he - #aj #h4he ohms ,:5 a circuit conta9s besides resi/ance1 bo? inductance & capacity1 ! =mula = imp$ance z giv5 9 equation 7#a71 page #a1jeh1 mu/ be modifi$ to include ! reactance due to capacity1 because1 z expla9$1 inductive & capacity reactances "w 9 opposition to ea* o!r1 9 ! s5se t ! reactance ( inductance acts 9 direct proportion to ! quantity #b;f,l1 & ! reactance ( capacity 9 inv]se proportion to ! quantity #b;f,c4 ,! net reactance due to bo?1 :5 bo? are 9 ! circuit1 is obta9$ by subtract+ "o f ! o!r4 ,illu/ration3 ,,fig4 #a1cjj4--;,diagram ( circuit = example ,,iv4 ,to prop]ly e/imate imp$ance !n1 9 su* circuits1 ! foll[+ equation is us$3 imp$ance 7resi/ance 7inductance reactance - capacity reactance77 or us+ symbols1 ,z 7,r 7,x - ,xc77 7#c7 ,,example ,,iv4--,a curr5t has a frequ5cy ( #ajj4 ,x passes ?r\gh a circuit ( #d ohms resi/ance1 ( #aej milli-h5rys inductance1 & ( #bb micr(>ads capacity4 ,:at is ! imp$ance8 a4 ,! ohmic resi/ance ,r1 is #d ohms4 b4 ,! inductance reactance1 or ,x #b;f,l #b #c4adaf #ajj 4#ae #id4c ohms4 7note t #aej milli-h5rys are r$uc$ to 4#ae h5ry be=e sub/itut+ 9 ! above equation74 ,illu/ration3 ,,fig4 #a1cja4--,simple *ok+ coil4 ,!re is an important diff]5ce 9 ! ob/ruction (f]$ to an alt]nat+ curr5t by ord9>y resi/ance & by reactance4 ,resi/ance ob/ructs ! curr5t by dissipat+ its en]gy1 :i* is conv]t$ into heat4 ,reactance ob/ructs ! curr5t by sett+ up a rev]se pressure1 & s r$uces ! curr5t 9 ! circuit1 )\t wa/+ mu* en]gy1 except by hy/]esis 9 any iron magnetiz$4 ,?is may be reg>d$ z "o ( ! advantages ( alt]nat+ ov] direct curr5t1 =1 by introduc+ reactance into a circuit1 ! curr5t may be cut d[n ) comp>atively little loss ( en]gy4 ,?is is g5]ally done by increas+ ! inductance 9 a circuit1 by means ( a device call$ v>i\sly a reactance coil1 imp$ance coil1 *ok+ coil1 or *ok]4 ,9 ! figure is a coil ( ?ick wire provid$ ) a lam9at$ iron core1 :i* may be ei!r fix$ or movable4 ,9 ! fir/ case1 ! inductance1 & !re=e also ! reactance ( ! coil1 is inv>iable1 ) a giv5 frequ5cy4 ,9 ! second case1 ! inductance & consequ5t reactance may be respectively increas$ or dim9i%$ by ins]t+ ! core f>!r )9 ! coil or by )draw+ x1 z 0 done 9 fig4 #a1bff1 ! results ( :i* are %[n 9 fig4 #a1cjb4 ,illu/ration3 ,,fig4 #a1cjb4--;,imp$ance curve = coil ) v>iable iron core4 ,! imp$ance ( an inductive coil may be increas$ by mov+ an iron wire core into ! coil4 ,9 mak+ a te/ ( ?is k9d1 ! curr5t %\ld be kept con/ant ) an adju/able resi/ance1 & voltmet] read+s tak51 fir/ )\t ! iron core1 & aga9 ) #a1 #b1 #c1 #d1 etc41 in*es ( core ins]t$ 9 ! coil4 ,by plott+ ! voltmet] read+s & ! positions ( ! iron core on section pap] z above1 ! effect ( inductance is cle>ly %[n4 c4 ,! capacity reactance1 or #a #a ,xc ------ -------------------------- #gb4d ohms #b;f,c #b #c4adaf #ajj 4#jjjjbb 7note t #bb micr(>ads are r$uc$ to 4#jjjjbb f>ad be=e sub/itut+ 9 ! =mula4 ,:y8 ,see page #a1jdb74 ,sub/itut+ values z calculat$ 9 equation 7#c71 page #a1jfj4 ,z 7#d 7#id4b - #gb4d77 7#dia7 #bb4b ohms4 ,illu/ration3 ,,fig4 #a1cjc4--;,diagram ( a resonant circuit4 ,a circuit is said to be resonant :5 ! inductance & capacity are 9 su* proportion t ! "o neutralizes ! o!r1 ! circuit !n act+ z ?\gh x conta9$ only resi/ance4 ,9 ! above circuit ,x #b;f,l #b #c4adaf #ajj 4#ja #f4bh ohms2 ,xc #a 7#b #c4adaf #ajj 4#jjjbec7 #f4bh ohms :5ce ! resultant reactance ,x - ,xc #f4bh - #f4bh #j ohms4 ,z 7,r 7,x - ,xc77 7#g #j7 #g ohms4 ,ques4 ,:y is capacity reactance giv5 a negative sign8 ,ans4 ,because x reacts 9 opposition to inductance1 t is x t5ds to r$uce ! spuri\s resi/ance due to inductance4 ,9 circuits hav+ bo? inductance & capacity1 ! tang5t ( ! angle ( lag or lead z ! case may be is ! algebraic sum ( ! two reactances divid$ by resi/ance4 ,if ! sign be positive1 x is an angle ( lag2 if negative1 ( lead4 ,resonance4--,! effects ( inductance & capacity1 z already expla9$1 oppose ea* o!r4 ,if inductance & capacity be pres5t 9 a circuit 9 su* proportion t ! effect ( "o neutralizes t ( ! o!r1 ! circuit acts z ?\gh x 7 purely non-inductive & is said to be 9 a /ate ( resonance4 ,= in/ance1 9 a circuit conta9+ resi/ance1 inductance1 & capacity1 if ! resi/ance be1 say1 #h ohms1 ! inductance #cj1 & ! capacity #cj1 !n ! imp$ance is 7#h 7#cj - #cj77 7#h7 #h ohms4 ,illu/ration3 ,,fig4 #a1cjd4--;,application ( a *ok+ coil to a light+ circuit4 ,! coil is divid$ into sections ) leads runn+ to contacts simil> to a rheo/at4 ,ea* lamp is provid$ ) an automatic %ort-circuit+ cut\t1 & %\ld "o1 two1 or m ( !m fail1 a correspond+ numb] ( sections ( ! *ok+ app>atus is put 9 circuit to take ! place ( ! brok5 lamp or lamps1 & ?us keep ! curr5t con/ant4 ,x mu/ n be suppos$ t ?is arrangem5t ( lamps1 etc4 is a g5]al "o2 x be+ adopt$ to suit c]ta9 special conditions4 ,! =mula = inductance reactance is ,x #b;f,l1 & = capacity reactance1 ,xc #a 7#b;f,c72 accord+ly if capacity & inductance 9 a circuit be equal1 t is1 if ! circuit be resonant #a #b;f,l ------ 7#a7 #b;f,c f :i* #a f ------- 7#b7 #b7;,,cl7 ,ques4 ,:at does equation 7#a7 %[8 ,ans4 ,x indicates t by v>y+ ! frequ5cy 9 ! prop] way z by increas+ or decreas+ ! spe$ ( ! alt]nator1 ! circuit may be made resonant1 ?is condition be+ obta9$ :5 ! frequ5cy has ! value indicat$ by equation 7#b74 ,ques4 ,:at is ! mutual effect ( inductance & capacity8 ,ans4 ,"o t5ds to neutralize ! o!r4 ,ques4 ,:at effect has resonance on ! curr5t8 ,ans4 ,x br+s ! curr5t 9 phase ) ! impress$ pressure4 ,illu/ration3 ,,fig4 #a1cje4--;,curve %[+ v>iation ( curr5t by increas+ ! frequ5cy 9 a circuit hav+ inductance & capacity4 ,! curve s]ves to illu/rate ! critical frequ5cy or frequ5cy produc+ ! maximum curr5t4 ,! curve is obta9$ by plott+ curr5t values correspond+ to diff]5t frequ5cies1 ! pressure be+ kept con/ant4 ,x is v seldom t a circuit is ?us balanc$ unless int5tionally br\ght ab\t2 :5 ?is condition exi/s1 ! effect is v m>k$1 ! pressure ris+ excessively & br++ great /ra9 ^u ! insulation ( ! circuit4 ,ques4 ,def9e critical frequ5cy4 ,ans4 ,9 br++ a circuit to a /ate ( resonance by increas+ ! frequ5cy1 ! curr5t w increase ) increas+ frequ5cy until ! critical frequ5cy is rea*$1 & !n ! curr5t w decrease 9 value = fur!r increase ( frequ5cy4 ,! critical frequ5cy occurs :5 ! circuit rea*es ! condition ( resonance4 ,ques4 ,h[ is ! value ( ! curr5t at ! critical frequ5cy det]m9$8 ,ans4 ,by ! resi/ance ( ! circuit4 ,sk9 ,effect4--,?is is ! t5d5cy ( alt]nat+ curr5ts to avoid ! c5tral portions ( solid conductors & to fl[ or pass mo/ly ?r\gh ! out] portions4 ,! s-call$ sk9 effect becomes m pron\nc$ z ! frequ5cy is increas$4 ,illu/ration3 ,,fig4 #a1cjf4--,section ( conductor illu/rat+ sk9 effect or t5d5cy ( ! alt]nat+ curr5t to di/ribute itself unequally ?r\gh ! cross section ( ! conductor z %[n by ! v>i$ %ad+ fl[+ mo/ /rongly 9 ! out] portions ( ! conductor4 ,= ?is reason x has be5 propos$ to use holl[ or flat conductors in/ead ( solid r\nd wires4 ,h[ev] ) frequ5cy n exce$+ #ajj ! sk9 effect is negligibly small 9 copp] conductors ( ! sizes usually employ$4 ,:]e ! conductor is l>ge or ! frequ5cy high ! effect may be judg$ by ! foll[+ examples calculat$ by ,pr(essor ,j4 ,j4 ,?omson3 ,9 ! case ( a copp] conductor expos$ to an electromotive =ce mak+ #ajj p]iods p] second at #a c5timetre f ! surface1 ! maximum curr5t w\ld be only 4#bjh times t at ! surface2 at a dep? ( #b c5timetres x w\ld be only 4#jdc2 & at a dep? ( #d c5timetres less ?an 4#jjb "p ( ! value at ! surface4 ,if ! frequ5cy be a million p] second ! curr5t at a dep? ( #a millimetre is less ?an "o six-million? "p ( its surface value4 ,! case ( an iron conductor is ev5 m rem>kable4 ,tak+ ! p]meability at #ajj & ! frequ5cy at #ajj p] second ! curr5t at a dep? ( #a millimetre is only 4#ac times ! surface value2 :ile at a dep? ( #e millimetres x is less ?an "o tw5ty-?\s&? "p ( its surface value4 ,! di/urbance ( curr5t d5sity may be look$ ^u z a self-induc$ eddy curr5t 9 ! conductor4 ,x necess>ily results 9 an increase ( ohmic loss2 z comp>$ ) a /eady curr5t3 proportional to ! squ>e ( ! total curr5t fl[+ & consequ5tly gives rise to an app>5t increase ( ohmic resi/ance4 ,! coeffici5t ( increase ( resi/ance dep5ds ^u ! dim5sions & ! %ape ( ! cross section1 ! frequ5cy & ! specific resi/ance4 ,a simil> b di/9ct effect is exp]i5c$ 9 conductors due to ! neighborhood ( simil> p>allel curr5ts4 ,= example 9 a heavy multicore cable ! non-uni=mity ( curr5t d5sity 9 any core may be consid]$ z p>tly due to eddy curr5ts induc$ by ! curr5ts 9 ! neighbor+ cores & p>tly to ! self-induc$ eddy curr5t4 ,x is only ! latt] effect :i* %\ld rightly be consid]$ z compris$ "u ! t]m sk9 effect4 ,ques4 ,:at is ! explanation ( sk9 effect8 ,ans4 ,x is due to eddy curr5ts induc$ 9 ! conductor4 ,consid] ! wire z be+ compos$ ( sev]al small insulat$ wires plac$ closely toge!r4 ,n[ :5 a curr5t is />t$ along ^! sep>ate wires1 mutual induction w take place betwe5 !m1 giv+ rise to mom5t>y rev]se pressures4 ,^? wires :i* are ne>] ! c5t]1 s9ce !y are completely surr\nd$ by neighbor+ wires1 w cle>ly h /rong] rev]se pressures set up 9 !m ?an ^? on or ne> ! out] surface1 s t ! curr5t w meet less opposition ne> ! surface ?an at ! c5t]1 & consequ5tly ! fl[ w be great] 9 ! out] portions4 ,ques4 ,:at is ! result ( sk9 effect8 ,ans4 ,x results 9 an app>5t increase ( resi/ance4 ,! coeffici5t ( increase ( resi/ance dep5ds ^u ! dim5sions & ! %ape ( ! cross section1 ! frequ5cy1 & ! specific resi/ance4 ,hughes1 ab\t #ahhc1 call$ att5tion to ! fact t ! resi/ance ( an iron telegraph wire 0 great] = rapid p]iodic curr5ts ?an = /eady curr5ts4 ,9 #ahhh ,kelv9 %[$ t :5 alt]nat+ curr5ts at mod]ately high frequ5cy fl[ ?r\gh massive conductors1 ! curr5t is practically conf9$ to ! sk91 ! int]ior portions be+ l>gely useless = ! purpose ( conduction4 ,! ma!matical !ory ( ! subject has be5 develop$ by ,kelv91 ,heaviside1 ,rayleigh1 & o!rs4 ,,*apt] ,,xlvii ,,alt]nat+ ,,curr5t ,,diagrams ,:5ev] an alt]nat+ pressure is impress$ on a circuit1 "p ( x is sp5t 9 ov]com+ ! resi/ance1 & ! re/ goes to balance ! rev]se pressure due to self-induction4 ,! total pressure appli$ to ! circuit is kn[n z ! impress$ pressure1 z di/+ui%$ f t portion ( x call$ ! active pressure :i* is us$ to ov]come ! resi/ance1 & t portion call$ ! self-induction pressure us$ to balance ! rev]se pressure ( self-induction4 ,! int5sity ( ! rev]se pressure induc$ 9 a circuit due to self-induction is proportional to ! rate ( *ange 9 ! curr5t /r5g?4 ,?us a curr5t1 *ang+ at ! rate ( "o amp]e p] second1 9 fl[+ ?r\gh a coil hav+ a coeffici5t ( self-induction ( "o h5ry1 w induce a rev]se pressure ( "o volt4 ,ques4 ,describe h[ ! rate ( *ange 9 curr5t /r5g? v>ies1 & h[ ?is affects ! rev]se pressure4 ,ans4 ,! alt]nat+ curr5t v>ies f z]o to maximum /r5g? 9 "o-qu>t] p]iod1 t is1 9 "o-qu>t] revolution ( ! g5]at+ loop or #ij z repres5t$ by ! s9e curve 9 fig4 #a1cjg4 ,n[1 dur+1 say1 ! fir/ #aj degrees ( rotation 7f #j to ,a71 ! curr5t jumps f z]o value to ,a'1 or #d amp]es1 accord+ to ! scale2 dur+ "s int]m$iate #aj degrees ( ! qu>t] revolution1 z f ,b to ,c1 ! curr5t increases f ,b' to ,c' or #b amp]es1 & dur+ ano!r #aj degrees z f ,d to ,e1 at ! end ( "o-qu>t] revolution :]e ! s9e curve rea*es its amplitude1 x rises & falls amp]e4 ,x is ?us se5 t ! rate ( *ange v>ies f a maximum :5 ! curr5t is lea/1 to z]o :5 ! curr5t is at its maximum4 ,accord+ly1 ! rev]se pressure ( self-induction be+ proportional to ! rate ( *ange 9 ! curr5t /r5g?1 is greate/ :5 ! curr5t is at z]o value1 & z]o :5 ! curr5t is at its maximum4 ,illu/ration3 ,,fig4 #a1cjg4--,s9e curve %[+ t ! rate ( *ange 9 ! /r5g? ( an alt]nat+ curr5t is greate/ :5 ! curr5t is lea/1 & z]o :5 ! curr5t is at a maximum4 ,?is is evid5t f ! diagram1 s9ce dur+ say ! fir/ #aj z ,,oa1 ! curr5t increases #d amp]es2 dur+ ,,bc1 #b amp]es2 dur+ ,,de x rises & falls amp]e4 ,! rev]se pressure ( self-induction be+ proportional to ! rate ( *ange ( ! curr5t1 is a maximum :5 ! curr5t is z]o1 & z]o :5 ! curr5t is a maximum1 giv+ a phase diff]5ce ( #ij betwe5 rev]se pressure ( self-induction & curr5t4 ,?is relation is %[n by curves 9 fig4 #a1cjh1 & x %\ld be not$ t ! rev]se pressure & curr5t are #ij ap>t 9 phase4 ,= ?is reason _m alt]nat+ curr5t problems may be solv$ graphically by ! use ( "r angle triangles1 ! sides1 drawn to "s arbitr>y scale1 to repres5t ! quantities involv$1 su* z resi/ance1 reactance1 imp$ance1 etc4 ,prop]ties ( ,"r ,angle ,triangles4--,9 ord] to und]/& ! graphical me?od ( solv+ alt]nat+ curr5t problems1 x is necess>y to "k :y c]ta9 relations exi/ betwe5 ! sides ( a "r angle triangle4 ,= in/ance1 9 e "r angle triangle3 ,! squ>e ( ! hypo!nuse is equal to ! sum ( ! squ>es on ! o!r two sides4 ,t is1 cond5s+ ?is /atem5t into ! =m ( an equation3 hypo!nuse base altitude 7#a7 ! horizontal side be+ call$ ! base & ! v]tical side1 ! altitude4 ,?is may be call$ ! equation ( ! "r angle triangle4 ,illu/ration3 ,,fig4 #a1cjh4--,s9e curves %[+ phase relation betwe5 curr5t & rev]se pressure ( self-induction4 ,?is rev]se pressure1 be+ proportional to ! rate ( *ange 9 ! curr5t /r5g?1 is greate/ :5 ! curr5t is at z]o value1 & z]o :5 ! curr5t is maximum1 & 9 phase is #ij beh9d ! curr5t4 ,illu/ration3 ,,fig4 #a1cji4--;,9 a "r angle triangle ! squ>e on ! hypo!nuse is equal to ! sum ( ! squ>es on ! o!r two sides4 ,t is3 hypo!nuse base altitude4 ,draw ,,ab1 #d in*es long1 & ,,bc1 #c in*es long & at "r angles to ,,ab4 ,jo9 ,,ac1 :i* w be f\nd to be #e in*es long4 ,f ! diagram1 x mu/ be cle> t ! squ>e on ,,ac sum ( squ>es on ,,ab & ,,bc2 t is1 #e #d #c4 ,fur!r1 #d #e - #c2 #c #e - #d2 #e 7#d #c72 #d 7#e - #c72 #c 7#e - #d74 ,ques4 ,:y is ! squ>e ( ! hypo!nuse ( a "r angle triangle equal to ! sum ( ! squ>es ( ! o!r two sides8 ,ans4 ,?is may be expla9$ ) ! aid ( fig4 #a1cji4 ,draw a l9e ,,ab1 #d in*es 9 l5g? & erect a p]p5dicul> ,,bc1 #c in*es 9 height2 connect ,a & ,c1 giv+ ! "r angle triangle ,,abc4 ,x w be f\nd t ,,ac ! hypo!nuse ( ?is triangle is #e in*es long4 ,if squ>es be con/ruct$ on all ?ree sides ( ! triangle1 ! squ>e on ! hypo!nuse w h an area ( #be sq4 ins42 ! squ>e on ! base1 #af sq4 ins41 & ! squ>e on ! altitude1 #i sq4 ins4 ,!n f ! figure #e #d #c1 t is #be #af #i4 ,repeat+ equation 7#a71 x is evid5t f ! figure t hypo!nuse base altitude #e #d #c t is1 #be #af #i4 ,9 ! "r angle triangle1 ! foll[+ relations also hold3 base hypo!nuse - altitude 7#b7 7#d #e - #c7 altitude hypo!nuse - base 7#c7 7#c #e - #d7 ,9 work+ imp$ance problems1 x is n ! squ>e ( any ( ! quantities :i* ! sides ( ! triangle are us$ to repres5t t is requir$1 b ! quantities !mselves1 t is1 ! sides4 ,h5ce extract+ ! squ>e root 9 equations 7#a71 7#b7 & 7#c71 ! foll[+ are obta9$3 hypo!nuse 7base altitude7 7#d7 7#e 7#d #c77 base 7hypo!nuse - altitude7 7#e7 7#d 7#e - #c77 altitude 7hypo!nuse - base7 7#f7 7#c 7#e - #d77 ,repres5tation ( ,=ces by ,l9es4--,a s+le =ce may be repres5t$ 9 a draw+ by a /raight l9e1 #a1 ! po9t ( application ( ! =ce be+ indicat$ by an extremity ( ! l9e1 #b1 ! int5sity ( ! =ce by ! l5g? ( ! l9e1 & #c1 ! direction ( ! =ce by ! direction ( ! l9e1 an arr[ head be+ plac$ at an extremity def9+ ! direction4 ,?us 9 fig4 #a1caj1 ! =ce necess>y to balance ! ?ru/ on ! /eam pi/on may be repres5t$ by ! /raight l9e f ^: l5g? measur$ on any conv5i5t scale repres5ts ! int5sity ( ! =ce1 & ^: direction repres5ts ! direction ( ! =ce4 ,illu/ration3 ,,fig4 #a1caj4--;,diagram illu/rat+ ! repres5tation ( =ces by /raight l9es4 ,if #hj lbs4 ( /eam be appli$ to a pi/on ( #d squ>e in*es area1 ! total pressure act+ on ! pi/on is #d #hj #cbj lbs4 ,?is may be balanc$ by an equal & opposite =ce4 ,to repres5t ! latt] by a l9e1 select any conv5i5t scale ^: divisions repres5t any conv5i5t numb] ( p\nds--#a1 #c1 #e or1 z "h tak51 #be lbs4 ,if ! scale select$ be divid$ into in*es ) -in* divisions1 !n ea* in* repres5ts a =ce ( #be lbs42 or1 z usually /at$1 #a #ajj lbs4 ,/rictly speak+ #a is equival5t to #ajj lbs4 ,draw ! l9e f #c4b ins41 !n its l5g? repres5ts ! magnitude ( ! =ce or #cbj lbs41 t is1 #c4b #ajj #cbj lbs4 ,composition ( ,=ces4--,?is is ! op]ation ( f9d+ a s+le =ce ^: effect is ! same z ! comb9$ effect ( two or m giv5 =ces4 ,! requir$ =ce is call$ ! resultant ( ! giv5 =ces4 ,! composition ( =ces may be illu/rat$ by ! effect ( ! w9d & tide on a sailboat z 9 fig4 #a1caa4 ,suppos+ ! boat be act$ ^u by ! w9d s t 9 a giv5 "t1 say half an h\r1 x w\ld be mov$ 9 ! direction & a di/ance repres5t$ by ! l9e ,,ab1 & t 9 ! same "t ! tide w\ld c>ry x f ,a to ,c4 ,n[1 lay d[n ,,ab1 to any conv5i5t scale1 repres5t+ ! effect ( ! w9d1 & ,,ac t ( ! tide1 & draw ,,bd equal & p>allel to ,,ac1 & ,,cd equal & p>allel to ,,ab1 !n ! diagonal ,,ad w repres5t ! direction & di/ance ! boat w move "u ! comb9$ effect ( w9d & tide4 ,illu/ration3 ,,fig4 #a1caa4--,p>allelogram ( =ces = boat act$ ^u by bo? w9d & tide4 ,ques4 ,9 fig4 #a1caa :at is ! l9e ,,ad call$8 ,ans4 ,! resultant1 t is1 x repres5ts ! actual movem5t ( ! boat result+ f ! comb9$ =ces ( w9d & tide4 ,ques4 ,:at are ! =ces1 ,,ab & ,,ad 9 fig4 #a1caa1 repres5t$ by ! sides ( ! p>allelogram1 & :i* act ^u a body to produce ! resultant1 call$8 ,ans4 ,! compon5ts4 ,illu/ration3 ,,fig4 #a1cab4--,p>allelogram ( =ces2 me?od ( obta9+ ! resultant ( two compon5ts act+ at "r angles4 ,,example4--,two =ces1 "o ( #c lbs4 & "o ( #d lbs4 act at a po9t a 9 a body & at "r angles1 :at is ! resultant8 ,take any conv5i5t scale1 say #a 94 #a lb41 & lay (f 7fig4 #acab47 ,,ab #d ins4 #d lbs42 also1 ,,ac 7at "r angles to ,,ab7 #c ins4 #c lbs4 ,draw ,,cd & ,,bd p>allel to ,,ab & ,,ac respectively1 & jo9 ,,ad4 ,! l9e ,,ad is ! resultant ( ! compon5ts ,,ab & ,,ac1 & :5 measur$ on ! same scale f :i* ,,ab & ,,ac 7 drawn w be f\nd to be #e in*es long1 :i* repres5ts #e lbs4 act+ 9 ! direction ,,ad4 ,circuits conta9+ ,resi/ance & ,inductance4--,9 circuits ( ?is k9d :]e ! impress$ pressure enc\nt]s bo? resi/ance & inductance1 x may be look$ ^u z split up into two compon5ts1 z already expla9$1 "o ( :i* is necess>y to ov]come ! resi/ance1 & ! o!r1 ! inductance4 ,t is1 ! impress$ pressure is split up into #a4 ,active pressure1 to ov]come resi/ance2 #b4 ,self-induction pressure to ov]come inductance4 ,illu/ration3 ,,fig4 #a1cac4--;,diagram illu/rat+ ! active1 & self-induction pressures1 or ! two compon5ts ( ! impress$ pressure 9 circuits conta9+ resi/ance & inductance4 ,! active pressure is ! volts requir$ to ov]come ! resi/ance ( ! circuit4 ,9 ! figure only ! portion f ,a to ,c is consid]$ z hav+ resi/ance 7! re/ be+ negligibly small7 except at ,r1 a resi/ance equival5t to t ( ! inductive coil is ins]t$ next to ! non-inductive coil1 s ,p w give ! total ohmic drop or active pressure1 t is1 ! pressure necess>y to =ce any equival5t direct curr5t f ,a to ,c4 ,?is active pressure ,p or compon5t ( ! impress$ pressure is 9 phase ) ! curr5t4 ,! o!r compon5t or self-induction pressure ,p t is ! reactance drop necess>y to ov]come ! rev]se pressure ( self-induction & is at "r angles to ! curr5t & #ij ahead ( ! curr5t 9 phase4 ,x is regi/]$ by a voltmet] betwe5 ,b & ,c1 less ! pressure due to ohmic resi/ance ( ! inductive coil4 ,! impress$ pressure ,p !n or total pressure requir$ to =ce electricity ar\nd ! circuit n includ+ ! resi/ance ,r1 7:i* is remov$ f ! circuit :5 ! read+ ( ! impress$ pressure is tak571 is equal to ! squ>e root ( ! sum ( ! squ>es ( ! two compon5ts1 t is1 ,p 7,p ,p74 ,! active pressure is 9 phase ) ! curr5t4 ,! self induction pressure is at "r angles to ! curr5t & #ij degrees ahead ( ! curr5t 9 phase4 ,ques4 ,:y is ! active pressure 9 phase ) ! curr5t8 ,ans4 ,! pressure us$ 9 ov]com+ resi/ance is f ,ohm's law1 ,e ,,ri4 ,h5ce1 :5 ! curr5t is z]o1 ,e is z]o1 & :5 ! curr5t is a maximum ,e is a maximum4 ,h5ce1 t compon5t ( ! impress$ pressure necess>y to ov]come ! resi/ance mu/ be 9 phase ) ! curr5t4 ,ques4 ,:y is ?is8 ,ans4 ,s9ce ! rev]se pressure ( self induction is #ij beh9d ! curr5t1 ! compon5t ( ! impress$ pressure necess>y to ov]come ! rev]se pressure ( self induction1 be+ opposite to ?is1 w be repres5t$ z be+ #ij ahead ( ! curr5t4 ,! di/9ction betwe5 ! rev]se pressure ( self-induction1 t is1 ! induc$ pressure1 & ! pressure necess>y to ov]come self-induction %\ld be c>efully not$4 ,!y are two equal & opposite =ces1 t is1 two balanc+ =ces j z is %[n 9 fig4 #a1caj4 ,"h1 9 analogy1 ! ?ru/ ( ! pi/on may repres5t ! induc$ pressure & ! equal & opposite =ce indicat$ by ! arr[ f1 ! compon5t ( ! impress$ pressure necess>y to balance ! induc$ pressure4 ,illu/ration3 ,,fig4 #a1cad4--;,graphical me?od ( obta9+ ! impress$ pressure 9 circuits conta9+ resi/ance & inductance1 hav+ giv5 ! ohmic drop1 & reactance drop due to inductance4 ,) any conv5i5t scale lay (f ,,ab ohmic drop & erect ! p]p5dicul> ,,bc reactance drop 7us+ same scale74 ,jo9 ,,ac1 ^: l5g? 7measur$ ) same scale7 w give ! impress$ pressure4 ,con/ruct+ a p>allelogram ) dott$ l9es ,,ad & ,,cd1 x is evid5t t ,,ac is ! resultant ( ! two compon5ts ,,ab & ,,bc1 or its equal ,,ad4 ,! ,active ,pressure or ,ohmic ,drop4--,! compon5t ( ! impress$ pressure necess>y to ov]come resi/ance1 is f ,ohm's law3 active pressure ohmic resi/ance virtual curr5t t is ,e ,r,i 7#a7 ?is is ! ohmic drop & may be repres5t$ by a l9e ,,ab1 fig4 #a1cad drawn to any conv5i5t scale1 z = in/ance1 #a 94 #aj volts4 ,! ,self-induction ,pressure or ,reactance ,drop4--,! compon5t ( ! impress$ pressure necess>y to ov]come ! induc$ pressure1 is f ,ohm's law3 inductance pressure inductance reactance virtual curr5t2 t is1 ,e ,x,i 7#b7 ,illu/ration3 ,,fig4 #a1cae4--;,diagram = impress$ pressure on circuit conta9+ #e volts ohmic drop & #ae volts reactance drop4 ,n[ ! reactance ,x1 t is ! spuri\s resi/ance1 is obta9$ f ! =mula ,x #b;f,l 7#c7 z expla9$ on page #a1jch1 & 9 ord] to obta9 ! volts necess>y to ov]come ?is spuri\s resi/ance1 t is1 ! reactance drop z x is call$1 ! value ( ,x 9 equation 7#c7 mu/ be sub/itut$ 9 equation 7#b71 giv+ ,e #b;f,,li 7#d7 writ+ simply ,i = ! virtual pressure4 ,s9ce ! pressure impress$ on a circuit is consid]$ z made up ( two compon5ts1 "o 9 phase ) ! curr5t & "o at "r angles to ! curr5t1 ! compon5t ,e or reactance drop z giv5 9 equation 7#d7 maybe repres5t$ by ! l9e ,,bc 9 fig4 #a1cad1 at "r angles to ,,ab1 & ( a l5g? ,,bc1 measur$ ) ! same scale z 0 measur$ ,,ab1 to correspond to ! value indicat$ by equation 7#d74 ,,example4--,9 an alt]nat+ circuit1 hav+ an ohmic drop ( #e volts1 & a reactance drop ( #ae volts1 :at is ! impress$ pressure8 ,) a scale ( say1 in* "o volt1 lay (f1 9 fig4 #a1cae1 ,,ab #e volts #a 941 &1 at "r angles to x1 ,,bc #ae volts _/ or #c ins4 ,jo9 ,,ac2 ?is measures #c4ie in*es1 :i* is equival5t to #c4ie #d #ae4h volts1 ! impress$ pressure4 ,by us+ good pap]1 su* z bri/ol bo>d1 a #f;,h p5cil1 eng9e]s' scale & triangles or squ>e1 su* problems are solv$ ) precision4 ,by calculation impress$ pressure 7#e #ae7 #ae4h volts4 ,note t ! diagram is drawn ) ! side ,,bc horizontal in/ead ( ,,ab--simply to save space4 ,illu/ration3 ,,fig4 #a1caf4--;,diagram ( circuit conta9+ #e volts ohmic drop1 & #ae volts reactance drop4 ,illu/ration3 ,,fig4 #a1cag4--;,diagram = obta9+ reactance drop 9 circuit conta9+ #e volts ohmic drop1 & #ae4h volts impress$ pressure4 ,,example4--,9 an alt]nat+ circuit1 hav+ an ohmic drop ( #e volts & an impress$ pressure ( #ae4h volts1 :at is ! reactance drop8 ,9 fig4 #a1cag1 draw a horizontal l9e ( indef9ite l5g? & at any po9t ,b erect a p]p5dicul> ,,ab #e volts4 ,) ,a z c5t] & radius ( l5g? equival5t to #ae4h volts1 describe an arc cutt+ ! horizontal l9e at ,c4 ,?is gives ,,bc1 ! reactance drop requir$1 :i* by measurem5t is #ae volts4 ,illu/ration3 ,,fig4 #a1cah4--;,diagram = obta9+ ohmic drop 9 ! circuit fig4 #a1caf :5 impress$ pressure & reactance drop are giv54 ,lay (f ,,bc to scale reactance drop2 draw ,,ab at "r angle & ( indef9ite l5g?2 ) ,c z c5t] & radius ( l5g? impress$ pressure1 describe an arc cutt+ ohmic drop l9e at ,a1 !n ,,ab ohmic drop #e volts by measurem5t4 ,illu/ration3 ,,fig4 #a1cai4--;,graphical me?od ( f9d+ angle ( lag :5 ! ohmic drop & reactance drop are giv54 ,! angle ( lag 1 is t angle includ$ betwe5 ! impress$ pressure & ! ohmic drop l9es1 t is1 betwe5 ,,ac & ,,ab4 ,,example4--,an alt]nat+ curr5t ( #aj amp]es hav+ a frequ5cy ( #fj1 is impress$ on a circuit conta9+ a resi/ance ( #e ohms & an inductance ( #ae milli-h5rys4 ,:at is ! impress$ pressure8 ,! active pressure or ohmic drop is #e #aj #ej volts4 ,illu/ration3 ,,fig4 #a1cbj4--;,diagram ( circuit conta9+ #e ohms resi/ance1 #ae milli-h5rys inductance1 ) #c amp]e #fj frequ5cy curr5t4 ,! inductance reactance or ,x is #b #c4adaf #fj 4#jae #e4ff ohms4 ,sub/itut+ ?is & ! curr5t value #aj amp]es 9 ! =mula = inductance pressure or reactance drop 7equation #b on page #a1jgg7 gives ,e #e4fe #aj #ef4e volts4 ,illu/ration3 ,,fig4 #a1cba4--;,diagram = impress$ pressure on circuit conta9+ #e ohms resi/ance & inductance ( #ae milli-h5rys1 ! curr5t be+ #aj amp]es ) frequ5cy ( #fj4 ,9 fig4 #a1cba1 lay (f ,,ab #ej volts1 & ,,bc #ef4f volts4 ,us+ a scale ( #bj volts to ! in* gives ,,ab #b4e ins41 & ,,bc #b4hc ins4 ,jo9+ ,,ac gives ! impress$ voltage1 :i* by measurem5t is #ge4d volts4 ,9 "s problems x is requir$ to f9d ! imp$ance ( a circuit 9 :i* ! ohmic & spuri\s resi/ances are giv54 ,?is is done 9 a mann] simil> to f9d+ ! impress$ pressure4 ,illu/ration3 ,,fig4 #a1cbb4--;,graphical me?od ( obta9+ ! imp$ance 9 circuits conta9+ resi/ance & inductance1 hav+ giv5 ! resi/ance & reactance1 t is1 ! ohmic resi/ance & spuri\s resi/ance4 ,) any conv5i5t scale lay (f ,,ab resi/ance1 & erect ! p]p5dicul> ,,bc reactance 7us+ ! same scale72 jo9 ,,ac1 ^: l5g? 7measur$ ) ! same scale7 w give ! imp$ance4 ,ohmic resi/ance & spuri\s resi/ance or inductance reactance bo? t5d to r$uce an alt]nat+ curr5t4 ,_! comb9$ action or imp$ance is equal to ! squ>e root ( ! sum ( _! squ>es1 t is1 imp$ance 7resi/ance reactance7 ,?is relation is repres5t$ graphically by ! side ( a "r angle triangle z 9 fig4 #acbb1 9 :i* ! hypo!nuse corresponds to ! imp$ance1 & ! sides to ! resi/ance & reactance4 ,,example4--,9 a c]ta9 circuit ! resi/ance is #d ohms1 & ! reactance #c ohms4 ,:at is ! imp$ance8 ,9 fig4 #a1cbc1 lay (f1 on any scale ,,ab #d ohms & erect ! p]p5dicul> ,,bc #c ohms4 ,jo9 ,,ac1 :i* gives ! imp$ance1 & :i* is1 measur$ ) ! same scale1 #e ohms4 ,,example4--,a coil ( wire has a resi/ance ( #bj ohms & an inductance ( #ae milli-h5rys4 ,:at is its imp$ance = a curr5t hav+ a frequ5cy ( #ajj8 ,illu/ration3 ,,fig4 #a1cbc4--;,diagram = obta9+ ! imp$ance ( a circuit conta9+ #d ohms resi/ance & #c ohms reactance4 ,! ohmic value ( ! inductance1 t is1 ! reactance is #b;f,l #b #c4adaf #ajj 4#jae #i4db ohms4 ,9 fig4 #a1cbd1 lay (f1 on any scale1 ,,ab #bj ohms1 & ! p]p5dicul> ,,bc to l5g? #i4db ohms4 ,jo9 ,,ac1 :i* gives ! imp$ance1 :i* is1 measur$ on ! same scale1 #bb4a ohms4 ,,example4--,:at is ! angle ( lag 9 a circuit hav+ a resi/ance ( #d ohms & a reactance ( #c ohms8 ,con/ruct ! imp$ance diagram 9 ! usual way z 9 fig4 #a1cbe1 !n ! angle includ$ betwe5 ! imp$ance & resi/ance l9es 7d5ot$ by 7 is ! angle ( lag1 t is1 ! angle ,,bac4 ,by measurem5t ) a protractor x is #cg degrees4 ,by calculation ! tang5t ( ! angle ( lag or ,,bc #c tan -- - or 4#ge ,,ab #d ,f ! table on page #dea1 ! angle is approximately #cg4 ,illu/ration3 ,,fig4 #a1cbd4--;,diagram = imp$ance ( circuit conta9+ #bj ohms resi/ance1 & inductance ( #ae milli-h5rys1 :5 ! frequ5cy is #ajj4 ,illu/ration3 ,,fig4 #a1cbe4--;,diagram %[+ angle ( lag = curr5t conta9+ #d ohms resi/ance & #c ohms reactance4 ,circuits conta9+ ,resi/ance & ,capacity4--,! effect ( capacity 9 an alt]nat+ curr5t circuit is to cause ! curr5t to lead ! pressure1 s9ce ! reaction ( a cond5s]1 in/ead ( t5d+ to prolong ! curr5t1 t5ds to drive x back4 ,c>eful di/9ction %\ld be made betwe5 capacity 9 s]ies ) a circuit & capacity 9 p>allel ) a bran* ( a circuit4 ,! discussion "h ref]s to capacity 9 s]ies1 :i* means t ! circuit is n cont9u\s b ! ends are jo9$ to a cond5s]1 z %[n at ! "r 9 fig4 #a1cbf1 s t no curr5t c fl[ except into & out ( ! cond5s]4 ,illu/ration3 ,,fig4 #a1cbf1--;,circuit diagram illu/rat+ ! di/9ction betwe5 capacity 9 s]ies & capacity 9 p>allel4 ,! condition = capacity 9 s]ies is t ! circuit mu/ be discont9u\s z at ,m2 = capacity 9 p>allel ! ma9 circuit mu/ be cont9u\s2 ?is means t ! capacity mu/ be ins]t$ 9 a bran* ( ! ma9 circuit z at ,a4 ,9 ! figure ! capacity ,s is connect$ 9 s]ies ) respect to ! bran*1 t is1 ! bran* is discont9u\s1 b x is 9 p>allel ) respect to ! ma9 circuit1 :5 ! latt] is cont9u\s1 t is1 :5 ! swit* ,w is clos$4 ,if ,w be op5$1 ! ma9 circuit becomes discont9u\s & ,s is *ang$ f 9 p>allel to 9 s]ies connection4 ,ques4 ,9 circuits conta9+ resi/ance & capacity ^u :at does ! am\nt ( lead dep5d8 ,ans4 ,^u ! relative values ( ! resi/ance & ! capacity reactance4 ,ques4 ,describe ! action ( a cond5s] :5 curr5t is appli$4 ,ans4 ,:5 ! curr5t beg9s to fl[ into a cond5s]1 t is1 :5 ! fl[ is maximum1 ! back pressure set up by ! cond5s] 7call$ ! cond5s] pressure7 is z]o1 & :5 ! fl[ f9ally becomes z]o1 ! cond5s] pressure is a maximum4 ,illu/ration3 ,,fig4 #a1cbg4--;,curr5t & pressure curves %[+ t ! cond5s] pressure is #ij ahead ( ! curr5t4 ,a curr5t fl[+ into a cond5s] enc\nt]s a gradually increas+ pressure :i* opposes x1 beg9n+ f z]o pressure :5 ! curr5t ent]s at maximum fl[ & increas+ to ! same value z ! curr5t pressure1 at :i* "t ! curr5t ceases to fl[4 ,h5ce1 s9ce ! curr5t v>ies f z]o to maximum 9 "o qu>t] p]iod1 or #ij1 ! phase diff]5ce betwe5 curr5t & cond5s] pressure is #ij4 ,! cond5s] pressure rea*+ a positive maximum :5 ! curr5t />ts f z]o on ! positive wave1 is #ij ahead ( ! curr5t4 ,ques4 ,:at does ?is indicate8 ,ans4 ,x %[s t ! phase diff]5ce betwe5 ! wave repres5t+ ! cond5s] pressure & ! curr5t is #ij1 z illu/rat$ 9 fig4 #a1cbg4 ,ques4 ,is ! cond5s] pressure ahead or beh9d ! curr5t & :y8 ,ans4 ,x is ahead ( ! curr5t4 ,! cond5s] pressure1 :5 ! cond5s] is dis*>g$ be+ z]o1 ! curr5t ent]s at maximum velocity z at ,a 9 fig4 #a1cbg1 & gradually decreases to z]o z ! cond5s] pressure rises to maximum at ,b1 ?is *ange tak+ place 9 "o-qu>t] p]iod4 ,?us ! cond5s] pressure1 :i* opposes ! curr5t1 be+ at a maximum :5 ! curr5t beg9s its cycle is #ij ahead ( ! curr5t1 z is m cle>ly se5 9 ! la/ qu>t] ( ! cycle 7fig4 #a1cbg74 ,illu/ration3 ,,fig4 #a1cbh4--;,curr5t & pressure curves1 %[+ phase relation betwe5 ! curr5t1 cond5s] pressure1 & impress$ or capacity pressure necess>y to ov]come ! cond5s] pressure4 ,! capacity pressure1 s9ce x mu/ ov]come ! cond5s] pressure1 is equal & opposite to ! cond5s] pressure1 t is1 ! phase diff]5ce is #ahj4 ,! cond5s] pressure be+ #ij ahead ( ! curr5t1 ! impress$ pressure is #ij beh9d ! curr5t4 ,ques4 ,:at is ! phase relation betwe5 ! cond5s] pressure & ! pressure appli$ to ! cond5s] to ov]come ! cond5s] pressure8 ,ans4 ,! pressure appli$ to ! cond5s] to ov]come ! cond5s] pressure1 or z x is call$1 ! capacity pressure1 mu/ be opposite to ! cond5s] pressure1 or #ij beh9d ! curr5t4 ,9 circuits conta9+ resi/ance & capacity1 ! total pressure impress$ on ! circuit1 or impress$ pressure1 z x is call$1 is made up ( two compon5ts3 #a4 ,! active pressure1 or pressure necess>y to ov]come ! resi/ance2 ,! active pressure is 9 phase ) ! curr5t4 #b4 ,! capacity pressure1 or pressure necess>y to ov]come ! cond5s] pressure1 ,! capacity pressure is #ij degrees beh9d ! curr5t4 ,illu/ration3 ,,fig4 #a1cbi4--;,graphical me?od ( obta9+ ! impress$ pressure 9 circuits conta9+ resi/ance & capacity1 hav+ giv5 ! ohmic drop & reactance drop due to capacity4 ,) any conv5i5t scale1 lay (f ,,ab ohmic drop1 & at "r angles to ,,ab draw ,,bc reactance drop 7us+ ! same scale74 ,jo9 ,,ac1 ^: l5g? 7measur$ ) ! same scale7 w give ! impress$ pressure4 ,! ma!matical expressions = ! ?ree quantities are giv5 inside ! triangle1 & expla9$ 9 ! text4 ,problems involv+ resi/ance & capacity are solv$ simil>ly to ^? includ+ resi/ance & inductance4 ,! ,active ,pressure or ,ohmic ,drop4--,?is1 z be=e expla9$ is repres5t$1 9 fig4 #a1cbi1 by a l9e ,,ab1 :i* 9 magnitude equals1 by ,ohm's law1 ! product ( ! resi/ance multipli$ by ! curr5t1 t is1 ,e ,r,i 7#a7 ,illu/ration3 ,,fig4 #a1ccj4--;,diagram ( circuit conta9+ a resi/ance ( #cj ohms & capacity ( #abe micr(>ads4 ,! calculation = impress$ pressure1 ohmic drop1 & reactance drop = a curr5t ( #h amp]es at frequ5cy #fj is giv5 9 ! example on page #a1jhi1 ! diagram = impress$ pressure be+ giv5 9 fig4 #a1cca4 ,! ,capacity ,pressure or ,reactance ,drop4--,?is compon5t ( ! impress$ pressure1 is1 apply+ ,ohm's law1 capacity pressure capacity reactance virtual curr5t4 ,ec ,xc,i 7#b7 ,t is1 ! expression = capacity reactance ,xc1 t is1 = ! value ( capacity 9 ohms is1 z expla9$ on page #a1jdh1 #a ,xc ------ 7#c7 #b;f,c ,sub/itut+ ?is value ( ,xc 9 equation 7#b7 & writ+ ,i = virtual curr5t4 ,i ,ec ------- 7#d7 #b;f,c ,,caution--,! read] %\ld di/+ui% betwe5 ! #a 7"o7 9 7#c7 & ! lett] ,i 9 7#d72 bo? look alike4 ,s9ce ! capacity pressure is #ij beh9d ! curr5t1 x is repres5t$ 9 fig4 #a1cbi1 by a l9e ,,bc1 drawn d[nw>d1 at "r angles to ,,ab1 & ( a l5g? correspond+ to ! capacity pressure1 t is1 to ! reactance drop4 ,! ,impress$ ,pressure4--,hav+ det]m9$ ! ohmic & reactance drops & repres5t$ !m 9 ! diagram1 fig4 #a1cbi1 by l9es ,,ab & ,,bc respectively1 a l9e ,,ac jo9+ ,a & ,c1 w !n be ! resultant ( ! two compon5t pressures1 t is1 x w repres5t ! impress$ pressure or total pressure appli$ to ! circuit4 ,9 ! diagram x %\ld be not$ t ! active pressure is call$ ! ohmic drop1 & ! capacity pressure1 ! reactance drop4 ,,example4--,a circuit z %[n 9 fig4 #a1ccj conta9s a resi/ance ( #cj ohms1 & a capacity ( #abe micr(>ads4 ,if an alt]nat+ curr5t ( #h amp]es ) frequ5cy #fj be fl[+ 9 ! circuit1 :at is ! ohmic drop1 ! reactance drop1 & ! impress$ pressure8 ,! ohmic drop or active pressure is1 sub/itut+ 9 =mula 7#a7 on page #a1jhg1 ,e #cj #h #bdj volts :i* is ! read+ ( voltmet] ,a 9 fig4 #a1ccj4 ,illu/ration3 ,,fig4 #a1cca4--;,diagram = obta9+ ! impress$ pressure ( ! circuit %[n 9 fig4 #a1ccj4 ,! reactance drop or ,i #h ,ec ------ ------------------------- #agj volts #b;f,c #b #c4adaf #fj 4#jjjabe 9 sub/itut+1 note t ! capacity ,c ( #abe micr(>ads is r$uc$ to 4#jjjabe f>ad4 ,us+ a scale ( say #a in* #hj volts1 lay (f 9 fig4 #a1cca1 ,,ab equal to ! ohmic drop ( #bdj volts2 on ?is scale ,,ab #c in*es4 ,lay (f at "r angles1 ,,bc reactance drop #agj volts #b4abe in*es4 ,jo9 ,,ac1 :i* gives ! impress$ voltage1 7t is ! read+ ( voltmet] ,i 9 fig4 #a1ccj17 :i* measures #bid volts4 ,by calculation1 impress$ pressure 7#bdj #agj7 #bid volts4 ,,example4--,9 ! circuit %[n 9 fig4 #a1ccj1 :at is ! angle ( lead8 ,! tang5t ( ! angle ( lead is giv5 by ! quoti5t ( ! reactance divid$ by ! resi/ance ( ! circuit4 ,t is1 reactance reactance drop tan ------------ ----------------- resi/ance resi/ance drop ,ec ,i tan -- ------ ,e 7#a7 ,e #b;f,c ,! tang5t is giv5 a negative sign because lead is oppos$ to lag & because ! positive value is assign$ to lag4 ,sub/itut+ 9 7#a7 #agj #b4abe tan --- or ------ -4#ga #bdj #c ! angle correspond+ is approximately #ce 7see table page #dea74 ,illu/ration3 ,,figs4 #a1ccb & #a1ccc4--;,diagrams = circuits conta9+ inductance & capacity4 ,s9ce inductance & capacity act #ahj ap>t1 _! reactances1 or _! ohmic drops may be repres5t$ by oppositely direct$ l9es4 ,^! may be drawn above & bel[ a ref]5ce l9e1 z 9 fig4 #a1ccb1 & _! algebraic sum tak51 or bo? may be drawn on ! same side ( ! ref]5ce l9e & _! diff]5ce 9 l5g?s1 z ,,cd1 fig4 #a1ccc1 measur$4 ,rec\rse to a diagram = obta9+ ! resultant reactance 9 circuits conta9+ inductance & capacity is unnecess>y z x is simply a matt] ( tak+ ! diff]5ce ( two quantities4 ,circuits ,conta9+ ,inductance & ,capacity4--,! effect ( capacity 9 a circuit is exactly ! opposite ( inductance1 t is1 "o t5ds to neutralize ! o!r4 ,! me?od ( repres5t+ ea* graphically has be5 %[n 9 ! prec$+ figures4 ,s9ce !y act oppositely1 t is #ahj ap>t1 ! reactance due to ea* may be calculat$ & ! values ?us f\nd1 repres5t$ by oppositely direct$ v]tical l9es3 ! inductance resi/ance upw>d f a ref]5ce l9e1 & ! capacity resi/ance d[nw>d f ! same ref]5ce l9e4 ,! diff]5ce !n is ! resultant imp$ance4 ,?is me?od is %[n 9 fig4 #a1ccb1 b x is m conv5i5tly done z 9 fig4 #a1ccc4 ,illu/ration3 ,,fig4 #a1ccd4--;,diagram ( circuit conta9+ #cj milli-h5rys inductance & #abe micr(>ads capacity1 ) curr5t ( #bj amp]es1 #ajj frequ5cy4 ,,example4--,9 a circuit1 z 9 fig4 #a1ccd1 conta9+ an inductance ( #cj milli-h5rys & a capacity ( #abe micr(>ads1 h[ _m volts mu/ be impress$ on ! circuit to produce a curr5t ( #bj amp]es hav+ a frequ5cy ( #ajj4 ,! inductance reactance is ,x #b;f,l #b #c4adaf #ajj 4#jc #ah4he ohms4 ,sub/itut+ ?is & ! curr5t value ( #bj amp]es 9 ! =mula = inductance pressure ,e ,r,i #ah4he #bj #cgg volts4 ,r$uc+ #abe micr(>ads to 4#jjjabe f>ad1 & sub/itut+ 9 ! =mula = capacity pressure ,i #bj ,ec ------ -------------------------- #bee volts4 #b;f,c #b #c4adaf #ajj 4#jjjabe ,a diagram is unnecess>y 9 obta9+ ! impress$ pressure s9ce x is simply ! diff]5ce betwe5 inductance pressure & capacity pressure 7! circuit be+ assum$ to h no resi/ance71 t is impress$ pressure ,e - ,ec #cgg - #bee #abb volts4 ,,example4--,a circuit 9 :i* a curr5t ( #bj amp]es is fl[+ at a frequ5cy ( #ajj1 has an inductance reactance ( #ah4be ohms1 & a capacity ( #abe micr(>ads4 ,:at is ! imp$ance8 ,! reactance due to capacity is #a #a ,xc ------ -------------------------- #ab4gf ohms4 #b;f,c #b #c4adaf #ajj 4#jjjabe ,! imp$ance ( ! circuit !n is ! diff]5ce betwe5 ! two reactances1 t is imp$ance inductance reactance - capacity reactance1 or ,z ,x - ,xc #ah4be - #ab4gf #e4di ohms4 ,illu/ration3 ,,fig4 #a1cce4--;,imp$ance diagram = circuit 7( above example7 conta9+ inductance & capacity4 ,) any conv5i5t scale1 erect a p]p5dicul> ,,ab #ah4be ohms1 & ,,cd #ab4gf ohms4 ,cont9ue ,,cd by dott$ l9e to ,d' s t ,,cd' ,,ab1 !n ,,dd' ,,ab - ,,cd inductance reactance - capacity reactance1 :i* is equal to ! imp$ance4 ,express$ by lett]s ,z ,x - ,xc ,,dd'1 :i* by measurem5t #e4di ohms4 ,circuits ,conta9+ ,resi/ance1 ,inductance1 & ,capacity4--,:5 ! ?ree quantities resi/ance1 inductance1 & capacity1 are pres5t 9 a circuit1 ! comb9$ effect is easily und]/ood by rememb]+ t inductance & capacity always act oppositely1 t is1 !y t5d to neutralize ea* o!r4 ,h5ce1 9 problems involv+ ! ?ree quantities1 ! resultant ( inductance & capacity is fir/ obta9$1 :i*1 toge!r ) ! resi/ance1 is us$ 9 det]m9+ ! f9al effect4 ,capacity introduc$ into a circuit conta9+ inductance r$uces ! latt] & if en\gh be introduc$1 inductance w be neutraliz$1 giv+ a resonant circuit :i* w act z ?\gh only resi/ance 7 pres5t4 ,illu/ration3 ,,fig4 #a1ccf4--;,imp$ance diagram = circuit conta9+ resi/ance1 inductance & capacity4 ,! symbols correspond to ^? us$ 9 equation 7#a7 bel[4 ,9 con/ruct+ ! diagram f ! giv5 values1 lay (f ,,ab resi/ance2 at ,b1 draw a l9e at "r angles1 on :i* lay (f above ! resi/ance l9e1 ,,bc inductive reactance1 & bel[1 ,,bd capacity reactance1 !n ! resultant reactance ,,bc - ,,bd ,,bd'4 ,jo9 ,a & ,d'1 !n ,,ad' imp$ance4 ,ques4 ,:at is ! expression = imp$ance ( a circuit conta9+ resi/ance1 inductance & capacity8 ,ans4 ,x is equal to ! squ>e root ( ! sum ( ! resi/ance squ>$ plus ! squ>e ( inductance reactance m9us capacity reactance4 ,?is is express$ pla9] 9 ! =m ( an equation z foll[s3 imp$ance 7resi/ance 7inductance reactance - capacity reactance77 or1 us+ symbols1 ,z 7,r 7,x - ,xc77 7#a7 ,ques4 ,if ! capacity reactance be l>g] ?an ! inductance reactance1 h[ does ?is affect ! sign ( 7,x-,xc78 ,ans4 ,! sign ( ! resultant reactance ( inductance & capacity w be negative if capacity be ! great]1 b s9ce 9 ! =mula ! reactance is squ>$1 ! sign w be positive4 ,illu/ration3 ,,fig4 #a1ccg4--;,imp$ance diagram ( a circuit conta9+ #be ohms resi/ance1 #cj ohms inductance1 & #dj ohms capacity4 ,! resultant reactance be+ due to excess ( capacity1 ! imp$ance l9e ,,ac' falls bel[ ! horizontal l9e ,,ab1 indicat+ t ! curr5t leads pressure4 ,,example4--,:at is ! imp$ance 9 a circuit hav+ #be ohms resi/ance1 #cj ohms inductance reactance1 & #dj ohms capacity reactance8 ,to solve ?is problem graphically1 draw ! l9e ,,ab1 9 fig4 #a1ccg1 equal to #be ohms resi/ance1 us+ any conv5i5t scale4 ,at ,b draw upw>d at "r angles ,,bc #cj ohms2 draw f ,c d[nw>d ,,cc' #dj ohms4 ,?is gives -,,bc' 7 ,,bc - ,,cc'7 %[+ ! capacity reactance to be #aj ohms 9 excess ( ! inductance reactance4 ,su* a circuit is equival5t to "o hav+ no inductance b ! same resi/ance & #aj ohms capacity reactance4 ,! diagram is complet$ 9 ! usual way by jo9+ ,,ac giv+ ! requir$ imp$ance1 :i* by measurem5t is #bf4i ohms4 ,by calculation1 ,z 7#be 7#cj - #dj77 7#be 7-#aj77 #bf4i4 ,=m ( ,imp$ance ,equation )\t ,ohmic ,values4-- ,us+ ! expressions #b;f,l = inductance reactance & #a _/ 7#b;f,c7 = capacity reactance1 & sub/itut+ 9 equation 7#a7 on page #a1jic gives ! foll[+3 ,z 7,r 7#b;f,l - #a _/ 7#b;f,c777 7#b7 :i* is ! prop] =m ( equation 7#a7 to use 9 solv+ problems 9 :i* ! ohmic values ( inductance & capacity mu/ be calculat$4 ,illu/ration3 ,,fig4 #a1cch4--;,,example3 ,a resi/ance ( #bj ohms & an inductance ( 4#jb h5ry are connect$ 9 p>allel z 9 ! diagram4 ,:at is ! imp$ance1 & h[ _m volts are requir$ = #ej amp]es1 :5 ! frequ5cy is #gh4f8 ,,solution3 ,! "t con/ants are n alike1 h5ce ! geometric sum ( ! reciprocals mu/ be tak5 z ! reciprocal ( ! requir$ imp$ance4 ,t is1 ! comb9$ conductivity w be ! hypo!nuse ( ! "r triangle1 ( :i* ! ohmic conductivity & ! reactive conductivity are ! two sides1 respectively4 ,accord+ly3 #a _/ ,r #a _/ #bj 4#je1 & #a _/ 7#b;f,l7 #a _/ #aj 4#a1 f :i*1 #a _/ ,r 77#a _/ ,r7 7#a _/ 7#b;f,l777 4#aaa4 ,:5ce ,z #a _/ 4#aaa #i ohms4 ,illu/ration3 ,,fig4 #a1cci4--;,diagram ( circuit conta9+ #bc ohms resi/ance1 #da milli-h5rys inductance1 & #ea micr(>ads capacity1 ) curr5t suppli$ at a frequ5cy ( #aej4 ,,example4--,a curr5t has a frequ5cy ( #aej4 ,x passes ?r\gh a circuit1 z 9 fig4 #a1cci1 ( #bc ohms resi/ance1 ( #da milli-h5rys inductance1 & ( #ea micr(>ads capacity4 ,:at is ! imp$ance8 ,! inductance reactance or ,x #b;f,l #b #c4adaf #aej 4#jda #ch4fd ohms 7note t #da milli-h5rys are r$uc$ to 4#jda h5ry be=e sub/itut+ 9 ! above equation74 ,! capacity reactance1 or #a #a ,xc ------ -------------------------- #bj4h ohms #b;f,c #b #c4adaf #aej 4#jjjjea 7note t #ea micr(>ads are r$uc$ to 4#jjjjea f>ad be=e sub/itut+ 9 ! above equation74 ,sub/itut+ ! values z calculat$ = #b;f,l & #a _/ 7#b;f,c7 9 equation 7#b7 ,z 7#bc 7#ch4fd - #bj4h77 #bi4a ohms4 ,to solve ! problem graphically1 lay (f 9 fig4 #a1cdj1 ! l9e ,,ab equal to #bc ohms resi/ance1 us+ any conv5i5t scale4 ,draw upw>d & at "r angles to ,,ab ! l9e ,,bc #ch4fd ohms inductance reactance1 & f ,c lay (f d[nw>d ,,cc' #bj4h ohms capacity reactance4 ,! resultant reactance is ,,bc' & be+ above ! horizontal l9e ,,ab %[s t inductance reactance is 9 excess ( capacity reactance by ! am\nt ,,bc'4 ,jo9 ,,ac' :i* gives ! imp$ance s\ght1 & :i* by measurem5t is #bi4a ohms4 ,9 ord] to obta9 ! impress$ pressure 9 circuits conta9+ resi/ance1 inductance & reactance1 an equation simil> to 7#b7 on page #a1jie is us$ :i* is made up f ! foll[+3 ,e ,,ri 7#c7 ,e #b;f,,li 7#d7 ,i ,ec ------ 7#e7 #b;f,c ,illu/ration3 ,,fig4 #a1cdj4--;,imp$ance diagram = ! circuit %[n 9 fig4 #a1cci4 ,note t ! resultant reactance be+ due to excess ( inductance1 ! imp$ance l9e ,,ac' falls above ! horizontal l9e ,,ab4 ,?is indicates t ! curr5t lags beh9d ! pressure4 ,:5 all ?ree quantities1 resi/ance1 inductance1 & capacity are pres5t1 ! equation is z foll[s3 impress$ pressure 7ohmic drop 7inductive drop - capacity drop77 ,e 7,e 7,e - ,ec77 7#f7 ,sub/itut+ 9 ?is la/ equation 7#f71 ! values giv5 9 7#c71 7#d7 & 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 ,illu/ration ,,fig4 #a1cda4--;,diagram ( circuit conta9+ #be ohms resi/ance1 4#ae h5ry inductance1 & #abe micr(>ads capacity1 ) curr5t ( #h amp]es at #fj frequ5cy4 ,ques4 ,:at does ! quantity "u ! squ>e root sign 9 equation 7#g7 repres5t8 ,ans4 ,x is ! imp$ance ( a circuit possess+ resi/ance1 inductance1 & capacity4 ,ques4 ,:y8 ,ans4 ,because x is t quantity :i* multipli$ by ! curr5t gives ! pressure1 :i* is 9 accordance ) ,ohm's law4 ,illu/ration3 ,fig4 #a1cdb4--;,diagram = f9d+ ! pressure necess>y to be impress$ on ! circuit %[n 9 fig4 #a1cda1 to produce a curr5t ( #h amp]es4 ,,example4--,an alt]nator is connect$ to a circuit hav+1 z 9 fig4 #a1cda1 #be ohms resi/ance1 an inductance ( 4#ae h5ry1 & a capacity ( #abe micr(>ads4 ,:at pressure mu/ be impress$ on ! circuit to all[ #h amp]es to fl[ at a frequ5cy ( #fj8 ,! ohmic drop is ,e ,,ri #be #h #bjj volts4 ,! inductance drop is ,e #b;f,,li #b #c4adaf #fj 4#ae #h #deb volts ,! capacity drop is ,i #h ,ec ------ ------------------------- #agj volts4 #b;f,c #b #c4adaf #fj 4#jjjabe ,sub/itut+ ! values ?us f\nd1 impress$ pressure 7,e 7,e - ,ec77 7#bjj 7#deb - #agj77 7#bjj #bhb7 7#aaiebd7 #cde4g volts4 ,,*apt] ,,xlviii ,,! ,,p[] ,,factor ,! det]m9ation ( ! p[] 9 a direct curr5t circuit is a simple matt] s9ce x is only necess>y to multiply toge!r ! volts & amp]es to obta9 ! output 9 watts4 ,9 ! case ( alt]nat+ curr5t circuits1 ?is holds true only :5 ! curr5t is 9 phase ) ! pressure--a condition r>ely f\nd 9 practice4 ,:5 ! curr5t is n 9 phase ) ! pressure1 ! product ( volts & amp]es z indicat$ by ! voltmet] & ammet] mu/ be multipli$ by a coeffici5t call$ ! p[] factor 9 ord] to obta9 ! true watts1 or actual p[] available4 ,!re are sev]al ways ( def9+ ! p[] factor1 any ( :i* requires "s explanation4 ,! p[] factor may be def9$ z3 ,! numb] ( watts indicat$ by a wattmet]1 divid$ by ! app>5t watts1 ! latt] be+ ! watts z measur$ by a voltmet] & ammet]4 ,! p[] factor may be express$ z be+ equal to true p[] true watts true watts ---------------- ---------------- ------------------- app>5t p[] app>5t watts volts amp]es ,ques4 ,:at are ! true watts8 ,ans4 ,! watts z measur$ by a wattmet]4 ,ques4 ,:at are ! app>5t watts8 ,ans4 ,! watts obta9$ by multiply+ toge!r ! simultane\s voltmet] & ammet] read+s4 ,ques4 ,:at is usually meant by p[] factor8 ,ans4 ,! multipli] us$ ) ! app>5t watts to det]m9e h[ mu* ( ! p[] suppli$ is available4 ,illu/ration3 ,,fig4 #a1cdc4--,m>9e analogy ( p[] factor4 ,a f]ry boat 9 cross+ a riv] to a slip ,c w\ld head = "s po9t ,b up /ream f ,c to all[ = ! effect ( ! tide4 ,"u su* conditions ! actual motion 7ref]r$ to ! wat]7 w\ld be f ,a to ,b1 & ! app>5t motion1 f ,a to ,c4 ,accord+ly1 ! en]gy exp5d$ 9 propell+ ! boat f ,a to ,b 9 /ill wat]1 w propel x f ,a to ,c :5 ! tide is runn+ 9 ! direction ( ! arr[4 ,! effect ( ! tide is ! same z t ( inductance or capacity 9 an alt]nat+ circuit1 t is1 x puts ! appli$ =ce or ?ru/ 7impress$ volts7 out ( phase ) ! motion ( ! boat 7amp]es71 ?is phase diff]5ce be+ indicat$ by ! angle ,,bac or 4 ,n[1 "w 7watts7 is ! product ( two factors1 pressure 7volts7 & di/ance 7amp]es72 accord+ly1 ! app>5t "w done 9 propell+ ! boat f ,a to ,c is ! product ( ! ?ru/ ( ! paddle :eels multipli$ by ,,ac1 :i* 9 analogy corresponds to ! product ( voltmet] & ammet] read+s at ! alt]nator1 call$ kva4 ,actually1 h[ev]1 ! p[] is only appli$ f ,a to ,b1 ! boat be+ c>ri$ sidewise by ! tide1 z x crosses1 a di/ance ,,bc :i* repres5ts no en]gy exp5d$ by ! paddle :eels4 ,9 analogy1 ! actual p[]1 exp5d$ 9 propell+ boat f ,a to ,b corresponds to ! wattmet] read+ 9 an alt]nat+ curr5t p[] circuit4 ,to obta9 ! actual "w done on ! boat1 ! product ( its app>5t motion ?ru/ mu/ be multipli$ by a coeffici5t or p[] factor because ! ?ru/ is appli$ at an angle to ! app>5t motion1 ! p[] factor be+ equal to ! cos9e ( ?is angle1 77 or ,,ab ,,ac4 ,simil>ly1 :5 !re is phase diff]5ce betwe5 pressure & alt]nat+ curr5t1 ! voltmet] & ammet] read+s mu/ be multipli$ by ! p[] factor or cos to give ! output ( an alt]nator available = ext]nal "w1 ! excess p[] indicat$ by ammet] & voltmet] read+s1 p]=m+ no ext]nal "w1 b caus+ objectionable heat+ ( ! alt]nator4 ,ques4 ,^u :at does ! p[] factor dep5d8 ,ans4 ,^u ! relative am\nts ( resi/ance inductance & capacity conta9$ 9 ! circuit4 ,ques4 ,h[ does ! p[] factor v>y 9 value8 ,ans4 ,x v>ies f "o to z]o4 ,! p[] factor1 z w be %[n lat]1 is equal to ! cos9e ( ! angle ( phase diff]5ce2 its range !n is f "o to z]o because ^! are ! limit+ values ( ! cos9e ( an angle 7neglect+ ! or-sign74 ,ques4 ,:at is ! effect ( lag or lead ( ! curr5t on ! p[] factor8 ,ans4 ,x causes x to become less ?an "o4 ,illu/ration3 ,,fig4 #a1cdd4--,me?od ( draw+ ! p[] curve f ! pressure & curr5t curves4 ,z %[n1 ! same scale is us$ = all curves4 ,?is z a rule1 makes ! p[] curve inconv5i5tly high1 h5ce x is usually drawn to small] scale z 9 fig4 #a1cde4 ,h[ to ,obta9 ! ,p[] ,curve4--,s9ce "u any phase condition1 ! p[] at any in/ant is equal to ! product ( ! pressure multipli$ by ! curr5t at t in/ant1 a curve may be easily plott$ f ! pressure & curr5t curves1 giv+ ! in/antane\s values ( ! p[] ?r\gh a complete cycle4 ,9 fig4 #a1cdd1 f ! z]o l9e ( ! curr5t & pressure curves1 draw any ord9ate z at ,f cutt+ ! curr5t curve at ,g & ! pressure curve at ,g'4 ,! values = curr5t & pressure at ?is po9t are f ! scale1 #b amp]es & #c4g volts4 ,s9ce watts amp]es volts1 ! ord9ate ,,fg is to be multipli$ by ord9ate ,,fg' t is1 #b #c4g #g4d4 ,project up ?r\gh ,f ! ord9ate ,,fg #g4d1 & ?is w give "o po9t on ! p[] curve4 ,simil>ly at ano!r po9t1 say ,m1 :]e ! curr5t & pressure are maximum ,,ms ,,ms' ,,ms1 t is #c #e #ae giv+ ,s ano!r po9t on ! curve4 ,obta9+ sev]al po9ts 9 ?is way ! p[] curve is !n drawn ?r\gh !m z %[n4 ,illu/ration3 ,,fig4 #a1cde4--,usual me?od ( draw+ p[] curve f ! pressure & curr5t curves4 ,a small] scale is employ$ = ! p[] curve 9 ord] to r$uce its height4 ,ques4 ,:y is ! p[] curve positive 9 ! second half ( ! p]iod :5 !re are negative values ( curr5t & pressure8 ,ans4 ,because ! product ( two negative quantities is positive4 ,ques4 ,does fig4 #a1cdd repres5t ! usual way ( draw+ a p[] curve8 ,ans4 ,s9ce ord9ates ( ! p[] curve are products ( ! curr5t & pressure ord9ates1 !y w be ( inconv5i5t l5g? if drawn to ! same scale2 x is !re=e cu/om>y to use a diff]5t scale = ! p[] ord9ates1 z 9 fig4 #a1cde4 ,! illu/ration is lett]$ id5tical ) fig4 #a1cdd1 ) :i* x %\ld be comp>$4 ,syn*ronism ( ,curr5t & ,pressure2 ,p[] ,factor ,unity4--,! curr5t & pressure w\ld be 9 phase z repres5t$ 9 fig4 #a1cdf 7 x possible to h a circuit conta9+ resi/ance only4 ,9 actual practice all circuits conta9 at lea/ a small am\nt ( reactance4 ,illu/ration3 ,,fig4 #a1cdf4--,syn*ronism ( curr5t & pressure4 ,p[] curve %[+ t ! p[] factor is unity4 ,?is is indicat$ by ! fact t ! p[] curve does n project bel[ ! base or z]o l9e4 ,a circuit supply+ no?+ b inc&esc5t lamps comes v ne>ly be+ all resi/ance1 & may be s consid]$ 9 ! discussion "h4 ,fig4 #a1cdg illu/rates a circuit conta9+ only resi/ance4 ,9 su* a circuit ! pressure & curr5t 7z %[n 9 fig4 #a1cdf7 pass ?r\gh z]o & ?r\gh _! maximum values toge!r4 ,multiply+ in/antane\s values ( volts & amp]es w give ! p[] curve1 z be=e expla9$1 ^: av]age value is half-way betwe5 ! z]o l9e & ! maximum ( ! curve2 t "p ( ! p[] curve above ! l9e ( av]age p[] ,,ww1 exactly fill+ ! op5 space bel[ ! l9e ,,ww4 ,t is1 av]age p[] maximum p[] #b maximum voltage maximum curr5t _/ #b virtual voltage virtual curr5t4 ,?is latt] is simply ! product ( ! voltmet] & ammet] read+s :i* gives ! watts j ! same z 9 direct curr5t4 ,illu/ration3 ,,fig4 #a1cdg4--;,diagram ( circuit conta9+ only resi/ance2 9 su* a circuit ! p[] factor is unity4 ,ques4 ,:at %\ld be notic$ ab\t ! p[] curve8 ,ans4 ,its position ) respect to ! z]o l9e2 x lies :olly above ! z]o l9e :i* d5otes t all ! p[] deliv]$ to ! circuit except t dissipat$ by friction is useful1 t is1 ! p[] factor is unity4 ,h5ce1 to keep ! p[] factor z ne> unity z possible is "o ( ! *ief problems 9 alt]nat+ curr5t di/ribution4 ,ques4 ,c ! p[] factor be less ?an unity if ! curr5t & pressure be 9 phase8 ,ans4 ,yes1 if ! waves ( curr5t & voltage be di/ort$ z 9 fig4 #a1cdh4 ,effect ( ,lag & ,lead4--,9 an alt]nat+ circuit ! am\nt ( p[] suppli$ dep5ds on ! phase relation%ip ( ! curr5t & pressure4 ,z j expla9$1 :5 !re is syn*ronism ( curr5t & pressure1 t is1 :5 !y are 9 phase 7z 9 fig4 #a1cdf7 ! p[] factor is unity1 assum+ no di/ortion ( curr5t & pressure waves4 ,9 all o!r cases ! p[] factor is less ?an unity t is1 ! effect ( lag or lead is to make ! p[] factor less ?an unity4 ,illu/ration3 ,,fig4 #a1cdh4--;,case ( syn*ronism ( curr5t & pressure ) p[] factor less ?an unity4 ,suppose ! waves ( curr5t & voltage to be 9 phase1 b di/ort$ 9 =m1 & n symmetrical1 s t !y d n run uni=mly toge!r1 z %[n 9 ! figure4 ,!n ! real p[] factor may n be unity1 al?\gh indicat$ z su* by ! p[] factor met]4 ,h[ev]1 ! swit*bo>d in/rum5ts are made to %[ ! angle ( lag z ! p[] factor1 because ! error due to wave di/ortion is g5]ally too small to be consid]$4 ,illu/ration3 ,,fig4 #a1cdi4--;,effect ( lag on ! p[] factor4 ,:5 ! curr5t lags beh9d ! pressure ! p[] factor becomes less ?an unity4 ,x w be se5 t ! p[] curve projects bel[ ! z]o l9e giv+ ! %ad$ area :i* repres5ts negative p[] :i* mu/ be subtract$ f ! areas above ! z]o l9e to get ! net p[]4 ,9 ! figure ! l9e ,,ww' is drawn at a height correspond+ to ! av]age p[]1 & ,,hn at a height correspond+ to ! av]age p[] t w\ld be develop$ if ! curr5t 7 9 phase ) ! pressure4 ,! p[] factor !n is repres5t$ by ,m ,s1 & by inspection ( ! figure x is se5 t ?is is less ?an unity4 ,illu/ration3 ,,fig4 #a1cej4--;,effect ( lead on ! p[] factor4 ,:5 ! curr5t is 9 advance ( ! pressure ! p[] factor becomes less ?an unity4 ,! curve1 z %[n1 projects bel[ ! z]o l9e1 giv+ ! %ad$ area :i* repres5ts negative p[] :i* mu/ be subtract$ f ! areas above ! z]o l9e to get ! net p[]4 ,z 9 fig4 #a1cdi1 ! l9e ,,ww' at a height ,m repres5ts ! av]age p[]1 & ,,hn ! av]age p[] = syn*ronism ( curr5t & pressure4 ,! p[] factor !n is ,m ,s :i* is less ?an unity4 ,! effect ( lag on ! p[] factor may be illu/rat$ by fig4 #a1cdi1 9 :i* ! angle betwe5 ! pressure & curr5t1 or ! angle ( lag is tak5 z #dj1 correspond+ to a p[] factor ( 4#gff4 ,plott+ ! p[] curve f ! products ( in/antane\s volts & amp]es tak5 at v>i\s po9ts1 ! p[] curve is obta9$1 a portion ( :i* lies bel[ ! horizontal l9e4 ,! significance ( ?is is t at c]ta9 times1 ! curr5t is fl[+ 9 ! opposite direction to t 9 :i* ! impress$ pressure w\ld s5d x4 ,dur+ ?is "p ( ! p]iod conditions are rev]s$1 & ! p[] 7indicat$ by ! %ad$ area71 in/ead ( be+ suppli$ by ! s\rce to ! circuit1 is be+ suppli$ by ! circuit to ! s\rce4 ,illu/ration3 ,,fig4 #a1cea4--,/eam eng9e analogy ( p[] factor4 ,! figure repres5ts an indicator c>d ( an eng9e 9 :i* ! /eam di/ribution is su* t ! /eam is exp&$ bel[ ! back pressure l9e1 t is bel[ ! pressure ( ! exhau/4 ,?is results 9 negative "w :i* mu/ be ov]come by ! mom5tum or k9etic en]gy previ\sly /or$ 9 ! fly :eel1 & :i* is repres5t$ on ! diagram by ! %ad$ loop ,s4 ,if ! exhau/ valve _h op5$ at ,g1 ! am\nt ( "w done dur+ ! revolution w\ld be repres5t$ by ! area ,m1 b cont9u+ ! expansion bel[ ! back pressure l9e1 ! "w done is ,m - ,s4 ,?is latt] case z comp>$ ) ! fir/ :5 expansion does n cont9ue bel[ ! back pressure l9e gives an effici5cy 7p[] factor7 ( 7,m - ,s7 ,m1 ! %ad$ area repres5t+ s mu* loss4 ,?is condition is exactly analog\s to ! case ( a /eam eng9e1 exp&+ ! /eam bel[ ! back or exhau/ pressure1 a condition sometimes caus$ by ! action ( ! gov]nor 9 consid]ably r$uc+ ! cut (f = v light load4 ,an indicator diagram ( su* /eam di/ribution is %[n 9 fig4 #a1cea4 ,?is gives a negative loop 9 ! diagram indicat$ by ! %ad$ section4 ,x mu/ be evid5t t ! av]age pressure ( ! %ad$ loop portion ( ! diagram mu/ be subtract$ f t ( ! o!r portion1 because dur+ ! expansion bel[ ! exhau/ pressure l9e1 ! back pressure is 9 excess ( ! =w>d pressure ex]t$ on ! pi/on by ! exp&+ /eam1 & ! eng9e w\ld accord+ly rev]se its motion1 7 x n = ! en]gy previ\sly /or$ up 9 ! fly :eel 9 ! =m ( mom5tum1 :i* keeps ! eng9e mov+ dur+ ?is p]iod ( back ?ru/4 ,evid5tly ! %ad$ area mu/ be subtract$ f ! positive area to obta9 ! net "w done dur+ ! /roke4 ,h5ce foll[+ ! analogy z f> z possible if ,m "w 7watts7 be done dur+ ea* revolution 7cycle7 :5 /eam does n exp& bel[ back pressure 7:5 curr5t & pressure are 9 phase71 & ,s negative "w 7negative watts7 be done :5 /eam exp&s bel[ back pressure 7:5 !re is lag71 ! effici5cy 7p[] factor7 is 7,m - ,s7 ,m4 ,illu/ration3 ,,fig4 #a1ceb4--,p[] curve illu/rat+ ! s-call$ wattless curr5t 9 :i* case ! p[] factor is z]o4 ,by not+ t ! curve projects equally on ea* side ( ! z]o l9e1 ! p[] areas equal ! negative p[] areas1 h5ce ! summation ( ^! areas = ! p]iod is z]o1 t is1 ! two areas m9us ! two %ad$ areas equal z]o4 ,x %\ld be not$ t ! l9e ( av]age p[] ,,ww'1 :i* is visible 9 ! o!r figures1 "h co9cides ) ! z]o l9e1 & ! av]age p[] !n is z]o1 s9ce ! positive "p above ! z]o l9e is equal to & (fsets ! negative 7%ad$7 "p bel[ ! l9e4 ,?is is ! case ( wattless curr5t & 7consid]+ a circuit ) resi/ance s small t x may be consid]$ z z]o7 %[s pla9ly ! possibility ( hav+ full load curr5t & voltage on a circuit yet deliv]+ no p[]1 ! curr5t simply surg+ to & fro )\t an actual transf] ( p[]4 ,wattless ,curr5t2 ,p[] ,factor ,z]o4--,:5 ! p[] factor is z]o1 x means t ! phase diff]5ce betwe5 ! curr5t & ! pressure is #ij4 ,! t]m wattless curr5t1 z und]/ood1 does n indicate an abs5ce ( electrical en]gy 9 ! circuit2 its elem5ts are !re1 b n 9 an available =m = ext]nal "w4 ,! false p[] due to ! s call$ wattless curr5t pulsates 9 & out ( ! circuit )\t accompli%+ any useful "w4 ,an example ( wattless curr5t1 %[+ t ! p[] factor is z]o is illu/rat$ 9 fig4 #a1cec4 ,"h ! angle ( lag is #ij1 t is1 ! curr5t is #ij beh9d ! pressure4 ,! p[] curve is con/ruct$ f ! curr5t & pressure curves1 &1 z %[n 9 ! diagram1 x lies z mu* bel[ ! z]o l9e z above1 t is1 ! two plus p[] areas :i* occur dur+ ea* p]iod are equal to ! two negative 7%ad$7 p[] areas1 %[+ t ! circuit returns z mu* en]gy z is s5t out4 ,h5ce1 ! total "w done dur+ ea* p]iod is z]o1 indicat+ t al?\gh a curr5t be fl[+1 ?is curr5t is n capable ( do+ ext]nal "w4 ,illu/ration3 ,,fig4 #a1cec4--;,example ( wattless curr5t %[+ t ! p[] factor is z]o :5 ! phase diff]5ce betwe5 curr5t & pressure is #ij4 ,= z]o p[] factor ! curr5t may lead #ij z 9 fig4 #a1ceb1 or lag #ij z "h %[n4 ,s9ce ! %ad$ or negative areas ! plus areas1 ! av]age p[] 7indicat$ by ,,ww' :i* co9cides ) ! z]o l9e7 is z]o1 t is ! circuit is c>ry+ curr5t "u pressure yet deliv]+ no p[]1 h5ce1 ! p[] factor is z]o4 ,ques4 ,is ! condition z j describ$ met ) 9 practice8 ,ans4 ,no4 ,ques4 ,:y n8 ,ans4 ,! condition j describ$ involves t ! circuit h no resi/ance1 all ! load be+ reactance1 b x is impossible to h a circuit )\t "s resi/ance1 ?\gh ! resi/ance may be made v small 9 comp>ison to ! reactance s t a close approa* to wattless curr5t is possible4 ,ques4 ,give "s examples :]e ! phase diff]5ce is v ne>ly #ij4 ,ans4 ,if an alt]nator supplies curr5t to a circuit hav+ a v small resi/ance & v l>ge inductance1 ! curr5t w\ld lag ne>ly #ij beh9d ! pressure4 ,! prim>y curr5t ( a trans=m] work+ ) its second>y on an op5 circuit is a practical example ( a curr5t :i* repres5ts v little en]gy4 ,illu/ration3 ,,fig4 #a1ced4--,p]=mance curves ( ,g5]al ,electric s+le phase repulsion induction motor4 ,ques4 ,:5 ! phase diff]5ce betwe5 ! curr5t & pressure is #ij1 :y is ! curr5t call$ wattless8 ,ans4 ,because ! product ( su* a curr5t multipli$ by ! pressure does n repres5t any watts exp5d$4 ,a man lift+ a weight1 & !n all[+ x to desc5d ! same di/ance to its initial position1 z %[n 9 figs4 #a1cee to #a1ceg1 pres5ts a me*anical analogy ( wattless curr5t4 ,let ! movem5t ( ! weight repres5t ! curr5t & ! weight ! pressure4 ,!n call+ ! weight #aj p\nds 7volts71 & ! di/ance two feet 7amp]es74 ,! "w done by ! man 7alt]nator7 on ! weight 9 lift+ x is #aj p\nds #b feet #bj foot p\nds 7#a7 7#aj volts #b amp]es #bj watts47 ,! "w done on ! man by ! weight 9 =c+ 8 h& d[n z 8 muscles relax is #aj p\nds #b feet #bj foot p\nds 7#b7 7#aj volts #b amp]es #bj watts47 ,f 7#a7 & 7#b7 x is se5 t ! "w done by ! man on ! weight is equal to ! "w done by ! weight on ! man1 h5ce no useful "w has be5 accompli%$2 t is1 ! pot5tial en]gy ( ! weight :i* x orig9ally possess$ has n be5 increas$4 ,illu/ration3 ,,figs4 #a1cee to #a1ceg4--,me*anical analogy ( wattless curr5t4 ,if a man lift a weight any di/ance1 z f ! position ( fig4 #a1cee to position ( fig4 #a1cef1 he does a c]ta9 am\nt ( "w on ! weight giv+ x pot5tial en]gy4 ,:5 he l[]s x to its orig9al position1 z 9 fig4 #a1ceg1 ! weight loses ! pot5tial en]gy previ\sly acquir$1 t is1 x is giv5 back to ! man1 ! sy/em 7man & weight7 hav+ return$ to its orig9al condition z 9 fig4 #a1cee4 ,dur+ su* a cycle1 ! "w done by ! man on ! weight is equal to ! "w done by ! weight on ! man & no useful ext]nal "w has be5 accompli%$4 ,:y ! ,p[] ,factor is equal to ,cos 4--,9 ! prec$+ figures %[+ p[] curves = v>i\s phase relations betwe5 curr5t & pressure1 ! curves %[ ! in/antane\s values ( ! fluctuat+ p[]1 b :at is ( m importance1 is to det]m9e ! av]age p[] develop$4 ,:5 ! curr5t is 9 phase ) ! pressure1 x is a simple matt]1 because ! p[] or watts amp]es volts t is1 ! product ( ! ammet] & voltmet] read+s w give ! p[]4 ,h[ev]1 ! condition ( syn*ronism ( curr5t & pressure h>dly ev] exi/s 9 practice1 !re be+ m or less phase diff]5ce4 ,illu/ration3 ,,fig4 #a1ceh4--,me?od ( obta9+ ! active compon5t ( ! curr5t2 diagram illu/rat+ :y ! p[] factor is equal to cos 4 ,if ,,ab & ,,ac be respectively ! giv5 curr5t & pressure1 or read+s ( ! ammet] & voltmet]1 & ! angle ( phase diff]5ce betwe5 curr5t & pressure1 !n draw+ f ,b1 ,,bd p]p5dicul> to ,,ac w give ,,ad ! active compon5t4 ,n[1 true p[] ,,ac ,,ad1 b ,,ad ,,ab cos 1 h5ce true p[] ,,ac ,,ab cos 4 ,aga91 app>5t p[] ,,ac ,,ab1 & s9ce true p[] app>5t p[] p[] factor1 ! p[] factor cos 4 ,:5 ! curr5t is n 9 phase ) ! pressure1 x is consid]$ z made up ( two compon5ts at "r angles to ea* o!r4 #a4 ,! active compon5t1 9 phase ) ! pressure2 #b4 ,! wattless compon5t1 at "r angles to ! pressure4 ,) phase diff]5ce betwe5 curr5t & pressure ! product ( ammet] & voltmet] read+s d n give ! true p[]1 & 9 ord] to obta9 ! latt]1 ! active compon5t ( ! curr5t 9 phase ) ! pressure mu/ be consid]$1 t is1 true p[] volts active amp]es 7#a7 ,! active compon5t ( ! curr5t is easily obta9$ graphically z 9 fig4 #a1ceh4 ,) any conv5i5t scale draw ,,ab equal to ! curr5t z giv5 or read on ! ammet]1 & ,,ac1 equal to ! pressure1 mak+ ! angle betwe5 ,,ab & ,,ac equal to ! phase diff]5ce betwe5 ! curr5t & pressure4 ,f ,b1 draw ! l9e ,,bd p]p5dicul> to ,,ac1 !n ,,bd w be ! wattless compon5t1 & ,,ad 7measur$ ) ! same scale z 0 us$ = ,,ab7 ! active compon5t ( ! curr5t1 or t compon5t 9 phase ) ! pressure4 ,h5ce f equation 7#a7 true p[] ,,ac ,,ad 7#b7 ,n[ 9 ! "r triangle ,,abd ,,ad -- cos ,,ab f :i* ,,ad ,,ab cos 7#c7 ,sub/itut+ ?is value ( ,,ad 9 equation 7#b7 gives true p[] ,,ac ,,ab cos 7#d7 ,n[ ! p[] factor may be def9$ z3 t quantity by :i* ! app>5t watts mu/ be multipli$ 9 ord] to give ! true p[]4 ,t is true p[] app>5t watts p[] factor 7#e7 ,comp>+ equations 7#d7 & 7#e71 ,,ac ,,ab 9 7#d7 is equal to ! app>5t watts1 h5ce1 ! p[] factor 9 7#e7 is equal to cos 4 ,t is1 ! p[] factor is num]ically equal to ! cos9e ( ! angle ( phase diff]5ce betwe5 curr5t & pressure4 ,,example ,i4--,an alt]nator supplies a curr5t ( #bjj amp]es at a pressure ( #a1jjj volts4 ,if ! phase diff]5ce betwe5 ! curr5t & pressure be #cj1 :at is ! true p[] develop$8 ,9 fig4 #a1cei1 draw ,,ab to scale1 equal to #bjj amp]es1 & draw ,,ac ( indef9ite l5g? mak+ an angle ( #cj ) ,,ab4 ,f ,b1 draw ,,bd p]p5dicul> to ,,ac :i* gives ,,ad1 ! active compon5t1 & :i* measur$ ) ! same scale z 0 us$ 9 lay+ (f ,,ab1 measures #agc4b amp]es4 ,! true p[] develop$ !n is true watts #agc4b #a1jjj #agc4b kw4 ,! true p[] may be calculat$ ?us3 ,f ! table cos #cj 4#hff1 h5ce true watts #bjj #a1jjj 4#hff #agc4b kw4 ,illu/ration3 ,,fig4 #a1cei4--;,diagram = obta9+ ! active compon5t ( ! curr5t 9 a circuit hav+ a curr5t ( #bjj amp]es & angle ( lag ( #cj4 ,,example ,,ii4--,if 9 an alt]nat+ curr5t circuit1 ! voltmet] & ammet] read+s be #aaj & #bj & ! angle ( lag #de1 :at is ! app>5t p[] & true p[]8 ,! app>5t p[] is simply ! product ( ! curr5t & pressure read+s or app>5t p[] #bj #aaj #b1bjj watts ,! true p[] is ! product ( ! app>5t p[] multipli$ by ! cos9e ( ! angle ( lag4 ,cos #de 4#gjg1 h5ce true p[] #b1bjj 4#gjg #a1eee4d watts4 ,ques4 ,does ! p[] factor apply to capacity reactance 9 ! same way z to inductance reactance8 ,ans4 ,yes4 ,! angles ( lag & ( lead1 are f ! practical /&po9t1 treat$ z if !y lay 9 ! fir/ quadrant ( ! circle4 ,ev5 ! negative sign ( ! tang5t :5 x occurs is simply us$ to det]m9e :e!r ! angle be "o ( lag or ( lead1 b 9 f9d+ ! value ( ! angle f a table x is treat$ z a positive quantity4 ,illu/ration3 ,,fig4 #a1cfj4--;,diagram = obta9+ ! p[] factor = example ,,ii4 ,) conv5i5t scale1 lay (f ,,ab #bj amp]es4 ,f ,a draw ,,ac at #de to ,,ab1 & f ,b1 draw ,,bd p]p5dicul> to ,,ac4 ,!n1 ! p[] factor :i* is equal to cos9e ( angle ( lag1 ,,ad ,,ab 7by measurem5t7 #ad4ae #bj 4#gjg4 ,ques4 ,9 introduc+ capacity into a circuit to increase ! p[] factor :at %\ld be consid]$8 ,ans4 ,! co/ & upkeep ( ! add$ app>atus z well z ! p[] lo/ 9 same4 ,ques4 ,h[ is p[] lo/ 9 a cond5s]8 ,ans4 ,! loss is pr9cipally due to a ph5om5on kn[n z dielectric hy/]esis1 :i* is some:at analog\s to magnetic hy/]esis4 ,! rapidly alt]nat+ *>ges 9 a cond5s] plac$ 9 an alt]nat+ circuit may be said to cause alt]nat+ pol>ization ( ! dielectric1 & consequ5t heat+ & loss ( en]gy4 ,ques4 ,:5 is inductance introduc$ into a circuit to increase ! p[] factor8 ,ans4 ,:5 ! phase diff]5ce is due to an excess ( capacity4 ,,example4--,a circuit hav+ a resi/ance ( #c ohms1 & a resultant reactance ( #d ohms1 is connect$ to a #ajj volt l9e4 ,:at is3 #a1 ! imp$ance1 #b1 ! curr5t1 #c1 ! app>5t p[]1 #d1 ! angle ( lag1 #e1 ! p[] factor1 & #f1 ! true p[]8 #a4 ,! imp$ance ( ! circuit4 ,z 7#c #d7 #e ohms4 #b4 ,! curr5t4 curr5t volts imp$ance #ajj #e #bj amp]es4 #c4 ,! app>5t p[]4 app>5t p[] volts amp]es #ajj #bj #b1jjj watts4 #d4 ,! tang5t ( ! angle ( lag4 tan reactance resi/ance #d #c #a4cc4 ,f table ( natural tang5ts 7page #dea7 #ec4 #e4 ,! p[] factor4 ,! p[] factor is equal to ! cos9e ( ! angle ( lag1 t is1 p[] factor cos #ec 4#fjb 7f table74 #f4 ,! true p[]4 ,! true p[] is equal to ! app>5t watts multipli$ by ! p[] factor1 or true p[] volts amp]es cos #ajj #bj 4#fjb #a1bjd watts4 ,ques4 ,prove t ! p[] factor is unity :5 !re is no resultant reactance 9 a circuit4 ,ans4 ,:5 !re is no reactance1 tan :i* is equal to reactance resi/ance becomes #j ,r #j4 ,! angle 7! phase diff]5ce angle7 ^: tang5t is #j is ! angle ( #j degrees4 ,h5ce1 ! p[] factor :i* is equal to cos cos #j #a4 ,illu/ration3 ,,figs4 #a1cfa to #a1cfe4--;,diagrams illu/rat+ :y ! p[] factor is unity or "o :5 !re is no resultant reactance 9 ! circuit1 t is1 :5 ! circuit is resonant or has only resi/ance4 ,! p[] factor is equal to ! cos9e ( ! angle ( lag 7or lead74 ,9 ! figures ?is angle is ,,bac or & ! value ( ! natural cos9e ,,ac gives ! p[] factor4 ,by inspection ( ! figures1 x is evid5t t decreas+ ! reactance decreases ! angle & increases cos or ! p[] factor4 ,! circul> arc 9 ea* figure be+ at unity di/ance f ! c5t] ,a1 ! p[] factor ) decreas+ reactance evid5tly approa*es unity z its limit1 ?is limit be+ %[n 9 fig4 #a1cfe :]e ! reactance ,b',c' #j4 ,ques4 ,:at is ! usual value ( ! p[] factor 9 practice8 ,ans4 ,slightly less ?an "o4 ,ques4 ,:y is x desirable to keep ! p[] factor ne> unity8 ,ans4 ,because ) a l[ p[] factor1 :ile ! alt]nator may be c>ry+ its full load & op]at+ at a mod]ate temp]ature1 ! consum] is pay+ only = ! actual watts :i* are s5t ov] ! l9e to him4 ,illu/ration3 ,,fig4 #a1cff4--;,diagram illu/rat+ p[] factor te/1 :5 on non-inductive & inductive circuits4 ,! in/rum5ts are connect$ z %[n & by means ( ! d\ble ?r[ swit* c be put on ei!r ! non-inductive or inductive circuit4 ,fir/ turn swit* to left s t curr5t passes ?r\gh ! lamps2 = illu/ration1 ! foll[+ read+s are assum$3 ammet] #aj1 voltmet] #aaj1 & wattmet] #a1ajj4 ,! p[] factor !n is wattmet] read+ volts amp]es #a1ajj actual watts #a1ajj app>5t watts #a1 t is1 on non-inductive circuit ! p[] factor is unity4 ,n[ ?r[+ ! swit* to ! "r connect+ in/rum5ts ) ! inductive circuits1 !n = illu/ration ! foll[+ read+s may be assum$3 ammet] #h1 voltmet] #aaj1 & wattmet] #fhd4 ,n[1 z be=e1 p[] factor wattmet] read+ volts amp]es #fhd 7#h #aaj7 #fhd #hhj 4#gh4 ,= in/ance1 if a l>ge alt]nator supply+ #a1jjj kil[atts at #f1fjj volts 9 a t[n :]e a numb] ( induction motors are us$ on ! l9e be op]at+ ) a p[] factor ( say 4#fbe dur+ a great portion ( ! "t1 ! swit*bo>d in/rum5ts connect$ to ! alt]nator w give ! foll[+ read+s3 ,voltmet] #f1fjj volts2 ammet] #bdb4d amp]es2 p[] factor met] 4#fbe4 ,! app>5t watts w\ld equal #a1fjj1jjj watts or #a1fjj kil[atts1 :i*1 if multipli$ by ! p[] factor 4#fbe w\ld give #ajj1jjj1jjj watts or #a1jjj kil[atts :i* is ! actual watts suppli$4 ,! alt]nator & l9e mu/ c>ry #bdb4d amp]es in/ead ( #aea amp]es & ! diff]5ce #bdb4d - #aea #ia4d amp]es repres5ts a wattless curr5t fl[+ 9 ! circuit :i* causes useless heat+ ( ! alt]nator4 ,! me*anical p[] :i* is requir$ to drive ! alt]nator is equival5t to ! actual watts produc$1 s9ce t portion ( ! curr5t :i* lags1 is out ( phase ) ! pressure & !re=e requires no en]gy4 ,ques4 ,h[ are alt]nators rat$ by manufactur]s 9 ord] to avoid disputes8 ,ans4 ,!y usually rate _! alt]nators z produc+ s _m kilovolt amp]es in/ead ( kil[atts4 ,illu/ration3 ,,fig4 #a1cfg4--;,ayrton & ,sumpn] me?od ( alt]nat+ curr5t p[] measurem5t4 ,?ree voltmet]s are requir$1 & accord+ly ! me?od is sometimes call$ ! ?ree voltmet] me?od4 ,x is a good me?od :]e ! voltage c be regulat$ to suit ! load4 ,9 ! figure1 let ! non-inductive resi/ance ,r be plac$ 9 s]ies ) ! load ,,ab4 ,measure ! foll[+ voltages3 ,v across ! t]m9als ( ,r1 ,v across ! load ,,ab1 & ,v across bo?1 t is f ,a to ,c4 ,!n1 true watts 7,v - ,v - ,v7 #b,r4 ,! be/ conditions are :5 ,v ,v1 &1 if ,r ohm1 !n ,w ,v - ,v - ,v4 ,ques4 ,:at is a kilovolt amp]e 7kva78 ,ans4 ,a unit ( app>5t p[] 9 an alt]nat+ curr5t circuit :i* is equal to "o kil[att :5 ! p[] factor is equal to "o4 ,! ma*9e m5tion$ on page #a1abj w\ld be design$ to c>ry #aea amp]es )\t ov]heat+ & also c>ry slight ov]loads = %ort p]iods4 ,x w\ld be rat$ z #f4f kilo volts & #aea amp]es :i* w\ld equal approximately #a1jjj kil[atts :5 ! p[] factor is #a or unity1 & x %\ld op]ate )\t undue heat+4 ,n[ ! l[] ! p[] factor becomes1 ! great] ! heat+ tr\ble w be 9 try+ to produce ! #a1jjj actual kil[atts4 ,illu/ration3 ,,fig4 #a1cfh--;,curves illu/rat+ p[] factor4 ,9 a circuit hav+ no capacity or inductance1 ! p[] is giv5 by ! product ( ! respective read+s ( ! voltmet] & ammet]1 z 9 ! case ( a direct curr5t4 ,9 ! case ( a circuit hav+ capacity or inductance1 ?is product is high] ?an ! true value z f\nd by a wattmet]1 & is kn[n z ! app>5t watts4 ,! ratio true watts app>5t watts is kn[n z ! p[] factor4 ,! curr5t fl[+ 9 an inductive circuit1 su* z ! prim>y ( a trans=m]1 is really made up ( two compon5ts1 z already expla9$1 "o ( :i* 7! load or active compon5t71 is 9 phase ) ! pressure1 :ile ! o!r ! magnetiz+ compon5t1 is at "r angles to x1 t is1 x atta9s its cre/ value :5 ! o!r is at z]o1 & vice v]sa4 ,to illu/rate1 take a complete cycle divid$ into #cfj degrees & lay out on x ! curr5t requir$ to correspond to a giv5 load on ! second>y ( a trans=m]1 say a cre/ value ( #ajj amp]es1 & at "r angles to ?is lay out ! curr5t requir$ = excit+ ! magnetic circuit ( ! trans=m]1 giv+ ,a1 m]ely = purposes ( illu/ration1 a cre/ value ( #be amp]es4 ,comb9+ ^! curves1 ! dott$ curve 9 ! figure is obta9$ & :i* repres5ts ! resultant curr5t t w\ld be indicat$ by an ammet] plac$ 9 ! prim>y circuit ( ! trans=m]4 ,x w be not$ t ?is curr5t atta9s its maximum at a po9t #ad #b lat] ?an ! load curr5t1 giv+ ! angle ( lag4 ,multiply+ ! app>5t watts by ! cos9e ( ! angle ( lag gives ! true watts4 ,n[ assum+ ! diagram to %[ ! full load condition ( ! trans=m]1 ! angle ( lag be+ #ad #b1 ! p[] factor at full load is 4#ig 74#ig be+ ! value ( ! natural cos9e ( #ad #b z obta9$ f table1 su* z on page #dea74 ,) no ext]nal load on ! trans=m]1 ! load compon5t ( ! curr5t is t necess>y to make up ! core losses4 ,= in/ance1 at #e amp]es1 :ile ! magnetiz+ curr5t rema9s z be=e at #be amp]es1 ! angle ( lag becomes #gh #da & ! p[] factor 4#aif4 ,x is ?us se5 t 9 trans=m]s1 induction motors1 etc41 ! p[] factor is a function ( ! load4 ,ques4 ,h[ c ! p[] factor be kept high8 ,ans4 ,by c>efully design+ ! motors & o!r app>atus & ev5 mak+ *anges 9 ! field curr5t ( motors :i* are already in/all$4 ,ques4 ,h[ is ! p[] factor det]m9$ 9 /ation op]ation8 ,ans4 ,n by calculation1 b by read+ a met] :i* =ms "o ( ! swit*bo>d in/rum5ts4 ,illu/ration3 ,,fig4 #a1cfh4--;,flem+'s comb9$ voltmet] & ammet] me?od ( measur+ p[] 9 alt]nat+ curr5t circuits4 ,x is q accurate & enables in/rum5ts 9 use to be *eck$4 ,9 ! figure1 ,r is a non-inductive resi/ance connect$ 9 %unt to ! inductive load4 ,! voltmet] ,v measures ! pressure across ! resi/ance ,,xy4 ,a & ,a are ammet]s connect$ z %[n4 ,!n1 true watts 7,a - ,a - 7,v_/,r77 ,r _/ #b4 ,if ! volt met] ,v take an appreciable am\nt ( curr5t1 x may be te/$ z foll[s3 disconnect ,r & ,v at ,y1 & see t ,a & ,a are alike2 !n connect ,r & ,v at ,y aga91 & disconnect ! load4 ,a w equal curr5t tak5 by ,r & ,v 9 p>allel4 ,ques4 ,:5 is ! p[] factor met] ( importance 9 /ation op]ation1 & :y8 ,ans4 ,:5 rot>y conv]t]s are us$ on alt]nat+ curr5t l9es = supply+ direct curr5ts & ! sub-/ation op]ators are kept busy adju/+ ! field rheo/at ( ! rot>y to ma9ta9 a high p[] factor & prev5t ov]heat+ ( ! alt]nators dur+ ! "t ( day :5 !re is ! maximum dem& = curr5t or ! peak ( ! load4 ,,example4--,an alt]nator deliv]s curr5t at #hjj volts pressure at a frequ5cy ( #fj1 to a circuit ( :i* ! resi/ance is #ge ohms & 4#be h5ry4 ,det]m9e3 a1 ! value ( ! curr5t1 b1 angle ( lag1 c1 app>5t watts1 d1 p[] factor1 e1 true p[]4 a4 ,value ( curr5t pressure ,e curr5t --------- ----------------- imp$ance 7,r 7#b;f,l77 #hjj --------------------------------- #f4g amp]es 7#ge 7#b #c4adaf #fj 4#be77 b4 ,! angle ( lag reactance #b;f,l #b #c4adaf #fj 4#be tan ---------- ------ --------------------- #a4be resi/ance ,r #ge angle ( lag #ea #ae 7f table1 page #dea74 c4 ,! app>5t p[] app>5t p[] volts amp]es #hjj #f4g #e1cfj watts #e4cf kva4 d4 ,! p[] factor p[] factor cos9e ( ! angle ( lag cos #ea #ae 4#fbf4 e4 ,! true p[] true p[] app>5t p[] p[] factor #e1cfj 4#fbf #c1cee watts4 ,illu/ration3 ,,fig4 #a1cfi4--,wattmet] me?od ( ?ree phase p[] measurem5t4 ,two wattmet]s are requir$ 9 unbalanc$ sy/ems z %[n 9 ! illu/ration4 ,! total p[] transmitt$ is !n ! algebraic sum ( ! read+s ( ! two wattmet]s4 ,if ! p[] factor be great] ?an 4#e1 ! p[] is ! ari?metical sum1 & if x be less ?an 4#e1 ! p[] is ! ari?metical diff]5ce ( ! read+s4 ,,*apt] ,,xlix ,,alt]nators ,use ( ,alt]nators4--,! great increase 9 ! application ( electricity = supply+ p[] & = light+ purposes 9 indu/ry1 comm]ce1 & 9 ! home1 is due *iefly to ! economy ( di/ribution ( alt]nat+ curr5t4 ,direct curr5t may be us$ to advantage 9 d5sely populat$ di/ricts1 b :]e ! load is scatt]$1 x requires1 on acc\nt ( its l[ voltage1 too great an inve/m5t 9 di/ribut+ l9es4 ,9 su* cases ! alt]nator is us$ to advantage1 = :ile commutators c be built = collect+ direct curr5t up to #a1jjj volts1 alt]nators c be built up to #ab1jjj volts or m1 & ?is voltage increas$1 by /ep up trans=m]s ( high economy1 up to #ge1jjj or #ajj1jjj volts4 ,s9ce ! copp] co/ is inv]sely z ! squ>e ( ! voltage1 ! great advantage ( alt]nat+ curr5t sy/ems is cle>ly app>5t4 ,! use ( alt]nat+ curr5t ?us p]mits a l>ge am\nt ( en]gy to be economically di/ribut$ ov] a wide area f a s+le /ation1 n only r$uc+ ! co/ ( ! wir+1 b secur+ great] economy by ! use ( "o l>ge /ation1 in/ead ( sev]al small /ations4 ,! high] voltages g5]at$ by alt]nators enables ! transmission ( electrical en]gy to va/ly great] di/ances ?an possible by a direct curr5t sy/em1 s t ! en]gy f _m wat]falls t o!rwise w\ld g to wa/e may be utiliz$4 ,classes ( ,alt]nator4--,!re are v>i\s ways ( classify+ alt]nators4 ,!y may be divid$ into gr\ps1 accord+ to3 #a1 ! nature ( ! curr5t produc$2 #b1 type ( drive2 #c1 me?od ( con/ruction2 #d1 field excitation2 #e1 s]vice requirem5ts1 etc4 ,f ^! sev]al po9ts ( view1 alt]nators !n may be classifi$3 #a4 ,) respect to ! curr5t1 z3 a4 ,s+le phase2 b4 ,polyphase4 #b4 ,) respect to ! type ( drive1 z3 a4 ,belt or *a9 driv52 b4 ,direct connect$4 #c4 ,) respect to con/ruction1 z3 a4 ,revolv+ armature2 b4 ,revolv+ field2 c4 ,inductor4 ,homopol> & het]opol>4 #d4 ,) respect to mode ( field excitation1 z3 a4 ,self-excit+2 b4 ,sep>ately excit$2 ,excit] direct connect$1 or ge> driv54 c4 ,compositely excit$4 #e4 ,) respect to s]vice requirem5ts1 z3 a4 ,sl[ spe$2 b4 ,fly :eel2 c4 ,high spe$2 d4 ,wat] :eel type2 e4 ,turb9e driv54 ,s+le ,phase ,alt]nators4--,z a g5]al rule1 :5 alt]nators are employ$ = light+ circuits1 ! s+le phase ma*9es are pref]able1 z !y are simpl] 9 con/ruction & d n g5]ate ! unbalanc+ voltages (t5 occurr+ 9 polyphase "w4 ,illu/ration3 ,,fig4 #a1cgj4--;,elem5t>y f\r pole s+le phase alt]nator4 ,x has f\r inductors ^: pit* is ! same z ! pole pit*4 ,!y are connect$ 9 s]ies & t]m9ate at ! two collector r+s z %[n4 ,! poles be+ alt]nate ,n & ,s1 x is evid5t t !re w be two cycles ( ! curr5t p] revolution ( ! armature4 ,= any numb] ( poles !n ! numb] ( cycles equals ! numb] ( poles divid$ by two4 ,apply+ ,flem+'s rule = induc$ curr5ts1 ! direction ( ! curr5t induc$ 9 ! inductors is easily f\nd z indicat$ by ! arr[s4 ,! field magnets are excit$ by coils suppli$ ) direct curr5t1 usually furni%$ f an ext]nal s\rce2 = simplicity ?is is n %[n4 ,! magnets may be consid]$ z ( ! p]man5t type4 ,ques4 ,:at are ! ess5tial features ( a s+le phase alt]nator8 ,ans4 ,fig4 #a1cgj %[s an elem5t>y s+le phase alt]nator4 ,x consi/s ( an armature1 ) s+le phase w9d+1 field magnets1 & two collector r+s & bru%es ?r\gh :i* ! curr5t g5]at$ 9 ! armature passes to ! ext]nal circuit4 ,ques4 ,9 :at respect d comm]cial ma*9es diff] mo/ly f ! elem5t>y alt]nator %[n 9 fig4 #a1cgj1 & :y8 ,ans4 ,!y h a l>ge numb] ( poles & inductors 9 ord] to obta9 ! desir$ frequ5cy1 )\t excessive spe$1 & electromagnets in/ead ( p]man5t magnets4 ,illu/ration3 ,,fig4 #a1cga4--;,develop$ view ( elem5t>y s+le phase f\r pole alt]nator & s9e curve %[+ ! alt]nat+ curr5t or pressure g5]at$ dur+ "o revolution4 ,! armature is "h %[n z a flat surface ^u :i* a complete view ( ! w9d+ is se54 ,if ,m be any position ( an inductor1 by project+ up to ! curve gives ,n1 ! correspond+ value ( ! curr5t or pressure4 ,magnetic l9es are %[n at ! poles repres5t+ a field decreas+ 9 int5sity f a maximum at ! c5t] to z]o at po9ts half way betwe5 ! poles1 ?is be+ ! field condition correspond+ to ! s9e =m ( wave4 ,9 actual ma*9es ! v>iation f ! s9e curve is consid]able 9 "s alt]nators4 ,see figs4 #a1bdg & #a1bdh4 ,ques4 ,9 actual ma*9es1 :y mu/ ! magnet cores be spac$ out ar\nd ! armature ) consid]able di/ance betwe5 !m8 ,ans4 ,9 ord] to get ! necess>y field w9d+ on ! cores1 & also to prev5t undue magnetic leakage tak+ place1 lat]ally f "o limb to ! next ( opposite sign4 ,ques4 ,is !re any ga9 9 mak+ ! wid? ( ! armature coils any great] ?an ! pole pit*1 & :y8 ,ans4 ,no1 because any additional wid? w n produce m voltage1 b on ! contr>y w increase ! resi/ance & inductance ( ! armature4 ,illu/ration3 ,,fig4 #a1cgb4--;,elem5t>y f\r pole two phase alt]nator4 ,! w9d+ consi/s ( "o inductor p] phase p] pole1 t is1 f\r inductors p] phase1 ! inductors ( ea* phase be+ connect$ 9 s]ies by ! connectors & t]m9at+ at ! collector r+s4 ,?is arrangem5t requires f\r collector r+s1 giv+ two indep5d5t circuits4 ,! pit* ( ! inductors ( ea* phase is equal to ! pole pit*1 & ! phase diff]5ce is equal to "o-half ! pole pit*1 t is1 phase ,b w9d+ beg9s at ,b1 a po9t half-way betwe5 inductors ,a & ,a' ( phase ,a w9d+4 ,h5ce :5 ! curr5t or pressure 9 phase ,a is at a maximum1 9 ! ideal case1 :5 inductor ,a = in/ance is "u ! c5t] ( a pole1 ! curr5t or pressure 9 ,b is z]o1 because ,b is !n half-way betwe5 ! poles4 ,polyphase ,alt]nators4--,a multiphase or polyphase alt]nator is "o :i* deliv]s two or m alt]nat+ curr5ts diff]+ 9 phase by a def9ite am\nt4 ,= example1 if two armatures ( ! same numb] ( turns ea* be connect$ to a %aft at #ij degrees f ea* o!r & revolv$ 9 a bipol> field1 & ea* t]m9al be connect$ to a collector r+1 two sep>ate alt]nat+ curr5ts1 diff]+ 9 phase by #ij degrees1 w be deliv]$ to ! ext]nal circuit4 ,?us a two phase alt]nator w deliv] two curr5ts diff]+ 9 phase by "o-qu>t] ( a cycle1 & simil>ly a ?ree phase alt]nator 7! ?ree armatures ( :i* are set #abj degrees f ea* o!r7 w deliv] ?ree curr5ts diff]+ 9 phase by "o-?ird ( a cycle4 ,9 practice1 in/ead ( sep>ate armatures = ea* phase1 ! sev]al w9d+s are all plac$ on "o armature & 9 su* sequ5ce t ! curr5ts are g5]at$ ) ! desir$ phase diff]5ce betwe5 !m z %[n 9 ! elem5t>y diagrams #a1cgb & #a1cgc = two phase curr5t1 & figs4 #a1cgd & #a1cge = ?ree phase curr5t4 ,illu/ration3 ,,fig4 #a1cgc4--;,develop$ view ( elem5t>y two phase f\r pole alt]nator & s9e curves1 %[+ ! alt]nat+ curr5t or pressure g5]at$ dur+ "o revolution ( ! armature4 ,! complete w9d+ = ! ?ree phases are "h visible1 ! field magnets be+ repres5t$ z transp>5t s t all ( ! inductors may be se54 ,by apply+ ,flem+'s rule1 z ! inductors progress "u ! poles1 ! directions & rev]sals ( curr5t are easily det]m9$1 z indicat$ by ! s9e curves4 ,x w be se5 f ! curves t f\r poles give two cycles p] revolution4 ,inductors ,a1 & ,b are lett]$ to correspond ) fig4 #a1cgb1 ) :i* !y %\ld be comp>$4 ,ques4 ,:at use is made ( two & ?ree phase curr5t8 ,ans4 ,!y are employ$ r = p[] purposes ?an = light+1 b su* sy/ems are (t5 in/all$ = bo? s]vices4 ,ques4 ,h[ are !y employ$ 9 ea* case8 ,ans4 ,= light+ purposes ! phases are isolat$ 9 sep>ate circuits1 t is1 ea* is us$ z a s+le phase curr5t4 ,= driv+ motors ! circuits are comb9$4 ,illu/ration3 ,,fig4 #a1cgd4--;,elem5t>y f\r pole ?ree phase alt]nator4 ,!re are ?ree sets ( inductors1 ea* set connect$ 9 s]ies & spac$ on ! drum ) respect to ea* o!r two-?irds pole pit* ap>t4 ,z %[n1 six collector r+s are us$1 b on actual ?ree phase ma*9es only ?ree r+s are employ$1 z previ\sly expla9$4 ,! inductors h di/9ctive cov]+s = ! diff]5t phases4 ,! arr[s indicate ! direction 9 :i* ! induc$ pressures t5d to cause curr5ts4 ,ques4 ,:y are !y comb9$ = p[] purposes8 ,ans4 ,on acc\nt ( ! difficulty enc\nt]$ 9 />t+ a motor ) s+le phase curr5t4 ,f]>ris1 ( ,italy1 9 #ahhh discov]$ ! important pr9ciple ( ! production ( a rotat+ magnetic field by means ( two or m ,illu/ration3 ,,fig4 #a1cge4--;,elem5t>y f\r pole ?ree-phase alt]nator & s9e curves %[+ curr5t or pressure conditions = "o revolution4 ,six collector r+s are %[n giv+ ?ree indep5d5t circuits4 ,! pit* ( ! inductors = ea* phase is ! same z ! pole pit*1 & ! phase diff]5ce is equal to two-?irds ( ! pole pit*1 giv+ ! sequ5ce ( curr5t or pressure waves z indicat$ by ! s9e curves4 ,! waves foll[ ea* o!r at p]iod1 t is1 ! phase diff]5ce is #abj degrees4 ,inductors ,a1 ,b1 & ,c1 ! beg9n+ ( ea* phase w9d+1 are lett]$ to correspond ) fig4 #a1cgd1 ) :i* !y %\ld be comp>$4 _/ alt]nat+ curr5ts displac$ 9 phase f "o ano!r1 & he ?us made possible by means ( ! induction motor1 ! use ( polyphase curr5ts = p[] purposes4 ,ques4 ,:at is ! difficulty enc\nt]$ 9 />t+ a motor ) s+le phase curr5t8 ,ans4 ,a s+le phase curr5t requires ei!r a syn*ron\s motor to develop me*anical p[] f x1 or a specially con/ruct$ motor ( dual type1 ! idea ( :i* is to provide a me?od ( gett+ rotation by =eign means & !n to ?r[ 9 ! s+le phase curr5t = p[]4 ,illu/ration3 ,,fig4 #a1cgf4--;,diagram ( six phase w9d+ ) /> gr\p+1 be+ equival5t to a ?ree phase w9d+ 9 :i* ! ?ree phases are disconnect$ f ea* o!r & _! middle po9ts unit$ at a common junction4 ,illu/ration3 ,,fig4 #a1cgg4--;,diagram ( six phase w9d+ ) me% gr\p+4 ,six ,phase & ,twelve ,phase ,w9d+s4--,^! are requir$ = ! op]ation ( rot>y conv]t]s4 ,! phase diff]5ce 9 a six phase w9d+ is #fj degrees & 9 a twelve phase w9d+ #cj degrees4 ,a six phase w9d+ c be made out ( a ?ree phase w9d+ by disconnect+ ! ?ree phases f ea* o!r1 unit+ _! middle po9ts at a common junction1 z %[n by diagram fig4 #a1cgf4 ,?is w give a /> gr\p+ ) six t]m9als4 ,9 ! case ( a me% gr\p+1 ea* ( ! ?ree phases mu/ be cut into two p>ts & !n reconnect$ z %[n 9 fig4 #a1cgg4 ,illu/ration3 ,,fig4 #a1cgh4--;,diagram ( twelve phase w9d+ /> gr\p+4 ,illu/ration3 ,,fig4 #a1cgi4--;,diagram ( six phase w9d+ consi/+ ( comb9ation ( me% & /> gr\p+4 ,z ! phase diff]5ce ( a twelve phase w9d+ is "o-half t ( a six phase w9d+1 ! twelve phases may be reg>d$ z a /> gr\p+ ( six pairs cross$ at ! middle po9t ( ea* pair z %[n 9 fig4 #a1cgh1 or 9 me% gr\p+ = conv]t]s !y may be arrang$ z a twelve po9t$ polygon4 ,!y may also be gr\p$ z a comb9ation ( me% & /> z %[n 9 fig4 #a1cgi1 :i*1 h[ev]1 is n ( g5]al int]e/4 ,belt or ,*a9 ,driv5 ,alt]nators4--,! mode 9 :i* p[] is transmitt$ to an alt]nator = ! g5]ation ( curr5t is gov]n$ *iefly by conditions met ) :]e ! ma*9e is to be in/all$4 ,9 _m small p[] /ations & isolat$ plants ! use ( a belt drive is unavoidable4 ,9 "s cases ! prime mov] is already in/all$ & _c be conv5i5tly arrang$ = direct connection1 9 o!rs ! advantage to be ga9$ by an increase 9 spe$ m ?an comp5sates = ! loss involv$ 9 belt transmission4 ,illu/ration3 ,,fig4 #a1chj4--;,belt-driv5 alt]nator4 ,by use ( a belt1 any desir$ spe$ ratio is obta9$1 enabl+ ! use ( a high spe$ alt]nator :i*1 be+ small] ?an "o ( sl[ spe$1 is *eap]4 ,x af=ds means ( drive = l9e %aft & has o!r advantages1 b requires consid]able space & is n a positive drive4 ,belt+ ex]ts a side pull :i* results 9 friction & we> ( be>+s4 ,means = tight5+ ! belt z %[n 9 fig4 #a1cha1 or equival5t1 mu/ be provid$4 ,!re are _m places :]e belt$ ma*9es may be us$ advantage\sly & economically4 ,!y are easily connect$ to an exi/+ s\rce ( p[]1 z1 = in/ance1 a l9e %aft us$ = driv+ o!r ma*9]y1 & = comp>atively small in/allations !y are l[] 9 fir/ co/ ?an direct connect$ ma*9es4 ,moreov]1 :5 connect$ to l9e %aft !y are run by ! ma9 eng9e :i* z a rule is m effici5t ?an a small eng9e direct connect$4 ,:]e !re is suffici5t room betwe5 pulley c5t]s1 a belt is a satisfactory m$ium = p[] transmission1 & "o t is l>gely us$4 ,x is important t !re be lib]al di/ance betwe5 c5t]s1 especially 9 ! case ( g5]ators or motors belt$ to a m$ium or sl[ spe$ eng9e1 because1 ow+ to ! high spe$ ( rotation ( ! electric ma*9es1 !re is consid]able diff]5ce 9 _! pulley diamet]s & ! drive pulley diamet]2 h5ce1 if !y 7 close toge!r1 ! arc ( contact ( ! belt ) ! small] pulley w\ld be appreciably r$uc$1 ?us dim9i%+ ! tractive p[] ( ! belt4 ,illu/ration3 ,,fig4 #a1cha4--,sub-base & rat*et device = mov+ alt]nator to tight5 belt4 ,a rat*et ,a1 op]at$ by lev] ,b1 works ! block ,c by screw connection1 caus+ x to move ! block4 ,! latt]1 engag+ ) ! frame1 causes x to move1 ?us provid+ adju/m5t = belt4 ,aft] tight5+ belt1 ! bolts ,d1 :i* pass ?r\gh ! slots 9 ! sub-base1 are tight5$1 ?us secur+ ! ma*9e firmly 9 position4 ,ques4 ,:at provision %\ld be made 9 ! design ( an alt]nator to adapt x to belt drive8 ,ans4 ,provision %\ld be made = tight5+ ! belt4 ,illu/ration3 ,,fig4 #a1chb4--;,allis-,*alm]s p$e/al type1 belt$ alt]nator4 ,! be>+s are ( ! r+ oil+ =m ) l>ge oil res]voirs4 ,! be>+s h sph]ical seats & are self align+4 ,ques4 ,h[ is ?is done8 ,ans4 ,sometimes by an idl] pulley1 b usually by m\nt+ ! ma*9e on a sub-base provid$ ) slide rails1 z 9 fig4 #a1cha1 ! belt be+ tight5$ by use ( a rat*et screw :i* moves ! ma*9e along ! base4 ,illu/ration3 ,,fig4 #a1chc4--;,diagram illu/rat+ rule = horse p[] transmitt$ by belts4 ,a s+le belt travell+ at a spe$ ( #a1jjj feet p] m9ute w transmit "o horse p[]2 a d\ble belt w transmit twice t am\nt1 assum+ t ! ?ickness ( a d\ble belt is twice t ( a s+le belt4 ,?is is cons]vative practice1 & a belt s proportion$ w d ! "w 9 practically all cases4 ,! above rule corresponds to a pull ( #cc lbs4 p] in* ( wid?4 ,_m design]s proportion s+le belts = a pull ( #de lbs4 ,= d\ble belts ( av]age ?ickness1 "s writ]s say t ! transmitt+ effici5cy is to t ( s+le belts z #aj is to #g4 ,?is %\ld n be appli$ to ! above rule = s+le belts1 z x w give an unnecess>ily l>ge belt4 ,ques4 ,give a rule = obta9+ ! prop] size ( belt to deliv] a giv5 horse p[]4 ,ans4 ,a s+le belt travell+ at a spe$ ( "o ?\s& feet p] m9ute w transmit "o horse p[]2 a d\ble belt w transmit twice t am\nt4 ,?is corresponds to a work+ /ra9 ( #cc lbs4 p] in* ( wid? = s+le belt1 or #ff lbs4 = d\ble belt4 ,_m writ]s give z safe practice = s+le belts 9 good condition a work+ t5sion ( #de lbs4 p] in* ( wid?4 ,ques4 ,:at is ! be/ spe$ = maximum belt economy8 ,ans4 ,f #d1jjj to #d1ejj feet p] m9ute4 ,,example4--,:at is ! prop] size ( d\ble belt = an alt]nator hav+ a #af in* pulley1 & :i* requires #ej horse p[] to drive x at #a1jjj revolutions p] m9ute full load8 ,! velocity ( ! belt is circumf]5ce 9 feet revolutions feet p] m9ute #af -- #c4adaf #a1jjj #d1ahh4 #ab ,horse p[] transmitt$ p] in* wid? ( d\ble belt at #d1ahh feet spe$ #d1ahh #b ----- #h4ch4 #a1jjj ,illu/ration3 ,,fig4 #a1chd4--;,=t ,wayne revolv+ field belt driv5 alt]nator4 ,x is design$ = belt$ excit]1 hav+ a %aft ext5sion at ! collector r+ end = excit] driv+ pulley4 ,wid? ( d\ble belt = #ej horse p[] #ej #h4ch #e4ig1 say #f in*4 ,ques4 ,:at are ! advantages ( *a9 drive8 ,ans4 ,! space requir$ is mu* less ?an ) belt drive1 z ! di/ance betwe5 c5t]s may be r$uc$ to a m9imum4 ,x is a positive drive1 t is1 !re c be no slip4 ,less liability ( becom+ deta*$1 &1 because x is n dep5d5t on frictional contact1 ! diamet]s ( ! sprockets may be mu* less ?an pulley diamet] = belt drive4 ,illu/ration3 ,,figs4 #a1che & #a1chf4--;,diagram %[+ ! di/9ction betwe5 direct connect$ & direct c\pl$ units4 ,9 a direct connect$ unit1 fig4 #a1che1 ! eng9e & g5]ator are p]man5tly connect$ on "o %aft1 !re be+ "o b$ plate ^u :i* bo? are m\nt$4 ,an eng9e & g5]ator are said to be direct c\pl$ :5 ea* is indep5d5t1 z 9 fig4 #a1chf be+ connect$ solely by a jaw or friction clut* or equival5t at times :5 x is desir$ to run ! g5]ator4 ,at o!r times ! g5]ator may be disconnect$ & ! eng9e run to supply p[] = o!r purposes4 ,ques4 ,:at are "s objections8 ,ans4 ,a lubricant is requir$ = satisfactory op]ation1 :i* causes m or less dirt to collect on ! *a91 requir+ frequ5t clean+2 climb+ ( tee? :5 l9ks & tee? become worn2 noise & friction4 ,illu/ration3 ,,fig4 #a1chg4--;,engb]g direct connect$1 or eng9e type alt]nator4 ,9 _m places direct connect$ units are us$1 ow+ to ! great sav+ 9 floor space1 conv5i5ce ( op]ation1 & abs5ce ( belts4 ,direct ,connect$ ,alt]nators4--,!re are a l>ge numb] ( cases :]e economy ( space is ( prime importance1 & to meet ?is condition ! alt]nator & eng9e are direct connect$1 mean+1 t !re is no int]m$iate ge>+ su* z belt1 *a91 etc41 betwe5 eng9e & alt]nator4 ,"o difficulty enc\nt]$ 9 ! direct connection ( eng9e & alt]nator is ! fact t ! mo/ desirable rotative spe$ ( ! eng9e is less ?an t ( ! alt]nator4 ,accord+ly a compromise is made by rais+ ! eng9e spe$ & l[]+ ! alt]nator spe$4 ,! insi/5t dem& = direct connect$ units 9 ! small & m$ium sizes1 especially = direct curr5t units1 0 ! *ief cause result+ 9 ! rapid & high developm5t ( :at is kn[n z ! high spe$ automatic eng9e4 ,increas+ ! eng9e spe$ means t m horse p[] is develop$ = any giv5 cyl9d] dim5sions1 :ile r$uc+ ! spe$ ( ! g5]ator involves t ! ma*9e mu/ be l>g] = a giv5 output1 & 9 ! case ( an alt]nator m poles are requir$ to obta9 a giv5 frequ5cy1 result+ 9 increas$ co/4 ,! compactness ( ! unit z a :ole1 simplicity1 & g5]al advantages are usually s great z to m ?an (fset any additional co/ ( ! g5]ator4 ,illu/ration3 ,,fig4 #a1chh4--;,crock]-,:eel] #b1jjj kva4 #b1djj volt c\pl$ type alt]nator4 ,! c\pl$ type ( alt]nator is desirable = use ) /eam1 gas1 & oil eng9es1 & wat] :eels :]e x is inconv5i5t to m\nt ! alt]nator on ! eng9e %aft or to ext5d ! eng9e base to accommodate a be>+4 ,?is type consi/s ( alt]nator complete ) %aft & be>+s simil> to belt type ma*9es1 b ) be>+s n necess>y design$ = ! side pull ( belts4 ,ques4 ,:at is ! diff]5ce betwe5 a direct connect$ & a direct c\pl$ unit8 ,ans4 ,a direct connect$ unit comprises an eng9e & g5]ator p]man5tly connect$2 direct c\pl+ signifies t eng9e & g5]ator are ea* complete 9 itself1 t is1 hav+ two be>+s1 & are connect$ by "s device su* z friction clut*1 jaw clut*1 or %aft c\pl+4 ,revolv+ ,armature ,alt]nators4--,?is type ( alt]nator is "o :i* has its p>ts arrang$ 9 a mann] simil> to a dynamo1 t is1 ! armature is m\nt$ on a %aft s x c revolve :ile ! field magnets are atta*$ to a circul> frame & arrang$ radially ar\nd ! armature1 z %[n 9 fig4 #a1chi4 ,x may be s+le or polyphase1 belt driv51 or direct connect$4 ,illu/ration3 ,,fig4 #a1chi4--,revolv+ armature alt]nator4 ,revolv+ armatures are suitable = ma*9es g5]at+ curr5t at comp>atively l[ pressure1 z no difficulty is exp]i5c$ 9 collect+ su* curr5t4 ,revolv+ armature alt]nators are also suitable = small p[] plants1 isolat$ light+ plants1 :]e m$ium or small size ma*9es are requir$4 ,ques4 ,:5 is ! revolv+ type ( armature us$ & :y8 ,ans4 ,x is us$ on ma*9es ( small size because ! pressure g5]at$ is comp>atively l[ & ! curr5t transmitt$ by ! bru%es small1 no difficulty be+ exp]i5c$ 9 collect+ su* a curr5t4 ,illu/ration3 ,,fig4 #a1cij4--,r+ w\nd dynamo arrang$ z alt]nator by replac+ commutator ) collector r+s connect$ to ! w9d+ at po9ts #ahj ap>t4 ,ques4 ,c\ld a dynamo be conv]t$ into an alt]nator8 ,ans4 ,yes4 ,ques4 ,h[ c ?is be done8 ,ans4 ,by plac+ two collector r+s on "o end ( ! armature & connect+ ^! two r+s to po9ts 9 ! armature w9d+ #ahj ap>t1 z %[n 9 fig4 #a1cij4 ,ques4 ,w\ld su* arrangem5t z %[n 9 fig4 #a1cij make a desirable alt]nator8 ,ans4 ,no4 ,alt]nat+ curr5t w9d+s are usually diff]5t f ^? us$ = direct curr5ts4 ,"o di/9ction is ! fact t a simple op5 coil w9d+ may be1 & (t5 is1 employ$1 b ! *ief diff]5ce is ! int]mitt5t action ( ! inductors4 ,9 a direct curr5t ,gramme r+ w9d+ a c]ta9 numb] ( coils are always active1 :ile ^? 9 ! space betwe5 ! pole pieces are n g5]at+4 ,9 ?is way a practically /eady pressure is produc$ by a l>ge fraction ( ! coils4 ,9 ! case ( an alt]nator all ( ! coils are ei!r active or inactive at "o "t4 ,h5ce1 ! w9d+ ne$ cov] only z mu* ( ! armature z is cov]$ by ! pole pieces4 ,illu/ration3 ,,fig4 #a1cia4--;,engb]g alt]nat+ curr5t g5]at+ set2 %[n also 9 cross section 9 fig4 #a1chg4 ,! set comprises a v]tical eng9e & alt]nator1 direct connect$ & plac$ on "o base4 ,! lubrication sy/em comprises an oil pump situat$ 9 ! base ( ! eng9e1 pump+ ! oil f an oil res]voir up into a sight fe$ oil cup :i* leads to a di/ribut+ oil tr\gh on ! inside ( ! eng9e frame1 f "h oil pipes lead to all movable be>+s1 :i* are groov$ to insure prop] di/ribution ( oil4 ,! oil is dra9$ f be>+s into ! base1 filt]$ & re-pump$4 ,a wat] %$ p>tition is provid$ 9 ! eng9e frame1 prev5t+ any wat] pass+ f ! cyl9d] d[n into ! eng9e base & mix+ ) ! oil1 consequ5tly leav+ good1 clean oil 9 ! oil res]voir at all times4 ,! details ( ! lubrication sy/em are %[n 9 fig4 #a1chg4 ,revolv+ ,field ,alt]nators4--,9 g5]at+ an electric curr5t by caus+ an inductor to cut magnetic l9es1 x makes no diff]5ce :e!r ! cutt+ ( ! magnetic l9es is effect$ by mov+ an inductor across a magnetic field or mov+ ! magnetic field across ! inductor4 ,illu/ration3 ,,fig4 #a1cib4--;,allis-,*alm]s revolv+ field self-conta9$ belt$ type alt]nator4 ,motion is purely a relative matt]1 t is1 an object is said to move :5 x *anges its position ) "s o!r object reg>d$ z /ation>y2 x may be mov+ ) respect to a second object1 & at ! same "t be at re/ ) respect to a ?ird object4 ,?us1 a dory has a spe$ ( f\r miles p] h\r 9 /ill wat]2 if x be run up /ream aga9/ a curr5t fl[+ f\r miles p] h\r x w\ld move at t spe$ ) respect to ! wat]1 yet rema9 at re/ ) respect to ! e>?4 ,x mu/ be evid5t !n t motion1 z /at$1 be+ a purely relative matt]1 x makes no diff]5ce :e!r ! armature ( a g5]ator move ) respect to ! field magnets1 or ! field magnets move ) respect to ! armature1 s f> z induc+ an electric curr5t is conc]n$4 ,illu/ration3 ,,fig4 #a1cic4--,m>9e view1 %[+ t motion is purely a relative matt]4 ,9 ord] t !re may be motion some?+ mu/ be reg>d$ z be+ /ation>y4 ,9 ! above illu/ration a catboat is %[n at an*or 9 a /ream :i* is fl[+ at a rate ( f\r miles p] h\r 9 ! direction ( ! arr[4 ,! small dory runn+ at a spe$ ( f\r miles p] h\r aga9/ ! curr5t is mov+ at t velocity relative to ! curr5t1 yet is at a /&/ill relative to ! catboat4 ,9 ?is in/ance bo? catboat & dory are mov+ ) respect to ! wat] if ! latt] be reg>d$ z /ation>y4 ,aga9 if ! e>? be reg>d$ z be+ /ation>y1 ! two boats are at re/ & ! wat] is mov+ relative to ! e>?4 ,= alt]nators ( m$ium & l>ge size !re are sev]al reasons :y ! armature %\ld be /ation>y & ! field magnets revolve1 z foll[s3 #a4 ,by mak+ ! armature /ation>y1 sup]ior insulation me?ods may be employ$1 enabl+ ! g5]ation ( curr5t at v mu* high] voltage ?an 9 ! revolv+ armature type4 #b4 ,because ! difficulty ( tak+ curr5t at v high pressures f collector r+s is avoid$4 ,! field curr5t only passes ?r\gh ! collector r+s4 ,s9ce ! field curr5t is ( l[ voltage & small 9 comp>ison ) ! ma9 curr5t1 small bru%es are suffici5t & sp>k+ tr\bles are avoid$4 ,illu/ration3 ,,fig4 #a1cid4--;,diagram %[+ ess5tial p>ts ( a revolv+ field alt]nator & me?od ( jo9+ ! p>ts 9 assembl+4 #c4 ,only two collector r+s are requir$4 #d4 ,! armature t]m9als1 be+ /ation>y1 may be enclos$ p]man5tly s t no "o c come 9 contact ) !m4 ,ques4 ,:at names are usually appli$ to ! armature & field magnets ) respect to :i* moves8 ,ans4 ,! /ator & ! rotor4 ,! t]ms armature & field magnets are to be pref]r$ to su* expressions4 ,an armature is an armature1 no matt] :e!r x move or be fix$1 & ! same applies to ! field magnets4 ,!re is no good reason to apply o!r t]ms :i* d n def9e ! p>ts4 ,ques4 ,expla9 ! ess5tial features ( a revolv+ field alt]nator4 ,ans4 ,! con/ruction ( su* alt]nators is indicat$ 9 ! diagram1 fig4 #a1cid4 ,atta*$ to ! %aft is a field core1 :i* c>ries ! latt]1 consi/+ ( field coils fitt$ on pole pieces :i* are dovetail$ to ! field core4 ,! armature is built into ! frame & surr\nds ! magnets z %[n4 ,! field curr5t1 :i* is transmitt$ to ! magnets by slip r+s & bru%es1 consi/s ( direct curr5t ( comp>atively l[ pressure1 obta9$ f "s ext]nal s\rce4 ,illu/ration3 ,,fig4 #a1cie4--,we/]n ,electric /ation>y armature & frame ( eng9e driv5 alt]nator4 ,x is ( ca/ iron & surr\nds ! lam9at$ iron core 9 :i* ! armature w9d+s are emb$d$4 ,heavy /eel clamp+ f+]s hold ! core pun*+s 9 place & num]\s v5tilat+ ducts are provid$ 9 ! core at frequ5t int]vals to all[ free circulation ( cool air4 ,! armature coils are =m w\nd1 insulat$1 & reta9$ 9 ! core slots by means ( w$ges4 ,inductor ,alt]nators4--,9 ?is class ( alt]nator bo? armature & field magnets are /ation>y1 a curr5t be+ induc$ 9 ! armature w9d+ by ! action ( a s call$ inductor 9 mov+ ?r\gh ! magnetic field s z to p]iodically v>y its int5sity4 ,illu/ration3 ,,figs4 #a1cif & #a1cig4--;,elem5t>y inductor alt]nator2 diagram %[+ pr9ciple ( op]ation4 ,x consi/s ( a field magnet1 at ! pol> extremities ( :i* is an armature w9d+ bo? be+ /ation>y z %[n4 ,inductors consi/+ ( iron discs are arrang$ on a %aft to rotate ?r\gh ! air gap ( ! magnet poles4 ,n[ 9 ! rotation ( ! inductors1 :5 any "o ( !m passes ?r\gh ! air gap z 9 fig4 #a1cif1 ! reluctance or magnetic resi/ance ( ! air gap is greatly r$uc$1 :i* causes a correspond+ increase 9 ! numb] ( magnetic l9es pass+ ?r\gh ! armature w9d+4 ,aga9 z an inductor passes out ( ! air gap z 9 fig4 #a1cig1 ! numb] ( magnetic l9es is greatly r$uc$2 t is1 :5 an inductor is 9 ! air gap1 ! magnetic field is d5se1 & :5 no inductor is 9 ! gap1 ! field is weak2 a v>iable flux is ?us made to pass ?r\gh ! armature w9d+1 induc+ curr5t !re94 ,! ess5tial feature ( ! inductor alt]nator is t iron only is revolv+1 & z ! design is usually homopol>1 ! magnetic flux 9 its field coils is n alt]nat+1 b undulat+ 9 "*4 ,?us1 ) a giv5 maximum flux ?r\gh ea* pol> mass1 ! total numb] ( armature turns requir$ to produce a giv5 voltage is j twice t :i* is requir$ 9 an alt]nator hav+ an alt]nat+ in/ead ( an undulat+ flux ?r\gh its field w9d+s4 ,! above & ! "o %[n 9 figs4 #a1cih & #a1cii are examples ( real inductor alt]nators1 ^? %[n 9 ! o!r cuts are simply s call$ inductor alt]nators1 ! di/9ction be+ t1 z above1 ! inductor con/itutes no "p ( ! field magnet4 ,ques4 ,:at influ5ce h ! inductors on ! field flux8 ,ans4 ,!y cause x to undulate2 t is1 ! flux rises to a maximum & falls to a m9imum value1 b does n rev]se4 ,ques4 ,h[ does ?is affect ! design ( ! ma*9e z comp>$ ) o!r types ( alt]nator8 ,ans4 ,) a giv5 maximum magnetic flux ?r\gh ea* pol> mass1 ! total numb] ( armature turns necess>y to produce a giv5 pressure is twice t :i* is requir$ 9 an alt]nator hav+ an alt]nat+ flux ?r\gh its armature w9d+s4 ,illu/ration3 ,,figs4 #a1cih & #a1cii4--;,a l[ t5sion ignition sy/em ) an inductor magneto ( ! oscillat+ type4 ,! inductor ,e is rotat$ to & fro by means ( a l9k ,r1 "o end ( :i* is atta*$ to ! inductor crank1 & ! o!r to ! ignit] cam ,c4 ,two views are %[n3 imm$iately be=e & aft] sp>k+4 ,s is ! gr\nd$ electrode ( ! ignit]2 ,t an adju/able hamm] :i* is secur$ 9 position by a lock nut ,n4 ,ques4 ,is ! disadvantage due to ! necessity ( d\bl+ ! numb] ( armature turns comp5sat$ 9 any way8 ,ans4 ,yes1 ! magnetic flux is n rev]s$ or entirely *ang$ 9 ea* cycle ?r\gh ! :ole mass ( iron 9 ! armature1 ! abrupt *anges be+ l>gely conf9$ to ! projections on ! armature surface betwe5 ! coils4 ,ques4 ,:at b5efit results f ?is peculi>ity8 ,ans4 ,x enables ! use ( a v high magnetic flux d5sity 9 ! armature )\t excessive core loss1 & also ! use ( a l>ge flux )\t an excessive increase 9 ! am\nt ( magnetic iron4 ,! use ( a l>ge flux p]mits a r$uction 9 ! numb] ( armature turns1 ?us comp5sat+1 m or less1 = ! disadvantage due to ! op]ation ( only "o-half ( ! armature coils at a "t4 ,illu/ration3 ,,figs4 #a1djj & #a1dja4--,"o =m ( inductor alt]nator4 ,z %[n1 ! frame c>ries ! /ation>y armature1 :i* is ( ! slott$ type4 ,inside ( ! armature is ! revolv+ inductor1 provid$ ) ! projections built up ( wr\ght iron or /eel lam9ations4 ,! circul> excit+ coil is also /ation>y & encircles ! inductor1 ?us sett+ up a magnetic flux ar\nd ! pa? indicat$ by ! dott$ l9e1 fig4 #a1dja4 ,! project+ poles are all1 !re=e1 ( ! same pol>ity1 & z !y revolve1 ! magnetic flux sweeps ov] ! coils4 ,al?\gh ?is arrangem5t does away ) collector r+s1 ! ma*9es are n s easily con/ruct$ z o!r types1 especially 9 ! l>ge sizes4 ,! magnetiz+ coil becomes l>ge & difficult to support 9 place1 & w\ld be h>d to repair 9 case ( breakd[n4 ,inductor alt]nators h become practically obsolete1 except 9 special cases1 z inductor magnetos us$ = ignition & o!r purposes requir+ a v small size ma*9e4 ,! reasons = ! type be+ displac$ by o!r =ms ( alt]nator are *iefly because only half z great a pressure is obta9$ by a flux ( giv5 am\nt1 z w\ld be obta9$ 9 ! ord9>y type ( ma*9e4 ,x is also m exp5sive to build two armatures1 to give ! same p[]1 ?an to build "o armature4 ,?is type has /ill o!r grave defects1 among :i* may be m5tion$ enorm\s magnetic leakage1 heavy eddy curr5t losses1 inf]ior heat emissivity1 & bad regulation4 ,classes ( ,inductor ,alt]nator4--,!re are two classes into :i* inductor alt]nators may be divid$1 bas$ on ! mode ( sett+ ( _! pol> projections3 #a4 ,homopol> ma*9es2 #b4 ,het]opol> ma*9es4 ,homopol> ,inductor ,alt]nators4--,9 ?is type ! positive pol> projections ( ! inductors are set opposite ! negative pol> projections z %[n 9 fig4 #a1djb4 ,:5 ! pol> projections are set 9 ?is mann]1 ! armature coils mu/ be /agg]$ or set displac$ along ! circumf]5ce ) respect to "o ano!r at a di/ance equal to half ! di/ance f ! positive pole to ! next positive pole4 ,illu/ration3 ,,figs4 #a1djb & #a1djc4--;,homopol> & het]opol> inductors4 ,homopol> inductors h _! ,n & ,s poles opposite ea* o!r1 :ile 9 ! het]opol> type1 !y are /agg]$ z %[n4 ,het]opol> ,inductor ,alt]nators4--,ma*9es ( ?is class are ^? 9 :i* ! pol> projections are !mselves /agg]$1 z %[n 9 fig4 #a1djc1 & !re=e1 d n require ! /agg]+ ( ! armature coils4 ,9 ?is case1 a s+le armature ( d\ble wid? may be us$1 & ! rotat+ inductor !n acts z a het]opol> magnet1 or a magnet :i* pres5ts alt]natively positive & negative poles to ! armature1 in/ead ( pres5t+ a s]ies ( poles ( ! same pol>ity z 9 ! case ( a homopol> magnet4 ,use ( ,inductor ,alt]nators4--,morday orig9ally design$ & introduc$ inductor alt]nators 9 #ahff4 ,!y are n ! prevail+ type1 z _! field ( application is comp>atively n>r[4 ,!y h to be v c>efully design$ ) reg>d to magnetic leakage 9 ord] to prev5t !m be+ relatively too heavy & co/ly = _! output1 & too defective ) respect to _! pressure regulation1 o!r defects be+ heavy eddy curr5t losses & inf]ior heat conductance4 ,hunt+ or ,s++ 9 ,alt]nators4--,hunt+ is a t]m appli$ to ! /ate ( two p>allel connect$ alt]nators runn+ out ( /ep1 or n syn*ron\sly1 t is1 see saw+4 ,:5 ! curr5t wave ( an alt]nator is peak$ & two ma*9es are op]at$ 9 p>allel x is v difficult to keep !m 9 /ep1 t is 9 syn*ronism4 ,any diff]5ce 9 ! phase relation :i* is set up by ! alt]nation w cause a local or syn*roniz+ curr5t to fl[ betwe5 ! two ma*9es & at times x becomes s great t !y mu/ be disconnect$4 ,illu/ration3 ,,fig4 #a1djd4--,revolv+ field ( ,=t ,wayne alt]nator equipp$ ) amortisseur w9d+4 ,! object ( ?is w9d+ is to *eck any t5d5cy t[>d hunt+ :5 ! alt]nator is to be run z a syn*ron\s motor1 ei!r = rot>y cond5s] or p[] s]vice4 ,! amortisseur w9d+ consi/s ( heavy copp] b>s1 plac$ ar\nd & ?r\gh ! pole faces & %ort circuit$ at ! ends by heavy copp] r+s2 x s]ves z a />t+ w9d+ to br+ ! rotor up to spe$ z an induction motor1 & also s]ves z a damp+ device to neutralize any t5d5cy t[>d hunt+ caus$ by v>iation 9 spe$ ( ! g5]ator supply+ ! curr5t4 ,alt]nators :i* produce a smoo? curr5t wave & are ma9ta9$ at uni=m spe$ by prop]ly design$ gov]nors1 op]ate fairly well 9 p>allel1 b are n entirely free f hunt+1 & o!r means are provid$ to ov]come ! difficulty4 ,:5 heavy copp] flanges1 call$ damp]s1 are put ov] ! pol> projections or copp] b>s laid 9 grooves on ! pole face & %ort circuit$ by connect+ r+s 7call$ amortisseur w9d+71 ! p[]ful induc$ curr5ts :i* are produc$ :5 ! alt]nators get out ( /ep t5d to quickly re-e/abli% ! phase relation4 ,illu/ration3 ,,fig4 #a1dje4--,we/+h\se field ) amortisseur or damp] w9d+ = #ge kva4 & l>g] belt$ alt]nators1 :i* prev5ts hunt+ & r$uces eddy curr5ts 9 ! pole pieces4 ,! copp] b>s ( ! amortisseur cage w9d+ are arrang$ 9 p>tially clos$ slots 9 ! pole pieces4 ,two examples ( a field provid$ ) amortisseur#d w9d+ are %[n 9 figs4 #a1djd & #a1dje4 #d ,,note4--,amortisseur w9d+s are (t5 errone\sly call$ squirrel cage w9d+s on acc\nt ( simil>ity ( con/ruction4 ,! latt] t]m %\ld be res]v$ = its prop] significance z be+ ! "n ( ! type ( armature w9d+ g5]ally us$ = induction motors1 ! "n be+ sugge/$ by ! resemblance ( ! f9i%$ armature to ! :eel ( a squirrel cage4 ,a comp>ison ( figs4 #a1dje & #a1gdf w %[ ! di/9ction4 ,9 a squirrel cage w9d+ !re is a l>ge numb] ( b>s uni=mly spac$2 an amortisseur w9d+ consi/s ( a comp>atively small numb] ( b>s1 usually unev5ly spac$1 t is !y are divid$ into gr\ps ) consid]able space betwe5 ! gr\ps1 z 9 fig4 #a1dje1 & less pron\nc$ 9 fig4 #a1djd4 ,! b>s are %ort circuit$ by r+s ! same z 9 squirrel cage w9d+4 ,illu/ration3 ,,fig4 #a1djf4--;,diagram ( monocyclic sy/em1 %[+ monocyclic armature & trans=m] connections4 ,! monocyclic sy/em is a s+le phase sy/em prim>ily int5d$ = ! di/ribution ( lights ) an incid5tal load ( motors4 ,! light+ load is entirely connect$ to "o s+le phase circuit1 & ! motors are />t$ & op]at$ f ?is circuit ) ! assi/ance ( ! teaz] wire4 ,! long coil indicates ! ma9 w9d+ ( ! armature1 :i* is simil> 9 its arrangem5t & size to ! ord9>y armature w9d+ ( a s+le phase alt]nator4 ,! %ort coil :i* connects at "o end to ! middle po9t ( ! coil above m5tion$1 & at ! o!r to a ?ird collector r+ is call$ ! teaz] coil4 ,its use is to g5]ate a pressure 9 quadrature ) t ( ! ma9 coil4 ,?is pressure is comb9$ ) ! ma9 pressure ( ! alt]nator by trans=m]s1 s z to give suitable phase relations = op]at+ induction motors4 ,9 ! diagram ! voltage has be5 assum$ to be #b1jhj volts1 & ! voltages m>k$ to correspond ) ! g5]at$ pressure4 ,! coils ( ! alt]nator armature are connect$1 z %[n1 to two ma9 leads & to a teaz] wire4 ,betwe5 ea* end ( ! ma9 coil & ! end ( ! teaz] coils1 a resultant pressure is g5]at$4 ,^! resultants are ab\t #ab p] c5t4 l>g] ?an half ! ma9 pressure4 ,!y also h a phase diff]5ce4 ,monocyclic ,alt]nators4--,?is type ( alt]nator 0 design$ prior to ! introduction ( ! polyphase sy/ems1 to ov]come ! difficulties enc\nt]$ 9 ! op]ation ( s+le phase alt]nators z motors4 ,a s+le phase alt]nator w n />t f re/ z a motor1 b mu/ fir/ be />t$ & br\ght up to ! prop] spe$ be=e be+ connect$ ) s+le phase ma9s4 ,?is condition con/itut$ a s]i\s difficulty 9 all cases :]e ! motor _h to be /opp$ & />t$ at comp>atively frequ5t int]vals4 ,illu/ration3 ,,fig4 #a1djg4--,monocyclic sy/em diagram %[+ trans=m] connections4 ,illu/ration3 ,,fig4 #a1djh4--;,diagram %[+ section ( monocyclic alt]nator armature illu/rat+ ! armature w9d+4 ,! ma9 coils are w\nd on e o!r too?1 & ! teaz] coils are plac$ 9 quadrature ) !m1 z %[n4 ,! monocyclic alt]nator is a s+le phase ma*9e provid$ ) an additional coil1 call$ a teas] coil1 w\nd 9 two phase relation%ip )1 & connect$ to ! c5t] ( ! ma9 s+le phase coil4 ,x is provid$ ) ?ree collector r+s2 two = ! s+le phase coil1 & "o = ! free end ( ! teas] coil4 ,illu/ration3 ,,fig4 #a1dji4--;,diagram %[+ connections ( ,g5]al ,electric ,monocyclic alt]nator4 ,= #b1cjj volt ma*9e1 connect z %[n by solid l9es4 ,= #a1aej volt ma*9e1 omit connections ,a to ,b1 ,c to ,d1 ,e to ,f1 & ,g to ,h1 & connect z %[n by dott$ l9es4 ,! armature ( a /&>d monocyclic alt]nator rotates 9 a c\nt] clockwise direction fac+ ! commutator4 ,:5 ! alt]nator is load$1 ! voltage betwe5 ! teaz] coil & ! two t]m9als ( ! ma9 coil may be diff]5t2 !re=e1 x is necess>y to h ! commutator connect$ 9 correspond+ ends ( ! ma9 coil4 ,if ! ma*9e has n be5 arrang$ = clockwise rotation1 ! foll[+ *ange 9 ! connections on ! commutator-collector mu/ be made if ! ma*9e is to be run 9 p>allel ) ano!r4 ,fig4 #a1daj %[s ! connections ( monocyclic alt]nators4 ,9 fig4 #a1dji1 ! /uds on ! commutator-collector m>k$ #a & #f are ! t]m9als ( ! ma9 coil4 ,^! %\ld be rev]s$4 ,! numb]s are /amp$ on ! ends ( ! /ud & may be se5 ) ! assi/ance ( a mirror4 ,by ref]5ce to ?is diagram x is a simple matt] to trace out ! connections ) a magneto1 aft] ! armature leads are disconnect$ & ! bru%es rais$4 ,by ?is arrangem5t ord9>y s+le phase inc&esc5t light+ c be accompli%$ by means ( a s+le pair ( wires tak5 f ! s+le phase coil4 ,:]e ?ree phase motors h to be op]at$1 h[ev]1 a ?ird wire1 call$ ! p[] wire1 :i* is usually small] ?an ! ma9 s+le phase wires is c>ri$ to ! po9t at :i* ! motor is locat$1 & by ! use ( two suitably connect$ trans=m]s ?ree phase curr5ts are obta9$ f ! comb9$ s+le phase & p[] wires = op]at+ ! motors4 ,illu/ration3 ,,fig4 #a1daj4--;,diagram %[+ connections ( ,g5]al ,electric monocyclic alt]nator4 ,! solid l9es %[ /&>d connections = c\nt]-clockwise rotation2 ! brok5 l9es %[ connection *ang$ = clockwise rotation4 ,fig4 #a1djf %[s ! connections ( ! monocyclic sy/em & x is only necess>y to c>ry ! teas] wire into build+s :]e motors are to be us$4 ,armature ,reaction4--,e conductor c>ry+ a curr5t creates a magnetic field ar\nd itself1 :e!r x be emb$d$ 9 iron or lie 9 air4 ,armature inductors1 !re=e1 create magnetic fluxes ar\nd !mselves1 & ^! fluxes w1 9 "p1 int]f]e ) ! ma9 flux f ! poles ( ! field magnet4 ,! effect ( ^! fluxes is3 #a4 ,to di/ort ! field1 or #b4 ,to weak5 ! field4 ,^! di/urb+ fluxes =m1 9 "p1 /ray fluxes l9k$ ar\nd ! armature inductors t5d+ to *oke ! armature curr5t4 ,illu/ration3 ,,figs4 #a1daa & #a1dab4--,section ( armature & field %[+ di/ort+ effect ( armature reaction on ! field4 ,:5 a coil is opposite a pole z 9 fig4 #a1daa1 no curr5t is fl[+ 7assum+ no self induction7 & ! field is undi/urb$1 b1 z ! inductors pass "u a pole face z 9 fig4 #a1dab1 curr5t is induc$ 9 !m1 & l9es ( =ce are set up z indicat$ by ! dott$ l9es4 ,?is di/orts ! ma9 field s t ! l9es ( =ce are cr[d$ t[>d ! =w>d "p ( ! pole face z %[n4 ,ques4 ,expla9 h[ ! field becomes di/ort$ by armature reaction4 ,ans4 ,consid]+ a slott$ armature & analyz+ ! electrical conditions z ! inductors move pa/ a pole piece1 x w be obs]v$3 #a1 :5 ! coil is 9 ! position %[n 9 fig4 #a1daa1 ! curr5t w be z]o1 assum+ no armature self-induction1 consequ5tly = ?is position ! armature coil has no di/urb+ effect ^u ! field set up by ! field magnet2 #b1 :5 ! inductors h mov$ "u ! pole face1 z 9 fig4 #a1dab1 curr5ts w be induc$ 9 !m1 & !y w t5d to set up a magnetic field z indicat$ by ! dott$ l9es1 & 9 direction1 by ! arr[ heads4 ,! effect ( ?is field w be to di/ort ! ma9 field1 /r5g!n+ "o side ( ! pole & weak5+ ! o!r side4 ,illu/ration3 ,,fig4 #a1dac4--,section ( armature & field %[+ weak5+ effect ( armature reaction 9 ! field4 ,self-induction be+ pres5t 7z x almo/ always is71 ! curr5t lags m or less beh9d ! pressure1 s t :5 ! coil is 9 ! position ( z]o induction1 z %[n1 ! curr5t has n yet come to re/4 ,accord+ly1 l9es ( =ce 7indicat$ by ! dott$ l9es7 are set up by ! curr5t fl[+ ?r\gh ! coils :i* are 9 opposition to ! field1 ?us weak5+ ! latt]4 ,! dots & crosses 9 inductor sections1 h _! usual significance 9 def9+ ! direction ( curr5t1 repres5t+ respectively ! heads & tails ( arr[s4 ,ques4 ,expla9 h[ ! field becomes weak5$ by armature reaction4 ,ans4 ,9 all armatures !re is m or less inductance :i* causes ! curr5t to lag beh9d ! pressure a correspond+ am\nt4 ,accord+ly1 ! curr5t does n /op fl[+ at ! same in/ant t ! pressure becomes z]o1 !re=e1 :5 ! coil is 9 ! position ( z]o pressure1 z 9 fig4 #a1dac1 ! curr5t is /ill fl[+ & sets up a magnetic field :i* opposes ! ma9 field z indicat$ by ! dott$ arr[s1 ?us weak5+ ! ma9 field4 ,ques4 ,9 :at k9d ( armature is ?is effect especially pron\nc$8 ,ans4 ,9 slott$ armatures provid$ ) coils ( a l>ge numb] ( turns4 ,illu/ration3 ,,fig4 #a1dad4--,section ( armature & field %[+ /r5g!n+ effect ( armature reaction :5 ! curr5t leads ! pressure4 ,if ! circuit conta9 an excess ( capacity ! curr5t w lead ! pressure1 s t :5 ! coil is 9 ! position ( z]o induction1 z %[n1 ! curr5t w h come to re/ & rev]s$4 ,accord+ly1 l9es ( =ce 7indicat$ by ! dott$ l9es7 are set up by ! curr5t fl[+ ?r\gh ! coil & :i* are 9 ! same direction z ! l9es ( =ce ( ! field1 ?us /r5g!n+ ! latt]4 ,ques4 ,:at w\ld be ! effect if ! curr5t lead ! pressure8 ,ans4 ,x w\ld t5d to /r5g!n ! field z %[n 9 fig4 #a1dad4 ,! value ( ! armature amp]e turns :i* t5d to di/ort & to dim9i% or augm5t ! effect ( ! amp]e turns on ! field magnet is sometimes calculat$ z foll[s3 4#gjg ,i ,t ,p ,a ---------------- s 9 :i* ,a armature amp]e turns2 ,i curr5t p] phase2 ,t turns p] pole p] phase2 ,p numb] ( phases2 s product ( ! di/ribution & pit* factors ( ! w9d+4 ,?is value ( amp]e turns1 comb9$ at ! prop] phase angle ) ! field amp]e turns gives ! value ( ! amp]e turns available = produc+ useful flux4 ,illu/ration3 ,,fig4 #a1dae4--;,=t ,wayne sep>ately excit$ belt driv5 alt]nator1 a =m adapt$ = in/allation 9 small plants :]e l[ p[] factor is to be enc\nt]$4 ,?is condition exi/s 9 a l9e :]e p[] is suppli$ to induction motors1 trans=m]s or o!r inductive app>atus4 ,! type "h %[n is built 9 sizes f #cg kw4 to #bjj kw41 #fj cycles1 two or ?ree phases & voltages ( #bdj1 #dhj1 #fjj1 #a1aej or #b1cjj volts4 ,!y may be op]at$ z s+le phase alt]nators by us+ two ( ! phases & may !n be rat$ at #gj p] c5t4 ( ! polyphase rat+4 ,! field is excit$ by direct curr5t at a pressure ( #abe volts4 ,^! alt]nators may be us$ z syn*ron\s motors & = ?is duty are fitt$ ) amortisseur w9d+ 9 ! pole faces :i* does n int]f]e ) _! use z alt]nators4 ,s+le ,phase ,reactions4--,unlike ?ree phase curr5ts1 a s+le phase curr5t 9 an alt]nator armature produces a p]iodic di/urbance ( ! flux ?r\gh ! ma*9e4 ,9 ! magnet sy/em ?is di/urbance is ( twice ! normal frequ5cy1 :ile 9 ! armature core x is ! ,illu/ration3 ,,figs4 #a1daf to #a1dbe4--;,diagrams illu/rat+ sup]position ( fields4 ,9 ! figures magnetic curves repres5t+ ! effect ( ! armature curr5ts 9 sev]al diff]5t cases are sup]pos$ ^u ! magnetic curves assum$ to be due to ! field magnet4 ,! upp]mo/ l9e %[s ! prim>y field due to ! excit+ coils on ! magnet poles4 ,!y are %[n pass+ into ! armature tee? 9 two pr9cipal positions1 :]e ! middle ( a pole is3 #a1 opposite a too?1 & #b1 opposite a slot4 ,9 ! second l9e is %[n ! field due to ! armature curr5ts assum+ no lag1 & t ! magnets are n excit$4 ,if !re be no lag1 ! places ( /ronge/ curr5t w be opposite ! poles4 ,z %[n 9 ! "r h& figure :5 ! curr5t 9 "o phase ,c1 is at its maximum1 ^? 9 ! o!r phases ,a & ,b w be ( half /r5g?4 ,9 ! left h& figure :5 ! curr5t 9 "o phase ,b1 is at its z]o value1 ^? 9 ! o!r phases w be ( equal value1 or #hg p] c5t4 ( ! maximum4 ,9 ! ?ird l9e is %[n ! effect ( sup]pos+ ^! fields due to ! curr5t ^u ^? due to ! magnets z depict$ 9 ! fir/ l9e4 ,inspection ( ?is resultant field %[s h[ ! armature curr5t di/orts ! field )\t alt]+ ! total numb] ( l9es p] pole4 ,9 ! f\r? & fif? l9es are %[n ! effects ( a lagg+ curr5t4 ,a lag ( #ij is assum$2 & 9 t case ! maximum curr5t occurs 9 any inductor "o qu>t] p]iod aft] ! pole has pass$1 or at a di/ance ( half a pole pit* beh9d ! middle po9t ( ! pole1 z 9 ! f\r? l9e4 ,:5 ^! armature fields are sup]pos$ on ^? ( ! magnets 9 ! fir/ l9e ! resultant fields are ^? depict$ 9 ! fif? l9e4 ,on inspection x w be se5 t 9 ?is case !re is no di/ortion1 b a dim9ution ( ! flux f ea* pole1 z ! l9es due to ! armature curr5ts1 t5d+ to pass ?r\gh ! pole cores 9 ! s5se opposite to ^? ( ! prim>y magnetism1 mu/ be d$uct$ f ! total4 ,! twelve l9es p] pole are correspond+ly r$uc$ to eight2 &1 ( ^! eight1 f\r g a/ray con/itut+ a leakage field4 ,?is illu/rates ! effect ( a lagg+ curr5t 9 demagnetiz+ ! field magnets & 9 increas+ ! disp]sion4 _/ same z ! normal frequ5cy4 ,9 bo? cases ! eddy curr5ts :i* are set up1 produce a m>k$ increase 9 ! load losses1 & ?us t5d to give ! ma*9e a high] temp]ature rise on s+le phase load+4 ,design]s cont9ue to be s+ul>ly he$less ( ^! s+le phase reactions1 result+ 9 _m cases ( unsatisfactory s+le phase alt]nators4 ,s+le phase reactions di/ort ! wave =m ( ! ma*9e4 ,?ree ,phase ,reactions4--,! action ( ! ?ree phase curr5ts 9 an alt]nator is to produce a resultant field :i* is practically uni=m1 & :i* revolves 9 syn*ronism ) ! field sy/em4 ,! resultant ?ree phase reaction1 because ( its uni=mity1 produces no great increase 9 ! load losses ( ! ma*9e1 ! small additional losses :i* are pres5t be+ due to w9d+s n be+ plac$ actually 9 space at #abj1 & to ! local leakage 9 ! tee?4 ,illu/ration3 ,,fig4 #a1dbf4--;,diagram %[+ lat]al field betwe5 adjac5t poles4 ,magnetic ,leakage4--,9 ! design ( alt]nators ! drop ( voltage on an inductive load is ma9ly dep5d5t ^u ! magnetic leakages1 prim>y & second>y4 ,!y increase ) ! load1 &1 :at is ( m importance1 !y increase ) ! fall ( ! p[] factor ( ! circuit on :i* !y may be work+4 ,?is is "o reason :y c]ta9 types ( alt]nator1 ?\gh satisfactory on a light+ circuit1 h prov$ !mselves unsatisfactory :5 appli$ to a load consi/+ *iefly ( motors4 ,! design] mu/ "k ! v>i\s causes :i* contribute to leakage & make prop] all[ance4 ,9 g5]al1 to keep ! leakage small1 ! pole cores %\ld be %ort1 & ( m9imum surface1 ! pole %oes %\ld n h too wide a span nor be too ?ick1 nor pres5t ne$less corn]s1 & ! axial l5g? ( ! pole face & ( ! armature core %\ld n be too great 9 proportion to ! diamet] ( ! work+ face4 ,illu/ration3 ,,figs4 #a1dbg & #a1dbh4--;,diagram %[+ respectively ! "* ( /ray field betwe5 adjac5t /raight poles1 & betwe5 adjac5t poles ) %oes4 ,across ! slightly ,v-%ap$ spaces ! /ray field passes 9 l9es t1 save ne> ! out] "p1 are ne>ly /raight4 ,q /raight !y w\ld n be1 ev5 7 ! sides p>allel1 because ! diff]5ce ( magnetic pressure increases f ! roots t[>ds ! pole ends4 ,at ! roots1 :]e ! cores are atta*$ to ! yoke1 ! magnetic pressure diff]5ce is almo/ z]o4 ,x w\ld be exactly z]o if !re 7 n a p]ceptible reluctance (f]$ by ! jo9ts & by ! metal ( ! yoke4 ,! reluctance ( ! jo9t causes a few ( ! l9es to take pa?s ?r\gh ! air by a leakage :i* adds to ! useful flux4 ,at ! tops ( ! cores !re is a diff]5ce ( magnetic pressure equal to ! sum ( ! amp]e turns on ! two cores1 t5d+ to drive magnetic l9es across4 ,?is diff]5ce ( magnetic pressure increases regul>ly all ! way up ! cores f root to top2 h5ce1 ! av]age value may be tak5 z equal to ! amp]e turns on "o core4 ,! /ray field1 !re=e1 w /eadily increase 9 d5sity f ! bottom upw>ds4 ,9 addition to ?is /ray field betwe5 ! pole cores !re is also a /ray field betwe5 ! project+ tips or edges ( ! pole %oes1 z %[n 9 fig4 #a1dbh4 ,9 "s ma*9es ! disp]sion due to ! pole %oes is great] ?an t betwe5 ! flanks ( ! cores4 ,to keep ! increase ( leakage betwe5 no load & full load f undue magnitude1 x is requir$ t armature reactions %all be relatively small1 t ! p]iph]al d5sity ( ! armature curr5t 7amp]e-conductors p] in*7 be n too great1 & t ! pole cores be n too highly saturat$ :5 excit$ = no load4 ,illu/ration3 ,,fig4 #a1dbi4--,l9coln revolv+ field alt]nator4 ,! frame has op5+s = v5tilation1 ! fann+ action ( ! pole pieces caus+ a curr5t ( air to pass n only ov] ! end ( ! w9d+s1 z is usual ) o!r designs1 b also ?r\gh v5tilat+ slots 9 ! w9d+s !mselves4 ,! armature core lam9ations are anneal$ aft] pun*+ & be=e assembl+ to gu>d aga9/ ! cry/aliz+ effect ( ! pun*+4 ,! armature coils are =m w\nd & insulat$ be=e be+ plac$ 9 ! slot4 ,!re is also slot insulation :i* is put 9 ! slot previ\s to ins]t+ ! coil4 ,:5 ! w9d+ is complet$1 x is te/$ ) a pressure ( #d to #aj times ! normal voltage ( ! ma*9e4 ,! be>+s are self-align+4 ,! ma*9e is normally design$ to op]ate at a p[] factor ( approximately #gj p] c5t41 :i* means t at t p[] factor1 ! armature & fields at full load w heat equally4 ,if x h a high] p[] factor ?an #gj p] c5t4 x means t ! field w9d+s w run consid]ably cool] ?an ! armature w9d+s ) full load4 ,if ! p[] factor be l[] ?an ?is1 x w mean t ! field w9d+s w run hott] ?an ! armature on full load2 h[ev]1 ! ma*9e is design$ s t h>mful heat+ does n occur on full load ) great] p[] factor ?an #dj p] c5t4 ,! g5]al "* ( ! /ray field betwe5 adjac5t poles is %[n 9 figs4 #a1dbg & #a1dbh = /raight poles & ^? hav+ %oes4 ,field ,excitation ( ,alt]nators4--,! fields ( alt]nators require a sep>ate s\rce ( direct curr5t = _! excitation1 & ?is curr5t %\ld be pref]ably automatically controll$4 ,9 ! case ( alt]nators t are n self excit+1 ! dynamo :i* g5]ates ! field curr5t is call$ ! excit]4 ,! excitation ( an alt]nator at its rat$ ov]load & 4#h p[] factor w\ld n1 9 "s cases1 if controll$ by h&1 exce$ #abe volts1 al?\gh1 9 ord] to make its armature voltage respond quickly to *anges 9 ! load & spe$1 ! excitation ( its fields may at times be mom5t>ily v>i$ by an automatic regulator betwe5 ! limits ( #gj & #adj volts4 ,illu/ration3 ,,fig4 #a1dcj4--,we/]n ,electric armature = self-excit$ alt]nator4 ,! ma9 w9d+ is plac$ at ! bottom ( ! slots1 ea* coil be+ surr\nd$ by an arm\r ( horn fibre4 ,! excit] w9d+ occupies a v small portion ( ! slot1 be+ plac$ on top ( ! ma9 w9d+1 & connect$ to ! commutator imm$iately 9 front ( ! core & betwe5 core & collector r+s z %[n4 ,! excit] %\ld1 9 turn1 respond at once to ?is dem& ^u its armature1 & exp]i5ce has %[n t to d ?is its %unt fields mu/ h suffici5t m>g9 at full load to deliv] mom5t>ily a range f #be to #afj volts at its armature t]m9als4 ,x is obvi\s f ! above t an excit] suitable = use ) an automatic regulator mu/ commutate successfully ov] a wide range 9 voltage1 &1 if prop]ly design$1 h lib]al m>g9s 9 its %unt fields & magnetic circuits4 ,alt]nator fields design$ = & op]at$ at unity p[] factor h (t5 prov$ unsatisfactory :5 ! ma*9es 7 call$ ^u to deliv] _! rat$ kva4 at 4#h p[] factor or l[]4 ,?is is due to ! increas$ field curr5t requir$ at ! latt] condition & results1 fir/1 9 ! ov]heat+ ( ! fields &1 second1 9 ! necessity ( rais+ ! direct curr5t excit+ voltage above #abe volts1 :i* (t5 requires ! pur*ase ( new excit]s4 ,ques4 ,:at is a self-excit$ alt]nator8 ,ans4 ,"o ^: armature has1 9 addition to ! ma9 w9d+1 ano!r w9d+ connect$ to a commutator = furni%+ direct field excit+ curr5t1 z %[n 9 fig4 #a1dcj4 ,illu/ration3 ,,fig4 #a1dca4--;,frame1 b$ plate & armature w9d+ = ,we/+h\se bracket be>+ polyphase alt]nator4 ,ques4 ,h[ is a direct connect$ excit] arrang$8 ,ans4 ,! excit] armature is m\nt$ on ! %aft ( ! alt]nator close to ! spid] hub1 or 9 "s cases at a di/ance suffici5t to p]mit a p$e/al & be>+ to be m\nt$ betwe5 ! excit] & hub4 ,9 o!r designs ! excit] is plac$ betwe5 ! be>+ & hub4 ,figs4 #a1dcb & #a1dcc are examples ( direct connect$ excit] alt]nators1 9 fig4 #a1dcb ! excit] be+ plac$ betwe5 ! field hub & be>+1 & 9 fig4 #a1dcc1 beyond ! be>+4 ,ques4 ,:at is ! advantage ( a direct connect$ excit]8 ,ans4 ,economy ( space4 ,?is is app>5t by comp>+ figs4 #a1dcb & #a1dcc ) fig4 #a1dcd1 :i* %[s a belt$ excit]4 ,illu/ration3 ,,fig4 #a1dcb4--;,g5]al ,electric alt]nator ) direct connect$ excit] m\nt$ on %aft betwe5 field hub & be>+4 ,9 ! small] sizes1 ! magnet frame is bolt$ to ! be>+ bracket1 b 9 ! l>g] sizes special con/ruction is us$ dep5d+ ^u ! conditions to be met4 ,! excit]s are capable ( furni%+ ! desir$ excitation = l[ p[] factors4 ,ques4 ,:at is ! disadvantage ( a direct connect$ excit]8 ,ans4 ,x mu/ run at ! same spe$ z ! alt]nator1 :i* is sl[] ?an desirable1 h5ce ! excit] mu/ be l>g] = a giv5 output ?an ! ge> driv5 type1 because ! latt] c be run at high spe$ & accord+ly be made proportionally small]4 ,ques4 ,:at =m ( ge> is g5]ally us$ on ge> driv5 excit]s8 ,ans4 ,belt ge>4 ,illu/ration3 ,,fig4 #a1dcc4--;,=t ,wayne alt]nator ) direct connect$ excit] m\nt$ on ! field %aft at su* di/ance z to p]mit a p$e/al & be>+ to be m\nt$ betwe5 ! excit] & revolv+ field4 ,9 ! view1 ! be>+ is hidd5 by ! excit]1 only ! foot ( ! p$e/al be+ visible4 ,ques4 ,:at are ! advantages ( ge> driv5 excit]s8 ,ans4 ,be+ ge>$ to run at high spe$1 !y are small] & !re=e less co/ly ?an direct connect$ excit]s4 ,9 l>ge plants conta9+ a numb] ( alt]nators "o excit] may be us$ hav+ suffici5t capacity to excite all ! alt]nators1 & :i* c be locat$ at any conv5i5t place4 ,ques4 ,:at is ! disadvantage ( ge> driv5 excit]s8 ,ans4 ,! space occupi$ by ! ge>4 ,illu/ration3 ,,fig4 #a1dcd4--;,diagram %[+ a ,we/+h\se #ej kva41 #b1djj volt1 ?ree phase1 #fj cycle revolv+ field sep>ately excit$ alt]nator direct connect$ to a /eam eng9e4 ,! excit] is belt$ to ! alt]nator %aft1 ! driv+ pulley be+ locat$ outside ! ma9 be>+4 ,! small pulley on ! excit] gives an indication ( its high spe$ z comp>$ ) t ( ! alt]nator4 ,9 ! case ( a *a9 drive v little space is requir$1 b = belts1 ! drive g5]ally us$1 !re mu/ be consid]able di/ance betwe5 c5t]s = satisfactory transmission4 ,sl[ ,spe$ ,alt]nators4--,by sl[ spe$ is "h und]/ood relatively sl[ spe$1 su* z ! usual spe$s ( reciprocat+ eng9es4 ,a sl[ spe$ alt]nator is "o design$ to run at a spe$ sl[ en\gh t x may be direct connect$ to an eng9e4 ,su* alt]nators are ( ! revolv+ field type & a little consid]ation w %[ t !y mu/ h a multiplicity ( field magnets to atta9 ! requir$ frequ5cy4 ,9 ord] t !re be room = ! magnets1 ! ma*9e evid5tly mu/ be ( l>ge size1 especially = high frequ5cy4 ,illu/ration3 ,,fig4 #a1dce4--;,crock]-,:eel] #cej kva41 sl[ spe$ alt]nator direct connect$ to a ,corliss eng9e4 ,9 front is se5 a belt$ excit] driv5 f a pulley on ! ma9 %aft betwe5 ! alt]nator & ! l>ge b& :eel4 ,! latt] s]ves to give ! additional fly :eel effect ne$$ = close spe$ regulation4 ,,example4--,h[ _m field magnets are requir$ on a two phase alt]nator direct connect$ to an eng9e runn+ #bdj revolutions p] m9ute1 = a frequ5cy ( #fj8 ,an eng9e runn+ #bdj revolutions p] m9ute w turn #bdj #fj #d revolutions p] second4 ,a frequ5cy ( #fj requires #fj #d #ae cycles p] phase p] revolution1 or #ae #b #cj poles p] phase4 ,h5ce = a two phase alt]nator ! total numb] ( poles requir$ is #cj #b #fj4 ,x is ?us se5 t a consid]able l5g? ( spid] rim is requir$ to atta* ! num]\s poles1 ! exact size dep5d+ ^u _! dim5sions & cle>ance4 ,illu/ration3 ,,fig4 #a1dcf4--,?ree ,crock]-,:eel] #ge kva41 sl[ spe$ alt]nators direct connect$ to high spe$ eng9es4 ,! alt]nator is /yl$ sl[ spe$ al?\gh connect$ to a high spe$ eng9e1 because :at is consid]$ high eng9e spe$ is sl[ spe$ = alt]nator op]ation4 ,! alt]nators h direct connect$ excit]s :i* are pla9ly se5 9 ! illu/ration plac$ on an ext5sion ( be>+ p$e/al4 ,direct connect$ excit]s on units ( ?is k9d d n1 z a rule1 assume too bulky proportions1 because ( ! high eng9e spe$4 ,fly ,:eel ,alt]nators4--,! diamet] ( ! revolv+ fields on direct connect$ alt]nators ( v l>ge sizes becomes s great t consid]able fly :eel effect is obta9$1 al?\gh ! revolutions be l[4 ,by giv+ lib]al ?ickness to ! rim ( ! spid]1 ! rotor !n answ]s ! purpose ( a fly :eel1 h5ce no sep>ate fly :eel is requir$4 ,9 fact1 ! revolv+ elem5t resembles v closely an ord9>y fly :eel ) magnets m\nt$ on its rim1 z illu/rat$ 9 fig1 #a1dcg4 ,illu/ration3 ,,fig4 #a1dcg4--;,g5]al ,electric #dh pole #gej kw41 ?ree phase fly :eel type alt]nator4 ,x runs at a spe$ ( #aej revolutions p] m9ute1 giv+ a frequ5cy ( #fj cycles p] second & a full load pressure ( #b1cjj volts4 ,! slip r+s & leads to ! field w9d+ are cle>ly %[n 9 ! figure4 ,! field magnets are m\nt$ directly on ! rim ( ! spid]1 :i* resembles v closely a fly :eel1 & :i* 9 fact x is--h5ce ! "n fly :eel alt]nator4 ,high ,spe$ ,alt]nators4--,s9ce alt]nators may be run at spe$s f> 9 excess ( desirable eng9e spe$s1 x mu/ be evid5t t bo? size & co/ may be r$uc$ by design+ !m = high spe$ op]ation4 ,s9ce ! desir$ velocity ratio or multiplication ( spe$ is s easily obta9$ by belt drive1 t =m ( transmission is g5]ally us$ = high spe$ alt]nators1 ! *ief objection be+ ! space requir$4 ,accord+ly :]e economy ( space is n ( prime importance1 a high spe$ alt]nator is usually in/all$1 except 9 ! l>ge sizes :]e ! conditions naturally sugge/ a direct connect$ unit4 ,illu/ration3 ,,fig4 #a1dch4--;,allis-,*alm]s high spe$ belt$ type alt]nator4 ,! small pulley at ! "r & ! angle ( ! belt sugge/ ! high spe$ at :i* su* alt]nators are run1 a #ej kva4 ma*9e turn+ #a1bjj revolutions p] m9ute4 ,an example ( high spe$ alt]nator is %[n 9 fig4 #a1dch4 ,ma*9es ( ?is class run at spe$s ( #a1bjj to #a1hjj or m1 accord+ to size4 ,no "o w\ld ?9k ( connect+ an alt]nator runn+ at any su* spe$ direct to an eng9e1 ! necess>y spe$ r$uction prop] = eng9e op]ation be+ easily obta9$ by means ( a belt drive4 ,wat] ,:eel ,alt]nators4--,9 ord] to meet mo/ successfully ! requirem5ts ( ! mod]n hydro-electric plant1 ! alt]nators mu/ comb9e ^? *>act]i/ics :i* result 9 high electrical effici5cy ) a me*anical /r5g? ( ! mov+ elem5ts :i* w insure un9t]rupt$ s]vice1 & an ample factor ( safety :5 op]at+ at ! relatively high spe$s (t5 us$ ) ?is class ( ma*9e4 ,illu/ration3 ,,fig4 #a1dci4--;,allis-,*alm]s #e1jjj kva41 #dej ,r4 ,p4 ,m41 #f1fjj volt1 #fj cycle1 #c phase1 horizontal wat] :eel alt]nator4 ,! %aft is ext5d$ = ! reception ( a flange c\pl+ = direct connection to wat] :eel4 ,ow+ to ! wide range 9 output ( ! g5]at+ units & also 9 ! spe$ at :i* !y mu/ op]ate to suit v>y+ conditions ( head1 types ( :eels us$1 & o!r features p]ta9+ to wat] p[] developm5ts1 x has be5 necess>y to design a v complete l9e ( ma*9es = ?is "w4 ,! be>+s are ( ! r+ oil+ type ) l>ge oil res]voirs4 ,:5 select+ an alt]nator = wat] :eel op]ation a c>eful analysis ( ! details ( con/ruction %\ld be made 9 ord] to det]m9e ! relative values :i* h be5 assign$ by ! design]s to ! prop]ties ( ! v>i\s mat]ials us$4 ,su* analysis w p]mit ! selection ( a type ( ma*9e be/ adapt$ to ! int5d$ s]vice & :i* possesses ! requir$ *>act]i/ics ( safety1 durability & effici5cy4 ,illu/ration3 ,,fig4 #a1ddj4--,/ator ( #ejj k4w4 ,allis-,*alm]s alt]nator = direct connection to v]tical %aft hydraulic turb9e4 ,! l>ge use ( electric p[] transmitt$ by means ( high pressure alt]nat+ curr5t has l$ to ! developm5t ( a l>ge numb] ( wat] p[]s & creat$ a correspond+ dem& = alt]nators suitable = direct connection to wat] :eels4 ,ques4 ,"n two =ms ( wat] :eel alt]nator4 ,ans4 ,horizontal & v]tical4 ,examples ( horizontal & v]tical =ms ( wat] :eel alt]nator are %[n 9 figs4 #a1dci & #a1ddj4 ,ques4 ,h[ %\ld ! rotor be design$8 ,ans4 ,x %\ld be ( v sub/antial con/ruction4 ,ques4 ,:y8 ,ans4 ,because wat] :eel alt]nators are frequ5tly requir$ to op]ate safely at spe$s consid]ably 9 excess ( normal4 ,illu/ration3 ,,fig4 #a1dda4--;,allis-,*alm]s revolv+ field = wat] :eel alt]nator4 ,9 ?is type ( alt]nator x is ess5tial t ! rotat+ "p be design$ to h a lib]al factor ( safety n only at ! ord9>y op]at+ spe$1 b also at spe$s mu* 9 excess ( normal4 ,frequ5tly ma*9es are requir$ to op]ate safely at a spe$ #ej to #ge p] c5t4 9 excess ( normal1 s t !re may be no dang] 9 case ! wat] :eel races4 ,9 mo/ ma*9es ! field spid] is ( /eel ca/ 9 a s+le piece = ! small] alt]nators & 9 two or m p>ts = ! l>g] sizes4 ,= alt]nators runn+ at high p]iph]al spe$1 ! rim is built up ( /eel lam9ations support$ by a ca/ /eel spid]2 ! latt] s]ves m]ely to rotate ! rim1 :i* is 9 itself able to )/& all /resses due to ! high spe$4 ,! field poles are lam9at$1 be+ built up ( /eel pun*+s held betwe5 malleable iron or bronze end plates1 ! latt] be+ us$ on high spe$ ma*9es4 ,) b v few exceptions ! poles are atta*$ by dovetail projections t fit into correspond+ slots4 ,/eel tap]$ keys are driv5 9 alongside ! dovetails1 & ! pole pieces _c become loose4 ,all field coils1 except on a few ( ! smalle/ ma*9es1 are ( edgewise w\nd copp] /rip4 ,?is /yle ( coil is ess5tial = revolv+ field alt]nators :]e ! pressure on ! insulation1 due to c5trifugal =ce1 is s great t cotton insulation on r\nd wire w n /&4 ,curr5t is l$ into ! r+s by means ( c>bon bru%es1 ! numb] ( bru%es be+ su* t ! curr5t d5sity at ! rubb+ contact is kept )9 cons]vative limits4 ,at lea/ two bru%es p] r+ are always provid$ s t "o c be remov$ = inspection )\t int]rupt+ ! excit+ curr5t4 ,9 l>ge ma*9es ! bru% hold] /uds are m\nt$ on a /& support$ f ! base2 9 small alt]nators !y are usually fa/5$ to ! cap ( "o ( ! be>+ p$e/als4 ,illu/ration3 ,,figs4 #a1ddb to #a1ddd4--;,diagram ( turb9e alt]nator w9d+s = revolv+ armature4 ,fig4 #a1ddb illu/rates a two pole design 9 :i* all ov]lapp+ is avoid$4 ,x has #gb slots ( :i* only #dh are fill$1 giv+ #h slots p] phase4 ,! project+ claws f ! brass end %ield :i* hold ! coils 9 position are %[n 9 section4 ,fig4 #a1ddc %[s a f\r pole design hav+ #dh slots or #d slots p] phase p] pole1 ! coils be+ made up ( #h inductors p] slot tap$ toge!r1 ! end b5ds =m+ two ranges4 ,fig4 #a1ddd %[s a two pole design = a two phase armature ) #ah slots p] pole p] phase4 ,! core discs are spac$ out z = #ajh slots1 b ( ^!1 #d lots ( #g ea* are n /amp$ out1 & #h ( ^? /amp$ are left empty1 s t !re are #gb slots fill$4 ,ques4 ,:at special provision is made = cool+ ! be>+s8 ,ans4 ,!y are 9 "s cases wat] cool$4 ,turb9e ,driv5 ,alt]nators4--,al?\gh ! pr9ciple ( op]ation ( ! /eam turb9e & t ( ! reciprocat+ eng9e are decid$ly unlike1 ! pr9ciple ( op]ation ( ! high spe$ turb9e driv5 alt]nator does n diff] f t ( g5]ators design$ = be+ driv5 by o!r types ( eng9e or by wat] :eels4 ,!re are1 !re=e1 ) ! turb9e driv5 alt]nator no new ideas = ! op]ator :o is famili> ) ! old] =ms to acquire4 ,x mu/ be obvi\s t ! proportions ( su* extra high spe$ ma*9es mu/ be v diff]5t f ^? p]missible 9 g5]ators ( mu* sl[] spe$s4 ,ques4 ,h[ does a turb9e rotor diff] f ! ord9>y con/ruction8 ,ans4 ,x is made v small 9 diamet] & unusually long4 ,ques4 ,:y8 ,ans4 ,to r$uce vibration & c5trifugal /resses4 ,ques4 ,:at are ! two classes ( turb9e driv5 alt]nators8 ,ans4 ,!y are class$ z v]tical or horizontal4 ,ques4 ,h[ d !y comp>e8 ,ans4 ,! v]tical type requires less floor space ?an ! horizontal design1 & :ile a /ep be>+ is necess>y to c>ry ! weight ( ! mov+ elem5t1 !re is v little friction 9 ! ma9 be>+s4 ,! horizontal ma*9e1 :ile x occupies m space1 does n require a /ep be>+4 ,ques4 ,describe a /ep be>+4 ,ans4 ,x consi/s ( two cyl9drical ca/ iron plates be>+ ^u ea* o!r & hav+ a c5tral recess betwe5 !m into :i* lubricat+ oil is =c$ "u consid]able pressure by a /eam or electrically driv5 pump1 ! oil pass+ up f b5ea?4 ,ques4 ,:at auxili>y is g5]ally us$ 9 connection ) a /ep be>+8 ,ans4 ,a weight$ accumulator is sometimes in/all$ 9 ,illu/ration3 ,,fig4 #a1dde4--e1jjj kw4 ,curtis turb9e alt]nators in/all$ = ! ,new ,york ,c5tral ,r4 ,r4 at ,yonk]s1 ,n4 ,y4 ,! illu/ration %[s also ! auxili>y app>atus consi/+ ( cond5s]s1 vacuum augm5t]s1 circulat+ pumps1 air pumps1 etc4 ,! augm5t] ( ! fir/ ma*9e is pla9ly se5 betwe5 ! cond5s] & c5trifugal circulat+ pump4 connection ) ! oil pipe z a conv5i5t device = gov]n+ ! /ep be>+ pumps1 & also z a safety device 9 case ! pumps fail4 ,alt]nators ( ,exceptional ,"*4--,!re are a few types ( alt]nator less frequ5tly enc\nt]$ ?an ^? already describ$4 ,! ess5tials ( su* ma*9es are "h briefly giv54 ,asyn*ron\s ,alt]nators4--,9 ^! ma*9es1 ! rotat+ magnet1 :i*1 ) def9ite poles1 is replac$ by a rotor hav+ clos$ circuits4 ,9 g5]al con/ruction1 !y are simil> to asyn*ron\s induction motors hav+ %ort circuit$ rotors2 = ^! alt]nators1 :5 op]at+ z motors1 run at a spe$ slightly bel[ syn*ronism & act z g5]ators :5 ! spe$ is increas$ above t ( syn*ronism4 ,ma*9es ( ?is class are n self-excit+1 b require an alt]nat+ or polyphase curr5t previ\sly suppli$ to ! ma9s to :i* ! /ation>y armature is connect$4 ,asyn*ron\s alt]nators may be advantage\sly us$ 9 c5tral /ations t may be requir$ to su/a9 a v sudd5 increase ( load4 ,9 su* cases1 "o or m asyn*ron\s ma*9es might be kept 9 op]ation z a non-load$ motor at a spe$ j bel[ syn*ronism until its output z a g5]ator is requir$2 :5 by m]ely increas+ ! spe$ ( ! eng9e x w be made to act z a g5]ator1 ?us avoid+ ! delays usually occurr+ be=e swit*+ 9 a new alt]nator4 ,image ,curr5t ,alt]nators4--,:5 ! g5]at$ frequ5cy ( alt]nators excit$ by l[ frequ5cy curr5ts is ei!r ! sum or ! diff]5ce ( ! excitation & rotation frequ5cies1 any load curr5t fl[+ ?r\gh ! armature ( ! ma*9e is exactly reproduc$ 9 its field circuit4 ,^! reproduc$ curr5ts are *>act]i/ic ( all types ( asyn*ron\s ma*9es1 & are call$ image curr5ts1 z !y are actually ! reflection f ! load curr5ts deliv]$ by ! armature circuit4 ,z ! excit] ( a ma*9e ( ?is type c>ries image curr5ts proportional to ! g5]at$ curr5ts1 its size mu/ be proportional to ! capacity ( ! ma*9e multipli$ by ! ratio ( ! excitation & g5]at$ frequ5cies2 !re=e1 9 ! comm]cial ma*9es1 ! excitation frequ5cy is r$uc$ to ! m9imum value possible2 f two to five cycles p] second be+ suitable = conv5i5t employm5t4 ,^! ma*9es z h]et(ore con/ruct$ are n self-excit+1 b z ! pr9ciple ( image curr5t enables ! con/ruction ( self-excit+ alt]nators1 x w be ( advantage to h a g5]al und]/&+ ( ! sep>ately excit$ ma*9e "u diff]5t conditions ( excitation4 ,illu/ration3 ,,fig4 #addf4--;,diagram ( con/ant pressure image curr5t alt]nator connections4 ,! image or reproduc$ curr5ts are *>act]i/ic ( all types ( asyn*ron\s ma*9es1 & are call$ image curr5ts because !y are actually ! reflection f ! load curr5ts deliv]$ by ! armature circuit4 ,! pr9ciple ( op]ation is expla9$ 9 ! accompany+ text4 ,:5 ! g5]at$ frequ5cy ( ! ma*9e is equal to ! diff]5ce ( ! excitation & rotation frequ5cies1 ! magnetization ( ! ma*9e is high] "u a non-inductive load ?an "u no load4 ,?is is pr9cipally due to ! ohmic resi/ance ( ! field circuit1 :i* prev5ts ! image curr5t f entirely neutraliz+ ! magnetomotive =ce ( ! armature curr5t4 ,9 o!r words1 ! result ( ! magnetomotive =ce ( ! armature & image curr5ts n only t5ds to increase ! no load magnetization ( ! ma*9e at non-inductive load1 b depresses ! orig9al magnetization at inductive load1 s t ! t]m9al voltage ( ! ma*9e increases ) non-inductive load1 & decreases ) inductive load4 ,aga91 ! g5]at$ frequ5cy is equal to ! sum ( ! excitation & rotation frequ5cies1 ! resi/ance ( ! field circuit reacts positively2 t is1 x t5ds to decrease ! magnetization1 & consequ5tly ! t]m9al voltage ( ! ma*9e at bo? inductive & non-inductive loads4 ,9 ! con/ant pressure ma*9e1 ! two effects are comb9$ & oppos$ to "o ano!r4 ,! connections ( two alt]nators ) diphase excitation are %[n by fig4 #a1ddf4 ,extra ,high ,frequ5cy ,alt]nators4--,alt]nators g5]at+ curr5ts hav+ a frequ5cy up to #aj1jjj or #ae1jjj cycles p] second h be5 propos$ sev]al times = special purposes1 su* z high frequ5cy exp]im5ts1 etc4 ,9 #aijb ,nikola ,tesla propos$ "s =ms ( alt]nators hav+ a l>ge numb] ( small poles1 :i* w\ld g5]ate curr5ts up to a frequ5cy ( #ae1jjj cycles p] second4 ,lat]1 ! ,we/+h\se ,company con/ruct$ an exp]im5tal ma*9e ( ! inductor alt]nator type = g5]at+ curr5ts hav+ a frequ5cy ( #aj1jjj cycles p] second4 ,?is ma*9e 0 design$ by ,samms4 ,x _h #bjj pol> projections ) a pole pit* ( only #j4be in*1 & a p]iph]al spe$ ( #be1jjj feet p] m9ute4 ,! armature core 0 built up ( /eel ribbon #b in*es wide & #c mils ?ick4 ,! armature _h #djj slots ) "o wire p] slot1 & a bore ( ab\t #be in*es4 ,! air gap 0 only #j4jcabe in*4 ,on con/ant excitation ! voltage dropp$ f #aej volts at no-load to #abc volts ) an output ( #h amp]es4 ,self-,excit+ ,image ,curr5t ,alt]nators4--,! type ( ma*9e describ$ 9 ! prec$+ p>agraph c be made self-excit+ by connect+ ea* pair ( bru%es1 :i* collect ! curr5t f ! armature1 ) a field coil s locat$ t ! flux x produces w be displac$ by a pr$et]m9$ angle dep5d+ on ! numb] ( phases requir$1 z %[n by fig4 #a1ddg4 ,! direction ( ! residual magnetism ( ! ma*9e is %[n by ! arr[s ,a1 ,a4 ,illu/ration3 ,,fig4 #a1ddg4--;,diagram ( connections ( self-excit+ image curr5t alt]nator4 ,:5 ! armature is rotat$1 a pressure w be g5]at$ betwe5 ! bru%es #b & #d1 & a curr5t w fl[ f ,c ?r\gh ! coils ,,xx to ,b1 produc+ a flux ?r\gh ! armature at "r angles to ! residual magnetism & e/abli%+ a resultant magnetic field betwe5 ,d1 ,b1 & ,d1 ,c4 ,?is field w g5]ate a pressure betwe5 ! bru%es #a & #c1 & a curr5t w fl[ ,d ?r\gh ,,xx to ,e 9 su* a direction t x w at fir/ be oppos$ to ! residual magnetism1 & aft]w>d rev]se ! direction ( ! latt]4 ,at ! mom5t ! residual magnetism becomes z]o1 ! only magnetism left 9 ! ma*9e w be due to ! curr5ts f ! bru%es #b & #d1 & _! field comb9+ ) ! v]tical rev]s$ field w produce a resultant pol> l9e betwe5 ,b & ,e4 ,z ^! op]ations are cyclic1 !y w recur at p]iodic int]vals1 & ! ph5om5a w become cont9u\s4 ,! negative field ?us set up 9 ! air gap ( ! ma*9e w cut ! conductors ( ! /ator & w be cut by ! conductors ( ! rotor 9 su* a mann] t ! electromotive =ces g5]at$ betwe5 ! bru%es ( ! armature w be equal & opposite to ^? betwe5 ! t]m9als ( ! /ator4 ,,*apt] ,l ,,con/ruction ,,( ,,alt]nators ,! con/ruction ( alt]nators foll[s mu* ! same l9es z dynamos1 especially 9 ! case ( ma*9es ( ! revolv+ armature type4 ,usually1 h[ev]1 m poles are provid$ ?an on direct curr5t ma*9es1 9 ord] to obta9 ! requir$ frequ5cy )\t be+ driv5 at excessive spe$4 ,! ess5tial p>ts ( an alt]nator are3 #a4 ,field magnets2 #b4 ,armature2 #c4 ,collector r+s2 & 9 actual con/ruction1 9 ord] t ^! necess>y p>ts may be reta9$ 9 prop] co-relation1 & ! ma*9e op]ate prop]ly !re mu/ also be includ$3 #d4 ,frame2 #e4 ,b$ plate2 #f4 ,pulley4 ,field ,magnets4--,! e>ly =ms ( alt]nator 7 built ) p]man5tly magnetiz$ /eel magnets1 b ^! 7 lat] disc>d$ = electromagnets4 ,alt]nators are built ) ?ree k9ds ( electromagnets1 class$ accord+ to ! mann] 9 :i* !y are excit$1 ! ma*9es be+ kn[n z1 #a4 ,self-excit$2 #b4 ,sep>ately excit$2 #c4 ,compositely excit$4 ,illu/ration3 ,,figs4 #a1ddh & #a1ddi4--,we/+h\se lam9at$ hub & lam9at$ pole piece = revolv+ field hav+ squirrel cage w9d+4 ,?9 /eel is us$ = ! lam9ations ( bo? hub & pole piece2 ^! are assembl$ & firmly rivet$ toge!r "u hydraulic pressure4 ,! lam9ations are ( ! same ?ickness 9 bo? hub & spid]4 ,illu/ration3 ,,figs4 #a1dej to #a1deb4--,views ( ,triumph pole pieces4 ,^! consi/ ( lam9at$ pun*+s securely clamp$ betwe5 two ca/ /eel end plates4 ,! lam9ations are %ap$ ) pol> horns or %oes z %[n1 & :i* s]ve to keep ! field coils securely w$g$ 9 position4 ,9 "s designs ! horns are sep>ate4 ,! two holes 9 ea* pole piece are = ?r\gh bolts :i* secure ! pole piece & coil to ! spid] run4 ,dovetail jo9ts are sometimes us$ in/ead ( ?r\gh bolts1 z 9 figs4 #a1ddh & #a1ddi4 ,ques4 ,:at is a self-excit$ alt]nator8 ,ans4 ,"o 9 :i* ! field magnets are excit$ by curr5t f "o or m ( ! armature coils1 or f a sep>ate w9d+ 7small 9 comp>ison ) ! ma9 w9d+71 ! curr5t be+ trans=m$ into direct curr5t by pass+ x ?r\gh a commutator4 ,illu/ration3 ,,fig4 #a1dec4--;,=t ,wayne armature = self-excit$ alt]nator4 ,!re are two indep5d5t w9d+s1 "o = ! ma9 curr5t1 & "o = ! excit+ curr5t4 ,! w9d+ = ! latt] curr5t occupies a v small am\nt ( space1 & is plac$ 9 ! slots on top ! ma9 w9d+4 ,! commutator to :i* ! excit] w9d+ is connect$1 is locat$ betwe5 ! collector r+s & ! core4 ,x is ( /&>d con/ruction ) end clamps hold+ ! b>s 9 place on ! insulat$ commutator drum4 ,! armature coils are =m w\nd & ! core is built ( %eet /eel lam9ations1 anneal$ & japann$ to prev5t hy/]esis & eddy curr5t losses4 ,v5tilat$ op5+s are provid$ to all[ a free circulation ( air bo? ar\nd ! ends ( ! w9d+s & ?r\gh ducts 9 ! lam9at$ core4 ,! core is clamp$ by bolts betwe5 ! flanges ( ! armature spid] :i* is key$ to ! %aft4 ,^! flanges h cyl9drical ext5sions ) ribb$ surfaces1 :i* =m a support = ! ends ( ! armature coils4 ,! ribb$ surfaces =m air passages f ! core outw>d ar\nd ! ends ( ! coils1 ?us v5tilat+ bo? core & coils4 ,fig4 #a1dec %[s an armature ( a self-excit$ ma*9e1 ! excit+ curr5t be+ g5]at$ 9 a sep>ate w9d+ & pass$ ?r\gh a commutator4 ,ques4 ,= :at class ( s]vice are self-excit+ alt]nators us$8 ,illu/ration3 ,,fig4 #a1ded4--;,allis-,*alm]s ?ree be>+ type alt]nator ) excit] direct connect$4 ,! be>+ p$e/als are bolt$ to a sub/antial ca/ iron base hav+1 9 ! l>ge sizes1 suffici5t l5g? to p]mit %ift+ frame sideways along ! base to give access to ! field & armature coils4 ,! field coils are design$ = #abj volt excitation1 & are w\nd edgewise ) copp] /rip4 ,!re is a lib]al m>g9 ( field excitation to take c>e ( ov]loads or = op]ation on loads ( l[ p[] factor4 ,! regulat+ qualities are z good z c be obta9$ )\t mak+ ! ma*9e unnecess>ily l>ge & exp5sive4 ,by regulation is meant ! p]c5tage rise 9 voltage :5 full load is ?r[n (f1 field excitation & spe$ be+ held con/ant2 ! p]c5tage is ref]r$ to normal full load voltage4 ,an alt]nator ) poor regulation w %[ l>ge v>iations 9 voltage ) *anges 9 load1 ! pressure fall+ :5ev] a load is ?r[n on & ris+ :5 x is ?r[n (f4 ,^! *anges w be especially pron\nc$ if ! load be inductive4 ,a badly design$ alt]nator might %[ v fair regulation on non-inductive load & yet be unable to give full voltage on inductive load4 ,ans4 ,!y are employ$ 9 small p[] plants & isolat$ light+ plants :]e inductive loads are enc\nt]$4 ,ques4 ,:at is a sep>ately excit$ alt]nator8 ,ans4 ,"o 9 :i* ! field magnets are excit$ f a small dynamo indep5d5tly driv5 or driv5 by ! alt]nator %aft1 ei!r direct connect$ or by belt z %[n 9 fig4 #a1dee4 ,illu/ration3 ,,fig4 #a1dee4--;,diagram ( sep>ately excit$ alt]nator4 ,! field w9d+ is suppli$ ) direct curr5t1 usually at #abe volts pressure by a small dynamo call$ ! excit]4 ,! latt] may be driv5 by indep5d5t p[]1 or by belt connection ) ! ma9 %aft1 & 9 "s cases ! excit] is directly connect$ to ! alt]nator %aft4 ,ques4 ,:at is a compositely excit$ alt]nator8 ,ans4 ,a composite alt]nator is simil> to a comp\nd w\nd dynamo 9 t x has two field w9d+s4 ,9 addition to ! regul> field coils :i* c>ry ! ma9 magnetiz+ curr5t f ! excit]1 !re is a second w9d+ ^u two or ^u all ( ! pole pieces1 c>ry+ a rectifi$ curr5t f ! alt]nator :i* /r5g!ns ! field to balance ! losses 9 ! ma*9e1 & also if s desir$1 ! losses on ! l9e z %[n 9 fig4 #a1def4 ,illu/ration3 ,,fig4 #a1def4--;,diagram ( compositely excit$ alt]nator4 ,! curr5t = excit+ ! field magnets is obta9$1 p>tly f an excit] & p>tly f ! w9d+s ( ! alt]nator1 be+ trans=m$ into direct curr5t by ! rectifi]4 ,! connections are z %[n4 ,"o end ( ! armature w9d+ is connect$ to "o ( ! collector r+s2 ! o!r end1 to ! light "p ( ! rectifi]1 z %[n1 ! solid black "p ( ! rectifi] be+ connect$ to ! o!r collector r+4 ,two bru%es be> on adjac5t tee? ( ! rectifi] & are connect$ to ! comp5sat+ w9d+ circuit across :i* is a %unt4 ,^! connections are %[n m cle>ly 9 fig4 #a1deg4 ,9 op]ation ! sep>ately excit$ coils set up ! magnetism necess>y = ! g5]ation ( ! voltage at no load4 ,! ma9 curr5t com+ f ! armature is %unt$1 "p go+ ?r\gh ! %unts & ! rema9d] ar\nd ! comp5sat+ w9d+1 furni%+ ! additional magnetism necess>y to supply ! voltage to ov]come ! armature imp$ance4 ,?is composite me?od ( field excitation is v simil> to t us$ on a comp\nd w\nd dynamo4 ,z %[n1 bo? field w9d+s encircle e pole1 b 9 "s ma*9es ! rectifi$ curr5t w trav]se a few poles only1 ! curr5t f ! excit] trav]s+ ! rema9d]4 ,ques4 ,:at is a magneto8 ,ans4 ,a special =m ( alt]nator hav+ p]man5t magnets = its field1 & us$ *iefly to furni% curr5t = gas eng9e ignition & = telephone call bells4 ,details ( con/ruction & op]ation are %[n 9 figs4 #a1deh to #a1dfa4 ,illu/ration3 ,,fig4 #a1deg4--;,diagram %[+ con/ruction ( rectifi] & connections ( compositely excit$ alt]nator4 ,! rectifi] consi/s ( two ca/+s ,m & ,s ) tee? :i* fit toge!r z %[n1 be+ insulat$ s !y d n come 9 contact ) ea* o!r4 ,e alt]nate too? be+ ( ! same ca/+ is connect$ toge!r1 ! same z ?\gh jo9$ by a conduct+ wire4 ,!re are z _m tee? z !re are poles4 ,"o end ( ! armature w9d+ is connect$ direct to "o ( ! collector r+s1 :ile ! o!r is connect$ to ,m ( ! rectifi]1 ! circuit be+ ?r\gh bru%es ,p & ,q1 ! %unt1 & comp5sat+ w9d+ to ! o!r collector r+4 ,! bru%es ,p & ,q contact ) adjac5t tee?1 :5 "o is 9 contact ) ! solid black ca/+ ! o!r t\*es ! light ca/+4 ,! pr9ciple ( action is ! same z a commutator1 briefly3 to rev]se ! connections t]m9at+ at ! bru%es ,p & ,q 9 syn*ronism ) ! rev]sals ( ! alt]nat+ curr5t induc$ 9 ! armature w9d+1 ?us obta9+ direct curr5t = ! comp5sat+ field w9d+4 ,! %unt resi/ance plac$ across ! comp5sat+ w9d+ circuit p]mits adju/+ ! comp\nd+ ( ! ma*9e to ! circuit on :i* x is to "w1 s9ce by v>y+ ! resi/ance ! p]c5tage ( ! total curr5t pass+ ?r\gh ! comp5sat+ w9d+ c be *ang$4 ,x w be se5 by trac+ ! pa? ( ! curr5t = ea* direction 9 ! armature w9d+ t :ile ! rectifi] causes ! curr5t to fl[ 9 ! same direction 9 ! comp5sat+ field w9d+1 x /ill rema9s alt]nat+ 9 ! ext]nal circuit4 ,illu/ration3 ,,fig4 #a1deh4--;,connecticut magneto2 view %[+ p]man5t magnets 9 dott$ l9es4 ,x consi/s ( ?ree p]man5t ,u %ape magnets1 betwe5 ! poles ( :i* is a %uttle type armature4 ,! latt] is ge>$ to a h& crank 9 suffici5t velocity ratio to give ! desir$ spe$ )\t too rapid turn+ ( ! crank4 ,?is type ( magneto is us$ to g5]ate curr5t = op]ation ( telephone call bells4 ,illu/ration3 ,,figs4 #a1dei to #a1dfa4--;,diagram illu/rat+ ! op]ation ( a magneto4 ,! %uttle %ap$ armature is w\nd f end to end ) insulat$ wire1 s t :5 rotat$1 a p[]ful alt]nat+ curr5t is produc$ 9 ! w9d+s by cutt+ ! magnetic l9es1 ^: v>y+ /r5g? is %[n by ! %ad$ portions 9 ! two views4 ,:5 9 ! position %[n 9 ! fir/ diagram1 ! l9es ( =ce mo/ly conv]ge at ! top & bottom1 f9d+ a direct pa? ?r\gh ! metal end flanges ( ! %uttle4 ,:5 9 ! position %[n 9 ! second diagram1 ! l9es are conv]g$ s z to pass ?r\gh ! armature core4 ,fig4 #a1dfj %[s detail ( ! armature core4 ,ques4 ,:at are ! two pr9cipal types ( field magnet8 ,ans4 ,/ation>y & revolv+4 ,ques4 ,:at is ! usual con/ruction ( /ation>y field magnets8 ,ans4 ,lam9at$ pole pieces are us$1 ea* pole be+ made up ( a numb] ( /eel /amp+s rivet$ toge!r & bolt$ or pref]ably ca/ into ! frame ( ! ma*9e4 ,! field coils are ma*9e w\nd & c>efully insulat$4 ,aft] w9d+ !y are tap$ to protect !m f me*anical injury4 ,ea* coil is !n dipp$ 9 an insulat+ comp\nd & aft]w>ds bak$ to r5d] x imp]vi\s to moi/ure4 ,illu/ration3 ,,fig4 #a1dfb4--,/ation>y field ( ,=t ,wayne multiphase revolv+ armature alt]nator2 view %[+ brass girds on pole pieces = syn*ron\s motor op]ation4 ,:5 design$ = ?is use ! ma*9e is provid$ ) amortisseur w9d+ on ! poles4 ,z %[n 9 ! illu/ration ?is w9d+ consi/s ( a brass coll> ar\nd ! pole tip ) a cross rib integral ) ! coll>1 fitt+ 9 a slot 9 ! pole face p>allel to ! %aft4 ,?is con/ruction assi/s 9 br++ ! ma*9e up to syn*ron\s spe$ z an induction motor1 ord9>ily *ecks any t5d5cy t[>d hunt+ & does n 9 any way affect ! op]ation ( ! ma*9e z an alt]nator4 ,! ma9 field w9d+ %\ld be connect$ ?r\gh swit*es on ! field frame 9 ord] t ! field circuit may be brok5 up to elim9ate any dang] t might arise f induc$ voltage4 ,x is n advisable to ?r[ on a full rat$ voltage & a comp5sator %\ld1 !re=e1 be provid$ to r$uce ! pressure4 ,illu/ration3 ,,fig4 #a1dfc4--,triumph #cf pole fly :eel type revolv+ field4 ,! spid] has ! =m ( a fly :eel hav+ spokes & rim to :i* ! field magnets are atta*$ by ?r\gh bolts4 ,! field coils are ( copp] /rap b5t on end1 ! k9d g5]ally us$ on l>ge ma*9es4 ,! s]ies connection ( ! coils is pla9ly %[n1 also ! two cables lead+ via "o ( ! spokes to ! slip r+s4 ,illu/ration3 ,,fig4 #a1dfd4--,wagn] ca/ /eel hub ) dovetail grooves = atta*+ ! revolv+ field magnets4 ,su* con/ruction is g5]ally us$ on ma*9es ( small & m$ium size4 ,illu/ration3 ,,fig4 #a1dfe4--,wagn] lam9at$ pole piece ) horns /amp$ 9 "o piece4 ,! lam9ations are held toge!r betwe5 two end pieces by ?r\gh rivets1 z %[n4 ,ques4 ,describe ! con/ruction ( a revolv+ field4 ,ans4 ,! entire /ructure or rotor consi/s ( a %aft1 hub or spid]1 field magnets & slip r+s4 ,! magnet poles consi/ ( lam9at$ iron /amp+s clamp$ 9 place by means ( ?r\gh bolts :i*1 act+ ?r\gh ! ag5cy ( /eel end plates1 =ce ! lam9at$ /amp+s into a uni=m1 rigid mass4 ,?is mass is magnetically subdivid$ into s _m small p>ts t ! heat+ effect ( eddy curr5ts is r$uc$ to a m9imum4 ,! cores are m\nt$ ^u a hub or spid] ei!r by dovetail con/ruction or by means ( ?r\gh bolts1 accord+ to ! c5trifugal =ce :i* !y mu/ )/& 9 op]ation1 ei!r me?od p]mitt+ ! easy removal ( any p>ticul> field pole if necess>y4 ,! field coils are secur$ ^u ! pole pieces ei!r by horns 9 "o piece ) ! lam9ations1 or sep>ate & bolt$4 ,all ! coils are connect$ 9 s]ies1 cable leads connect+ !m to slip r+s plac$ on ! %aft4 ,illu/ration3 ,,fig4 #a1dff4--,wagn] revolv+ field ( #cjj kil[att alt]nator dur+ con/ruction1 illu/rat+ ! me?od ( atta*+ ! field magnets to ! hub by dovetail jo9ts4 ,aft] ! not*$ ends ( ! pole pieces are slid into ! grooves 9 ! hub1 tap]$ keys1 :i* are pla9ly se51 are driv5 91 ?us mak+ a tight jo9t :i* w n %ake loose4 ,ques4 ,:at are slip r+s8 ,ans4 ,insulat$ r+s m\nt$ ^u ! alt]nator %aft to receive direct curr5t = ! revolv+ field1 z di/+ui%$ f collector r+s :i* collect ! alt]nat+ curr5ts g5]at$ 9 an alt]nator ( ! revolv+ armature type4 ,9 con/ruction provision is made = atta*+ ! field w9d+ leads4 ,! r+s are usually made ( ca/ iron & are support$ me*anically ^u ! %aft1 b are insulat$ f x & f "o ano!r4 ,! curr5t is introduc$ by means ( bru%es z ) a commutator4 ,c>bon bru%es are g5]ally us$4 ,a good design ( slip r+ %\ld provide = air circulation und]nea? & betwe5 ! r+s4 ,illu/ration3 ,,fig4 #a1dfg4--;,g5]al ,electric field coil1 %[+ "o me?od ( w9d+4 ,9 ! small] ma*9es ! wire is w\nd on spools :i* are slipp$ ov] ! pole pieces1 :i* are built ( %eet iron1 spread+ at ! pole face s z to secure n only a wide pol> arc = ! prop] di/ribution ( ! magnetic flux1 b also to hold ! field w9d+s 9 place4 ,ques4 ,:at =m ( spid] is us$ on l>ge alt]nators8 ,ans4 ,x is practically ! same =m z a fly :eel1 consi/+ ( hub1 spokes1 & rim to :i* ! magnets are bolt$4 ,illu/ration3 ,,fig4 #a1dfh4--;,g5]al ,electric field coil %[+ ano!r me?od ( w9d+4 ,! field coils on ! l>g] ma*9es consi/ ( a s+le /rip ( flat copp]1 w\nd on edge z %[n1 s t ! surface ( e turn is expos$ to ! air = cool+4 ,! flat sides ( ! copp] /rip re/ aga9/ ea* o!r & ! entire coil =ms a /ructure ( great solidity :i* c be easily remov$ = inspection & repair4 ,illu/ration3 ,,fig4 #a1dfi4--;,allis-,*alm]s #fj kva4 belt$ two be>+ alt]nator on base arrang$ s ! armature c be %ift$ sideways z %[n1 to give access to ! field & armature coils4 ,on alt]nators ( ! fly :eel type ! spid] rim is made ( suffici5t weight to obta9 full fly :eel effect1 ?us mak+ a sep>ate fly :eel unnecess>y4 ,illu/ration3 ,,fig4 #a1dgj4--,revolv+ field ( ,=t ,wayne #aj pole alt]nator4 ,9 con/ruction1 ! cores ( ! field poles are built up f pun*+s ( lam9at$ /eel1 & assembl$ "u consid]able pressure betwe5 malleable iron or /eel end plates & rivet$ toge!r4 ,sub/antial insulation is plac$ on ! pole cores & ov] ?is is w\nd ! field coils ( cotton cov]$ wire4 ,aft] ! wire is 9 place1 ! complet$ poles are bak$ to expel any moi/ure & are !n treat$ ) insulat+ v>ni%4 ,!y are !n assembl$ on a lam9at$ spid]1 be+ held 9 place by dovetail jo9ts made tight by ! use ( tap] keys4 ,special ca/+ plates are f9ally fa/5$ 9 place ov] ! dove tails effectually clos+ !m4 ,! assembly ( ! field is complet$ by ! ins]tion ( ! %aft into ! field spid] "u heavy hydraulic pressure4 ,all ! coils are connect$ 9 s]ies1 cable leads connect+ !m to slip r+s plac$ on ! %aft4 ,ea* slip r+ is provid$ ) a d\ble type bru% hold]1 mak+ x possible to clean bru%es :ile ! alt]nator is 9 s]vice1 by simply remov+ "o bru% at a "t4 ,illu/ration3 ,,fig4 #a1dga4--;,g5]al ,electric slip r+s2 view %[+ con/ruction & atta*m5t ( cable leads to field w9d+4 ,!y are s design$ t all surfaces ( ! r+s h easy access to ! air1 9 ord] to obta9 good v5tilation4 ,slip r+s1 ?r\gh :i* curr5t is transmitt$ to a revolv+ field1 are to be di/+ui%$ f collector r+s ^: function x is to collect or transmit ! alt]nat+ curr5ts induc$ 9 ! armature to ! bru%es4 ,armatures4--,9 con/ruction1 armatures = alt]nators are simil> to ^? employ$ on dynamos2 !y are 9 mo/ cases simpl] ?an direct curr5t armatures due to ! small] numb] ( coils1 abs5ce ( commutator ) its multi-connections1 etc4 ,alt]nator armatures may be classifi$ 9 sev]al ways3 #a4 ,) respect to op]ation1 z a4 ,revolv+2 b4 ,/ation>y4 ,illu/ration3 ,,fig4 #a1dgb4--;,allis-,*alm]s bru% hold] & slip r+s4 ,! latt] are made ( ca/ copp]1 :i* ! build]s claim to be m satisfactory ?an ca/ iron4 ,on "s ( ! l>ge l[ spe$ ma*9es ! collector r+s are split1 b on ! majority ( alt]nators !y are 9 "o piece4 ,curr5t is l$ into ! r+s by means ( c>bon bru%es1 ! numb] ( bru%es be+ su* t ! curr5t d5sity at ! rubb+ contact is kept )9 cons]vative limits4 ,at lea/ two bru%es p] r+ are provid$1 s t "o c be remov$ = inspection )\t int]rupt+ ! excit+ curr5t4 ,9 l>ge ma*9es ! bru% hold] /uds are m\nt$ on a /& support$ f ! base2 on small alt]nators !y are usually fa/5$ to ! cap ( "o ( ! be>+ p$e/als4 ,illu/ration3 ,,fig4 #a1dgc4--;,=t ,wayne multiphase revolv+ armature alt]nator1 design$ = use 9 small p[] plants & isolat$ light+ plants :]e inductive loads are enc\nt]$4 ,built = pressures ( #abj1 #bdj1 #dhj1 & #fjj volts4 ,^! voltages h be5 recomm5d$ by ! ,am]ican ,in/itute ( ,electrical ,eng9e]s1 & w cov] ! ne$s ( any set ( conditions ord9>ily met )4 ,^! /&>d voltages n only p]mit economical di/ribution1 b !y are su* t no trans=m]s are necess>y to r$uce ! l9e pressure = ord9>y cases4 ,= transmitt+ p[] relatively long di/ances1 #fjj volts is usually employ$4 ,:]e !re is a dem& = #dhj volt s]vice1 a #dhj volt alt]nator %\ld be select$ & if l[] voltages are also desir$ an auto-trans=m] may be furni%$ by means ( :i* #bdj volts c be obta9$4 ,:5 #abj volt circuits are necess>y = light+1 etc41 ! #bdj volt pressure c be /ill fur!r r$uc$ to #abj volts by means ( ano!r auto-trans=m]4 ,h[ev]1 ?is d\ble r$uction w r>ely be f\nd necess>y4 ,illu/ration3 ,,fig4 #a1dgd4--,we/]n ,electric /ation>y armature4 ,9 ?is type ( armature1 ! core ^u :i* ! w9d+ is plac$1 is built into ! frame z %[n1 ! core tee? project+ inw>dly l int]nal ge> tee?1 =m+ a cyl9drical *amb] = ! revolv+ field4 ,! core is built up ( iron1 lam9at$ & japann$ to prev5t eddy curr5ts & hy/]esis losses4 ,! lam9ations are rigidly bolt$ betwe5 two heavy end plates4 ,! armature coils are ( copp] b> impregnat$ ) insulat+ comp\nd4 ,!y are held 9 ! slots by w$ges :i* all[ _! ready removal = inspection or repairs4 ,illu/ration3 ,,figs4 #a1dgd to #a1dgg4--,v>i\s types ( armature2 fig4 #a1dgd r+ armature2 fig4 #a1dge disc armature2 fig4 #a1dgf drum armature4 ,! latt] type is n[ almo/ univ]sally us$1 ! o!rs be+ practically obsolete4 ,a ,gramme r+ w\nd & connect$ to collector r+s z 9 fig4 #a1dgd1 w yield an alt]nat+ curr5t4 ,9 a multipol> field1 ! r+ w ne$ multipol> connections alt]nat$ at po9ts correspond+ to ! pit* ( ! poles4 ,fig4 #a1dge illu/rates ! s-call$ ,siem5s disc armature4 ,! armature coils are arrang$ ar\nd ! p]iph]y ( a ?9 disc4 ,! field magnets consi/ ( two cr[ns ( fix$ coils1 ) iron cores arrang$ s t _! free poles are opposite "o ano!r4 ,?is type 0 creat$ 9 #ahgh by ,h]r von ,hefn]1 eng9e] to ,messrs4 ,siem5s & ,halske4 ,fig1 #a1dgf %[s a mod]n drum armature ( a ?ree phase ma*9e4 ,x is simil> 9 appe>ance to a direct curr5t armature except = ! abs5ce ( ! commutator & its connections4 ,! drum armature is ! prevail+ type4 #b4 ,) respect to ! core1 z a4 ,r+2 b4 ,disc2 c4 ,drum4 ,r+ & disc armatures are practically obsolete & ne$ n be fur!r consid]$4 ,a r+ armature has ! inh]5t defect t ! copp] inside ! r+ is inactive4 ,disc armatures 7 employ$ by ,pac9otti 9 #ahgh1 & aft]w>ds adopt$ by ,bru% 9 8 arc light+ dynamos4 ,! design fail$ = me*anical reasons1 b electrically x is1 9 a s5se1 an improvem5t ^u ! ,gramme r+1 9 t inductors on bo? sides ( ! r+ are active1 ^! be+ connect$ toge!r by circumf]5tial connectors f pole to pole1 ?us1 correspond+ to ! end connectors on mod]n drum armatures4 #c4 ,) respect to ! core surface1 z a4 ,smoo? core2 b4 ,slott$ core4 ,9 e>ly dynamos ! armature w9d+s 7 plac$ ^u an iron core ) a smoo? surface4 ,a *ief disadvantage ( ?is arrangem5t is t ! magnetic drag comes ^u ! inductors & t5ds to displace !m ar\nd ! armature4 ,to prev5t ,illu/ration3 ,,fig4 #a1dgh4--;,a /yle ( disc l>gely us$ = armature cores4 ,! tee? are provid$ ) dovetail grooves ne> ! circumf]5ce4 ,aft] ! coil is ins]t$ 9 a groove1 a wood5 w$ge is driv5 9 ! groove :i* encloses ! coil & secures x firmly 9 position4 ,?is obviates ! necessity ( b&s to resi/ ! c5trifugal =ce act+ on ! inductors4 ,illu/ration3 ,,fig4 #a1dgi4--,l>ge revolv+ armature con/ruction ) segm5tal discs dovetail$ to spid] spokes4 ,illu/ration3 ,,fig4 #a1dhj4--;,con/ruction ( l>ge /ation>y armature2 view %[+ section ( core & frame4 ,! core discs are 9 segm5ts & are atta*$ to ! frame by dovetail jo9ts z %[n4 ,! jo9ts are /agg]$ 9 build+ up ! core1 t is1 !y are ov]lapp$ s z n to unduly increase ! reluctance ( ! magnetic circuit4 ,dovetail jo9ts obviate ! use ( ?r\gh bolts :i*1 if n insulat$1 are liable to give rise to eddy curr5ts by %ort circuit+ ! discs4 _/ ?is1 project+ metal pieces call$ driv+ horns 7 fix$ into ! core s z to take ! pressure1 b !y prov$ unsatisfactory4 ,?is defect toge!r ) ! long air gap necess>y 9 smoo? core con/ruction result$ 9 ! type be+ displac$ by slott$ core armatures4 ,a slott$ core is "o ^: surface is provid$ ) slots or tee? :i* c>ry ! inductors1 z %[n 9 ! accompany+ illu/rations1 & is ! type almo/ univ]sally us$4 ,! inductors are laid 9 ! slots1 ! sides & bottoms ( :i* are fir/ c>efully insulat$ by tr\ghs ( mica-canvas1 micanite or o!r suitable insulat+ mat]ial4 ,ques4 ,:at are ! advantages ( slott$ core armatures8 ,ans4 ,! tee? protect ! inductors1 reta9 !m 9 place aga9/ ! electrical drag & c5trifugal =ce1 & ! con/ruction p]mits a r$uction ( air gap to a m9imum1 ?us r$uc+ ! am\nt ( copp] requir$ = ! field4 ,illu/ration3 ,,fig4 #a1dha4--;,g5]al ,electric revolv+ field & excit] armature4 ,?is is an example ( direct connect$ excit] con/ruction4 ,9 ?is arrangem5t ! armature ( ! excit] is c>ri$ on ! alt]nator %aft at ! end f>!/ f ! pulley4 ,9 ! small] sizes ! magnet frame is bolt$ to ! be>+ bracket1 b 9 ! l>g] sizes special con/ruction is us$ dep5d+ ^u ! conditions to be met4 ,on all alt]nators ( /&>d design1 ! field is built = #abe volts excitation & on acc\nt ( ! increas$ dang] f induc$ voltage1 9 case ! ma*9e is us$ z a syn*ron\s motor1 ! build]s consid] any high] voltage undesirable4 ,illu/ration3 ,,fig4 #a1dhb4--,section ( ,g5]al ,electric ,alt]nator %[+ me?od ( dovetail+ core lam9ations to frame4 ,! latt] is made 9 two g5]al /yles1 kn[n z ! box type & skeleton type4 ,! box type consi/s ( a s+le ca/+ = ! small] sizes1 b = l>ge capacity alt]nators ! frame ca/+s are usually divid$ into upp] & l[] sections4 ,! skeleton type consi/s ( two side ca/+s betwe5 :i* sub/antial spac+ rods are set at regul> int]vals4 ,! core consi/s ( ! usual %eet iron lam9ation slott$ & assembl$2 !y are m\nt$ on ! inn] p]iph]y ( ! frame1 mak+ lap jo9ts 7t is /agg]$ z 9 fig4 #a1dhj71 ea* section be+ dovetail$ to ! frame4 ,heavy clamp+ r+s or end plates are m\nt$ on bo? sides ( ! core by means ( bolts1 & support+ f+]s ext5d along ! slot projections4 ,! design is su* z to provide = air circulation z %[n 9 figs4 #a1dhc & #a1dhd4 ,armature ,w9d+s4--,9 g5]al1 ! s*emes = armature w9d+s = alt]nators are simpl] ?an ^? = direct curr5t ma*9es1 z 9 ! majority ( cases ! inductors are an ev5 multiple ( ! numb] ( poles1 & ! gr\p+s are usually symmetrical ) respect to ea* pole or ea* pair ( poles4 ,fur!rmore1 z a g5]al rule1 all ! inductors ( any "o phase are 9 s]ies ) "o ano!r2 !re=e1 !re is only "o circuit p] phase1 & ?is is z x %\ld be1 s9ce alt]nators are usually requir$ to g5]ate high voltages4 ,^! g5]al pr9ciples e/abli% ! rule1 t 9 ! circuit 9 a s+le phase armature1 & 9 ! individual circuits 9 a polyphase armature1 ! w9d+ is nev] re-entrant1 b ! circuits h def9ite end+s & beg9n+s4 ,9 exceptional cases1 z ^? ( polyphase conv]t]s1 re-entrant circuits are employ$1 & ! armature w9d+s are s con/ruct$ t a commutator c be connect$ to !m exactly z 9 direct curr5t ma*9es4 ,^! armatures are usually ( ! lap w\nd drum type4 ,illu/ration3 ,,fig4 #a1dhc4--,section ( ,g5]al ,electric alt]nator frame %[+ air ducts & support+ f+]s ext5d+ along ! slot projections4 ,! air circulation is provid$ = by means ( ducts =m$ by suitable spac+ blocks ins]t$ at int]vals betwe5 ! lam9ations1 z %[n "h & 9 fig4 #a1dhd4 ,! armature coils are =m w\nd & design$ s !y c be readily replac$ 9 case ( injury4 ,!y are tap$ & treat$ ) an impregnat+ comp\nd1 9 ! usual way1 !n ins]t$ 9 ! armature slots 9 an arm\r ( horn fibre & reta9+ w$ges ( wood are dovetail$ into ! slot walls4 ,alt]nator w9d+s are usually describ$ 9 t]ms ( ! numb] ( slots p] phase p] pole4 ,= in/ance1 if ! armature ( a #bj pole ?ree phase ma*9e h #cjj slots1 x has #ae slots p] pole or #e slots p] ea* phase p] pole1 & w be describ$ z a five slot w9d+4 ,!re=e1 9 ord] to trace ! connections ( a w9d+1 x is necess>y to consid] ! numb] ( slots p] pole = any "o phase on "o ( ! foll[+ assumptions3 #a1 t ea* slot holds "o inductor2 #b1 t !re is "o side ( a coil 9 ea* slot2 & #c1 t "o side ( a coil is subdivid$ s z to p]mit ( its di/ribution 9 two or m adjac5t slots4 ,! voltage dep5ds ^u ! numb] ( inductors 9 a slot1 b ! bread? coeffici5t & wave =m are influ5c$ by ! numb] ( slots p] pole1 & n by ! numb] ( inductors )9 ! slots4 ,illu/ration3 ,,fig4 #a1dhd4--,section ( ,g5]al ,electric /ation>y armature %[+ me?od ( assembl+ ! coils4 ,^! are =m w\nd & are held 9 ! slots by suitable w$ges1 ! op5 slot con/ruction p]mitt+ ! use ( =m w\nd coils t c be easily remov$ & replac$ 9 case ( damage4 ,:]e heavy w9d+s project beyond ! lam9ations1 an additional support is provid$ by means ( an insulat$ metal r+1 to :i* ! out] ends ( ! coils are fa/5$2 ! coils are !reby protect$ f me*anical displacem5t1 or di/ortion due to ! magnetic di/urbances caus$ by viol5t fluctuations ( ! load or %ort circuits4 ,! figure %[s a section ( a support+ r+ ( ?is type & indicates ! me?od ( connect+ ! coils to x4 ,9 ord] to admit ( ! prompt replacem5t ( damag$ coils1 suffici5t space is usually provid$ betwe5 ! alt]nator be>+s to all[ ample movem5t ( ! armature to p]mit ( ready access to bo? armature & field coils4 ,:]e space necessitates ! use ( a %ort %aft1 access to ! w9d+s may be _h by disconnect+ "s ( ! coils & lift+ ! upp] half ( ! armature4 ,classification ( ,w9d+s4--,! fact t alt]nators are built 9 s _m diff]5t types1 gives rise to num]\s k9ds ( armature w9d+ to meet ! v>i$ conditions ( op]ation4 ,9 divid+ ^! =ms ( w9d+ into di/9ctive gr\ps1 !y may be classifi$1 accord+ to sev]al po9ts ( view1 z foll[s3 #a4 ,) respect to ! =m ( ! armature1 z3 a4 ,revolv+2 b4 ,/ation>y4 #b4 ,) respect to ! mode ( progression1 z3 a4 ,lap w9d+2 b4 ,wave w9d+4 #c4 ,) respect to ! relation betwe5 numb] ( poles & numb] ( coils1 z3 a4 ,half coil w9d+2 b4 ,:ole coil w9d+4 #d4 ,) respect to ! numb] ( slots1 z3 a4 ,conc5trat$ or uni-coil w9d+2 b4 ,di/ribut$ or multi-coil w9d+4 ,p>tially di/ribut$2 ,fully di/ribut$4 #e4 ,) respect to ! =m ( ! inductors1 z3 a4 ,wire w9d+2 b4 ,/rap w9d+2 c4 ,b> w9d+4 #f4 ,) respect to ! numb] ( coils p] phase p] pole1 z3 a4 ,"o slot w9d+2 b4 ,two slot w9d+2 etc4 #g4 ,) respect to ! k9d ( curr5t deliv]$1 z3 a4 ,s+le phase w9d+2 b4 ,two phase w9d+2 c4 ,?ree phase w9d+4 ,illu/ration3 ,,fig4 #a1dhe4--,section ( ,we/]n ,electric /ation>y armature core %[+ lam9ations clamp$ 9 place1 & v5tilat+ ducts4 ,! /ator or /ation>y armature consi/s ( s(t iron lam9ations assembl$ 9 ! magnet frame ) /ator coils emb$d$ 9 ! core slots4 ,! lam9ations are pun*$ sep>ately & !n c>efully anneal$ to r$uce hy/]esis losses4 ,aft] anneal+1 a coat ( japan is appli$1 effectively prev5t+ ! fl[ ( eddy curr5ts 9 ! assembl$ core4 ,! frame is ca/ iron & ( ! box type con/ruction4 ,! frames ( ! small] sizes are ca/ 9 "o piece1 :ile frames ( ! l>g] sizes are split to facilitate in/allation4 ,l>ge op5+s are provid$ 9 ! box type frame1 9 ord] to improve ! v5tilation4 ,! lam9ations are securely held 9 place 9 ! frame by heavy end r+s & by /eel clamp+ f+]s :i* are firmly bolt$ to ! frame4 ,! out] circumf]5ce ( ! core is dovetail$ to ! frame1 & ! inn] circumf]5ce is slott$ to receive ! w9d+s4 ,! alignm5t ( ! slots is insur$ by means ( metal w$ges1 & no fil+ is done on ! slots1 s t ea* lam9ation is always insulat$ f ! next "o4 ,num]\s v5tilat+ ducts all[ ! free circulation ( cool air ?r\gh & ar\nd ! coils4 ,! op5 slot con/ruction is employ$ & ! coils are fitt$ into insulat+ tr\ghs :i* (f] excell5t me*anical & electric protection4 ,! coils are held 9 place by suitable w$ges4 #h4 ,) respect to ! %ape ( ! coil ends1 z3 a4 ,s+le range2 b4 ,two range2 etc4 ,9 addition to ^! sev]al classes ( w9d+1 !re are a numb] ( miscellane\s w9d+s ( :i* ! foll[+ might be m5tion$3 a4 ,*a9 or basket w9d+2 b4 ,skew coil w9d+2 c4 ,f$-9 w9d+2 d4 ,imbricat$ w9d+2 e4 ,mummifi$ w9d+2 f4 ,spiral w9d+2 g4 ,%uttle w9d+2 h4 ,creep+ w9d+2 i4 ,turb9e alt]nator w9d+4 ,illu/ration3 ,,fig4 #a1dhf4--,me?od ( assembl+ =m w\nd coils4 ,! picture %[s a section ( a ,g5]al ,electric armature ) "p ( ! coils 9 place4 ,a lay] ( insulat+ mat]ial is fir/ plac$ 9 ! slots1 be=e ins]t+ ! coils z se5 at ! left4 ,:5 ! coils are 9 place & surr\nd$ by ?is lay] ( insulat+ mat]ial ! reta9+ w$ges are ins]t$ 9 ! not*es1 ?us clos+ ! slots & protect+ ! coils f me*anical injury4 ,a few w$ges are se5 9 position at ! "r4 ,ques4 ,def9e a revolv+ & a /ation>y w9d+4 ,ans4 ,! words are self-def9+2 a w9d+ is said to be revolv+ or /ation>y accord+ z ! armature =ms ! rotor or /ator ( ! ma*9e4 ,ques4 ,:at is ! significance ( ! t]ms lap & wave z appli$ to alt]nator w9d+s8 ,ans4 ,!y h ! same mean+ z !y d :5 appli$ to dynamo w9d+s4 ,illu/ration3 ,,fig4 #a1dhg4--,section ( ,g5]al ,electric /ation>y armature v5tilat+ ducts & w9d+ 9 position4 ,^! are describ$ 9 detail 9 ,*apt] ,,xviii4 ,briefly a lap w9d+ is "o compos$ ( lap coils2 a wave w9d+ is "o :i* r\ghly resembles 9 its diagram1 a section ( waves4 ,half ,coil & ,:ole ,coil ,w9d+s4--,! di/9ction z to :e!r ! adjac5t sides ( consecutive coils are plac$ toge!r "u "o pole or :e!r !y are sep>at$ a di/ance equal to ! pole pit*1 gives rise to :at is kn[n z half coil & :ole coil w9d+s4 ,a half coil or hemitropic w9d+ is "o 9 :i* ! coils 9 any phase are situat$ opposite e o!r pole1 t is1 a w9d+ 9 :i* !re is only "o coil p] phase p] pair ( poles1 z 9 fig4 #a1dhh4 ,a :ole coil w9d+ is "o 9 :i* !re is "o coil p] phase p] pole1 z 9 fig4 #a1dhi1 ! :ole 7e "o7 ( ! poles be+ subt5d$ by coils4 ,illu/ration3 ,,figs4 #a1dhh & #a1dhi4--;,elem5t>y bipol> alt]nators ) half coil & :ole coil w9d+s4 ,9 a half coil w9d+ !re is "o coil p] phase p] pair ( poles2 9 a :ole coil w9d+ !re is "o coil p] phase p] pole4 ,conc5trat$ or ,uni-,coil ,w9d+4--,fig4 #a1dib %[s ! simple/ type ( s+le phase w9d+4 ,x is a "o slot w9d+ & is sometimes call$ monotoo? or uni-coil w9d+4 ,! surface ( ! armature is consid]$ z divid$ into a s]ies ( l>ge tee?1 "o too? to ea* pole1 & ea* too? is w\nd ) "o coil1 ( "o or m turns p] pole4 ,s9ce all ! turns ( ! coil are plac$ 9 s+le slots1 ! w9d+ is call$ conc5trat$4 ,illu/ration3 ,,fig4 #a1dij4--,multi-pol> revolv+ armature alt]nator ) half coil w9d+1 %[n 9 radially develop$ diagram to cle>ly indicate ! pa? ( ! w9d+4 ,a half coil or hemitropic w9d+ has a slightly high] reactance ?an a w9d+ 9 :i* two di/9ct coils are us$ 9 ! same slot1 "o go+ =w>d & ! o!r backw>d4 ,! mo/ usual ?ree phase w9d+s are ( ! half coil type z ! ?ree sets ( coils are equispac$ ov] a pair ( poles4 ,illu/ration3 ,,fig4 #a1dia4--,multi-pol> revolv+ armature alt]nator ) :ole coil w9d+ %[n 9 radially develop$ diagram to cle>ly indicate ! pa? ( ! w9d+4 ,ques4 ,:at are ! features ( conc5trat$ w9d+s8 ,ans4 ,*eap con/ruction1 maximum voltage = a giv5 numb] ( inductors4 ,conc5trat$ w9d+s h great] armature reaction & inductance ?an o!r types h5ce ! t]m9al voltage ( an alt]nator ) conc5trat$ w9d+ falls (f m ?an ) di/ribut$ w9d+ :5 ! curr5t output is increas$4 ,an alt]nator1 !re=e1 does n h z good regulation ) conc5trat$ w9d+ z ) di/ribut$ w9d+4 ,illu/ration3 ,,figs4 #a1dib & #a1dic4--;,conc5trat$ w9d+s4 ,a conc5trat$ w9d+ is "o 9 :i* ! armature has only "o too? p] phase p] pole1 t is1 ! numb] ( tee? equals ! numb] ( poles4 ,a conc5trat$ w9d+ ( ! half coil type has only "o side ( a coil 9 ea* slot z 9 fig4 #a1dib4 ,9 ! :ole coil v>iety1 ea* slot conta9s neighbor+ sides ( adjac5t coils1 z 9 fig4 #a1dic4 ,9 con/ruction1 w$ges are g5]ally us$ = reta9+ ! half coils1 & ) :ole coils ! tee? h project+ horns = ?is purpose4 ,ques4 ,:at %\ld be not$ ) respect to conc5trat$ w9d+s8 ,ans4 ,a conc5trat$ w9d+1 ?\gh giv+ high] voltage ?an ! di/ribut$ type ) no load1 may give a l[] voltage ?an ! latt] at full load4 ,illu/ration3 ,,fig4 #a1did4--,lam9at$ core ) two coils 9 position2 type ( pun*+s us$ on "s ma*9es hav+ conc5trat$ :ole coil w9d+s4 ,! mann] ( assembl+ ! coils is %[n 9 fig4 #a1die4 ,ques4 ,:at is ! wave =m ) a conc5trat$ w9d+8 ,ans4 ,! pressure curve rises sudd5ly 9 value z ! armature slots pass "u ! pole pieces1 & falls sudd5ly z ! armature slots rec$e f "u ! pole pieces4 ,illu/ration3 ,,fig4 #a1die4--,we/+h\se s+le phase conc5trat$ coil armature2 view %[+ me?od ( plac+ coils4 ,! coils are ma*9e w\nd on =m]s & aft] be+ tap$1 v>ni%$ & bak$1 are spread out slightly s z to pass ov] ! tee? & are !n =c$ into place 9 ! deep slots by means ( wood5 w$ges1 be+ securely held 9 place by reta9+ w$ges1 z %[n 9 fig4 #a1did4 ,di/ribut$ or ,multi-,coil ,w9d+s4--,in/ead ( w9d+ an armature s x w occupy only "o slot p] phase p] pole1 x may be spread out s z to fill sev]al slots p] phase p] pole4 ,?is arrangem5t is call$ a di/ribut$ w9d+4 ,to illu/rate1 fig4 #a1dif repres5ts a coil ( say fifte5 turns4 ,?is c\ld be plac$ on an armature j z x is1 9 :i* case only "o slot w\ld be requir$ = ea* side1 t is1 two 9 all4 ,9 place ( ?is ?ick coil1 ! wire c\ld be divid$ into sev]al coils ( a less] numb] ( turns ea*1 arrang$ z 9 fig4 #a1dig2 x is !n said to be p>tially di/ribut$1 or x c\ld be arrang$ z 9 fig4 #a1dih1 :5 x is said to be fully di/ribut$4 ,illu/ration3 ,,figs4 #a1dif to #a1dih4--;,alt]nator coils1 %[+ diff]5ce betwe5 ! conc5trat$1 p>tially di/ribut$1 & fully di/ribut$ =ms4 ,fig4 #a1dif %[s a conc5trat$ coil 9 :i* all ! wire is w\nd 9 "o l>ge coil2 9 ! p>tially di/ribut$ type fig4 #a1dig1 ! wire ( fig4 #a1dif1 is w\nd 9 two or m coils or sections connect$ z %[n1 leav+ "s space inside n tak5 up by ! subdivisions4 ,9 fig4 #a1dih ! wire ( fig4 #a1dif is fully di/ribut$1 be+ w\nd 9 a s]ies ( coils1 s t all ! int]ior space is tak5 up by ! wire1 t is to say1 ! spaces n occupi$ by ! wire 7! tee? :5 plac$ on ! armature7 are ( equal size4 ,a p>tially di/ribut$ w9d+1 !n1 is "o1 z 9 fig4 #a1dii1 9 :i* ! coil slots d n occupy all ! circumf]5ce ( ! armature2 t is1 ! core tee? are n cont9u\s4 ,a fully di/ribut$ w9d+ is "o 9 :i* ! entire surface ( ! core is tak5 up ) slots1 z 9 fig4 #a1ejj4 ,ques4 ,9 a di/ribut$ coil :at is und]/ood by ! bread? ( ! coil8 ,ans4 ,! di/ance betwe5 ! two out] sides1 z ,b 9 figs4 #a1dig & #a1dih4 ,illu/ration3 ,,fig4 #a1dii4--,p>tially di/ribut$ w9d+4 ,ea* coil unit is "h divid$ into two conc5tric coils ( diff]5t dim5sions & connect$ 9 s]ies1 z %[n 9 detail 9 fig4 #a1dig4 ,?is be+ a :ole coil w9d+ ! sev]al units are s connect$ t ! w9d+ ( adjac5t units proce$s 9 opposite directions1 t is1 "o coil is w\nd clockwise1 & ! next c\nt] clockwise1 etc41 s t ! induc$ curr5ts fl[ 9 a common direction z indicat$ by ! arr[s = ! position %[n4 ,illu/ration3 ,,fig4 #a1ejj4--;,fully di/ribut$ w9d+4 ,9 ?is type ( w9d+ ea* coil consi/s ( s _m sub-coils t ! w9d+ occupies ! entire surface ( ! armature core2 t is1 !re are no ext5sive spaces unoccupi$1 ! spac+ be+ uni=m z %[n4 ,ques4 ,h[ f> is x advisable to spread di/ribut$ coils ( a s+le phase alt]nator8 ,ans4 ,!re is n mu* advantage 9 r$uc+ ! int]ior bread? mu* bel[ t ( ! bread? ( ! pole faces1 nor is !re mu* advantage 9 mak+ ! ext]ior bread? great] ?an ! pole pit*4 ,undue spread+ ( di/ribut$ coils l[]s ! value ( ! ,kapp coeffici5t 7lat] expla9$7 by r$uc+ ! bread? coeffici5t & makes necess>y a l>g] numb] ( inductors to obta9 ! same voltage4 ,! increase 9 ! numb] ( inductors causes m armature self-induction4 ,f ?is po9t ( view1 x w\ld be pref]able to conc5trate ! w9d+ 9 few] slots t 7 clos] toge!r4 ,?is1 h[ev]1 w\ld acc5tuate ! di/ort+ & demagnetiz+ reactions ( ! armature4 ,accord+ly1 betwe5 ^! two disadvantages a compromise is made1 z to ! ext5t ( di/ribut+ ! coils & spac+ ( ! tee?1 ! proportions assign$ be+ ^? :i* exp]i5ce %[s be/ suit$ to ! conditions ( op]ation = :i* ! ma*9e is design$4 ,illu/ration3 ,,fig4 #a1eja4--;,develop$ diagram ( s+le phase conc5trat$ :ole coil w9d+ 9 two slot /amp+ = six pole alt]nator4 ,if ! sides ( adjac5t :ole coils be slightly sep>at$ by plac+ ! w9d+ 9 a two slot /amp+ ! electrical result w n diff] mat]ially f ! monotoo? :ole coil w9d+1 b if ! w9d+ be hemitropic1 z 9 fig4 #a1ejb1 & has coils ( two sizes z %[n1 x w be suitable = high voltages4 ,! ,kapp ,coeffici5t4--,a volt or unit ( electric pressure is def9$ z ! pressure induc$ by ! cutt+ ( #ajj1jjj1jjj or #aj l9es ( =ce p] second4 ,9 ! op]ation ( an alt]nator ! maximum pressure g5]at$ may be express$ by ! foll[+ equation3 f,,zn ,e ------ 7#a7 #aj 9 :i* f frequ5cy2 ,z numb] ( inductors 9 s]ies 9 any "o magnetic circuit2 ,n magnetic flux1 or total numb] ( magnetic l9es 9 "o pole or 9 "o magnetic circuit4 ,! maximum value ( ! pressure1 z express$ 9 equation 7#a71 occurs :5 #ij4 ,illu/ration3 ,,fig4 #a1ejb4--;,develop$ diagram ( s+le phase p>tially di/ribut$ half coil w9d+ = six pole alt]nator 9 two slot /amp+1 same z 9 fig4 #a1eja4 ,9 ?is arrangem5t ! direction ( rotation is n rev]s$4 ,x is a "q z to h[ f> ! coils ( a s+le-phase armature may be spread ) advantage4 ,!re is n mu* advantage 9 r$uc+ ! int]ior bread? ( ! coils bel[ t ( ! pole face1 nor 9 wid5+ ! ext]ior bread? beyond t ( ! pole pit*4 ,! virtual value ( ! volts is equal to ! maximum value divid$ by #b1 or multipli$ by #b1 h5ce1 #b f,,zn #b4bb;f,,zn ,e -------------- --------- 7#b7 #aj #aj ,?is is usually tak5 z ! fundam5tal equation 9 design+ alt]nators4 ,x is1 h[ev]1 d$uc$ on ! assumptions t ! di/ribution ( ! magnetic flux foll[s a s9e law1 & t ! :ole ( ! loops ( active inductors 9 ! armature circuit acts simultane\sly1 t is to say1 ! w9d+ is conc5trat$4 ,illu/ration3 ,,fig4 #a1ejc4--;,develop$ diagram ( s+le phase w9d+ ) fully di/ribut$ coils4 ,z expla9$1 excessive spread+ l[]s ! value ( ! ,kapp coeffici5t1 & consequ5tly ! voltage2 also ! use ( a l>g] numb] ( inductors to obta9 ! same voltage results 9 an increase ( armature self-induction4 ,on ! o!r h&1 if ! w9d+ 7 conc5trat$ 9 few] slots & ^! slots 7 clos] toge!r1 ! result w be an increase 9 di/ort+ & demagnetiz+ reactions ( ! armature4 ,!re=e1 a compromise betwe5 ^! two disadvantages mu/ be made4 ,! common practice is to w9d 9 two or ?ree slots p] pole p] phase4 ,illu/ration3 ,,fig4 #a1ejd4--;,allis-,*alm]s lap w\nd coils =m+ a ?ree slot di/ribut$ coil unit4 ,9 con/ruction1 aft] ! coils h be5 cov]$ ) insulat+ mat]ials & treat$ ) insulat+ comp\nd1 ! p>ts t lie 9 ! slots are press$ to exact size 9 /eam-heat$ m\lds4 ,?is runs ! insulat+ mat]ial into all ! small spaces 9 ! coil1 exclud+ moi/ure & r5d]+ ! insulation firm & solid4 ,! ends ( ! coils1 :]e !y project beyond ! slots1 are heavily tap$4 ,illu/ration3 ,,fig4 #aeje4--;,allis-,*alm]s armature con/ruction2 view %[+ section ( frame & two lay] w9d+4 ,9 practice1 ! coils are (t5 m or less di/ribut$1 t is1 !y d n always subt5d an exact pole pit*2 moreov]1 ! flux di/ribution1 :i* dep5ds on ! %ap+ & bread? ( ! poles1 is (t5 q diff]5t f a s9e di/ribution4 ,h5ce1 ! coeffici5t #b4bb 9 equation 7#b7 is (t5 dep>t$ f1 & 9 ! g5]al case equation 7#b7 may be writt5 kf,,zn ,e ------- 7#c7 #aj :]e k is a numb] :i* may h diff]5t values1 accord+ to ! con/ruction ( ! alt]nator4 ,?is numb] k is call$ ! ,kapp coeffici5t because its significance 0 fir/ po9t$ out by ,pr(4 ,gisb]t ,kapp4 ,illu/ration3 ,,figs4 #a1ejf & #a1ejg4--;,effect ( bread? ( coils 9 di/ribut$ w9d+s4 ,9 ! section ( ! alt]nator %[n 9 fig4 #a1ejf ! directions ( ! pressures induc$ z ! armature rotates clockwise are repres5t$ by dots = ^? :i* act t[>ds ! read]1 & by crosses = ^? :i* act f ! read] 7! dots & crosses repres5t+ respectively ! heads & tails ( arr[s74 ,s9ce ! field is n uni=m b maximum at ! c5t] & gradually weak5+ t[>ds ! extremities1 x is obvi\s t ! maximum pressure is induc$ 9 any inductor z x passes ! c5t] ( ! pole1 ?is v>iation be+ indicat$ by ! heavi] dots & crosses t[>d ! c5t]4 ,n[ if a numb] ( ^! inductors be connect$ up to =m a di/ribut$ coil z 9 fig4 #a1ejg1 ! pressures induc$ 9 ea* w be add$1 b all ! maximum pressure w n be induc$ 9 all at ! same "t1 h5ce ! total pressure induc$ 9 ! di/ribut$ coil is less ?an x w\ld be if ! coil 7 conc5trat$ z 9 fig4 #a1eji4 ,illu/ration3 ,,fig4 #a1ejh4--;,diagram ( di/ribut$ coil ^: inn] bread? is less ?an ! bread? ( ! pole face1 %[+ ! disadvantage ( su* arrangem5t4 ,! pressures induc$ 9 ! inn] w9d+s ( su* a coil are oppos+ ea* o!r at ! in/ant depict$1 t is1 :ile ! inductors are "u ! pole face1 su* action ( c\rse be+ objectionable4 ,! value ( k is fur!r influ5c$ by a bread? coeffici5t or w9d+ factor4 ,! effect ( bread? 9 di/ribut$ w9d+s is illu/rat$ 9 figs4 #a1ejf to #a1ejh4 ,wire1 ,/rap1 & ,b> ,w9d+s4--,9 ! con/ruction ( alt]nators1 ! w9d+s may be ( ei!r wire1 /rap1 or b>1 accord+ to :i* is be/ suit$ = ! conditions to be met4 ,ques4 ,:at conditions pr9cipally gov]n ! type ( inductor8 ,ans4 ,x dep5ds *iefly ^u ! curr5t to be c>ri$ & ! space 9 :i* ! inductor is to be plac$4 ,illu/ration3 ,,fig4 #a1eji4--,simple =m ( alt]nator coil1 consi/+ ( num]\s turns ( insulat$ wire w\nd ar\nd a =m1 !n cov]$ ) a tape w9d+1 v>ni%$ & bak$4 ,ques4 ,:at k9d ( inductors are us$ on ma*9es int5d$ = high voltage & mod]ate curr5t8 ,ans4 ,! w9d+ is compos$ ( :at is call$ magnet wire1 ) d\ble or triple cotton insulation4 ,ques4 ,:]e consid]able cross section is requir$ h[ is a wire inductor arrang$8 ,ans4 ,9 ord] t ! coil may be flexible sev]al small wires 9 multiple are us$ in/ead ( a s+le l>ge wire4 ,ques4 ,h[ is ! insulation arrang$ on inductors ( ?is k9d8 ,ans4 ,b>e wire is us$ = ! wires 9 p>allel1 insulation be+ wrapp$ ar\nd !m z 9 fig4 #a1eaj4 ,?is con/ruction r$uces ! space occupi$ by ! wires1 & ! insulation s]ves to hold !m 9 place4 ,illu/ration3 ,,figs4 #a1eaj & #a1eaa4--,multi-wire inductors4 ,:5 ! cross section ( inductor necess>y to c>ry ! curr5t is l>ge1 ! use ( a s+le wire w\ld pres5t difficulties 9 w9d+ on acc\nt ( its /iffness4 ,accord+ly two or m small] wires are us$ 9 p>allel to secure ! requir$ cross section4 ,b>e wire is us$ & ! sev]al sections encas$ 9 insulation z %[n1 ! comb9ation be+ m flexible ?an an equival5t s+le wire4 ,illu/ration3 ,,fig4 #a1eab4--,two coil slot = :ole coil w9d+4 ,! slot has two recesses ,a & ,b = ! reception ( sep>ate coils4 ,9 assembl+ ! w9d+1 ! inn] w$ge is fir/ plac$ 9 position & !n ! slot l9e ) ! insulat+ mat]ial4 ,?is usually consi/s ( alt]nate lay]s ( mica & pressbo>d4 ,! coils compos$ ( sev]al turns ( wire or copp] /rip are w\nd 9 place1 & aft] cov]+ ) a lay] ( insulation1 ! out] w$ge is pu%$ 9 place to reta9 ! inductors 9 position4 ,ques4 ,:at precaution is tak5 9 insulat+ a wire w\nd coil conta9+ a l>ge numb] ( turns8 ,ans4 ,on acc\nt ( ! consid]able diff]5ce ( pressure betwe5 lay]s1 x is necess>y to insulate ea* lay] ( turns z well z ! outside ( ! coil1 z %[n 9 fig4 #a1eac4 ,illu/ration3 ,,fig4 #a1eac4--,me?od ( w9d+ a coil conta9+ a l>ge numb] ( turns1 :5 !re is consid]able diff]5ce ( pressure betwe5 ! lay]s4 ,9 su* cases to gu>d aga9/ %ort circuits or breakd[n ( ! insulation1 ea* lay] ( turns is insulat$ f ! next lay] by ! insulat+ /rips ,a1 ,b1 ,c1 9 addition to ! regul> insulation ar\nd ea* wire4 ,aft] ! coil is made up x is w\nd ) insulat+ tape1 v>ni%$ & bak$4 ,ques4 ,d di/ribut$ coils require insulation betwe5 ! sep>ate lay]s8 ,ans4 ,s9ce !y are subdivid$ into sev]al coils insulation betwe5 lay]s is usually n necess>y4 ,ques4 ,h[ is a coil cov]$8 ,ans4 ,x is w\nd ) a m or less heavy wrapp+ ( tape dep5d+ ^u ! voltage4 ,illu/ration3 ,,figs4 #a1ead & #a1eae4--,s+le & d\ble lay] multi-wire inductors & me?ods ( plac+ !m on ! core4 ,"h ! t]m lay] means unit1 9 fact ea* unit is made up ( sev]al lay]s ( wires4 ,9 fig4 #a1ead1 :]e s _m wires are bun*$ toge!r 9 "o unit1 ea* lay] ( turns is sep>at$ f ^? adjac5t by insulat+ /rips on acc\nt ( ! consid]able diff]5ce ( pressure betwe5 lay]s4 ,?is insulation is n necess>y 9 fig4 #a1eae :]e !re are two units or s call$ lay]s4 ,9 bo? cases ! inductors are held 9 place by w$ges driv5 into dovetail grooves4 ,l95 tape ( good quality1 treat$ ) l9se$ oil1 =ms a desirable cov]+4 ,:]e extra high insulation is requir$ ! tape may be int]leav$ ) %eet mica4 ,ques4 ,is ! insulation plac$ ar\nd ! coils all t is necess>y8 ,ans4 ,! slots into :i* ! coils are plac$1 are also insulat$4 ,illu/ration3 ,,fig4 #a1eaf4--;,copp] /rap or ribbon ) insulation4 ,^! are g5]ally f _/ to _/ in* ?ick ) r\nd$ edges z %[n to avoid cutt+ ! insulation4 ,illu/ration3 ,,fig4 #a1eag4--;,b> inductor4 ,its %ape enables putt+ ! maximum cross section ( copp] into ! slot & is us$ to advantage on ma*9es :i* g5]ate l>ge curr5ts4 ,illu/ration3 ,,fig4 #a1eah4--,/yle ( armature core /amp+ us$ ) b> w\nd ma*9es4 ,?is con/ruction1 s9ce !re are no ind5tations 9 ! tee? = w$ges1 makes x necess>y to provide b&s to hold ! b>s 9 place4 ,ques4 ,h[ are b> w9d+s sometimes arrang$8 ,ans4 ,9 two lay]s1 z 9 fig4 #a1ebc4 ,s+le & ,multi-,slot ,w9d+s4--,^! classifications correspond to conc5trat$ & di/ribut$ w9d+s1 previ\sly describ$4 ,9 usual mod]n practice1 only two-?irds ( ! total numb] ( slots 7assum+ ! spac+ to be uni=m7 ,illu/ration3 ,,figs4 #a1eai & #a1ebj4--;,b5t b> inductor & me?od ( connection ) sold]$ jo9t4 ,fig4 #a1eai %[s "o b> & %ape ( b5t ends4 ,! portion f ,c to ,d is plac$ 9 ! slot2 ,b to ,c & ,d to ,e1 b5t or connector sections2 ,a to ,b & ,e to ,f1 ends b5t p>allel to slot = sold]+4 ,fig4 #a1ebj %[s two b> inductors connect$4 ,illu/ration3 ,,figs4 #a1eba & #a1ebb4--,me?od ( avoid+ a sold]$ jo9t at "o end ( a b> inductor by us+ a b> ( twice ! l5g? %[n 9 fig4 #a1eai1 & b5d+ x into a long ,u =m1 z 9 fig4 #a1eba1 aft] :i* x is spread out =m+ two inductors1 z 9 fig4 #a1ebb4 ( a s+le phase armature are w\nd ) coils4 ,! reason = ?is may be expla9$ by aid ( fig4 #a1ebd1 :i* %[s an armature ) six slots p] pole1 f\r ( :i* are w\nd4 ,ow+ to ! diff]5t positions (1 say1 coils ,a & ,b1 !re w be a diff]5ce 9 phase betwe5 ! pressure g5]at$ 9 !m & consequ5tly ! resultant pressure ( ! two coils jo9$ 9 s]ies w be less ?an ! sum ( ! pressure 9 ea* coil4 ,illu/ration3 ,,fig4 #a1ebc4--;,arrangem5t 9 slot ( two lay] b> w9d+4 ,) b> inductors1 z mu/ be evid5t f ! illu/ration1 ! maximum cross section ( copp] c be plac$ 9 a slot ( giv5 dim5sion1 h5ce a b> w9d+ is us$ to advantage = alt]nators design$ to c>ry a l>ge curr5t4 ,b> inductors1 on acc\nt ( ! %ape ( _! ends1 mu/ be plac$ 9 ! slots f ! top1 because ! b5t ends d n admit ( pu%+ !m 94 ,/raight slots are !re=e necess>y1 ! inductors be+ held 9 place by wood5 /rips & tie b&s z %[n4 ,fig4 #a1ebe %[s ! pressure plott$ out z vector quantities1 & ! table :i* foll[s gives ! relative effectiv5ess ( w9d+s ) v>i\s numb]s ( slots w\nd 9 s]ies4 ,! figures 9 ! la/ column ( ! table %[ t a l>ge increase 9 ! weight ( active mat]ial is requir$ if ! inductors 9 a s+le phase ma*9e are to be di/ribut$ ov] m ?an two-?irds ! pole pit*4 ,aga91 if mu* less ?an two-?irds ( ! surface be w\nd1 x is m difficult to provide a s9e wave ( pressure4 ,illu/ration3 ,,fig4 #a1ebd4--;,diagram ( s+le phase multi-coil or di/ribut$ w9d+ to %[ *>act]i/ic diff]5ces 9 action & con/ruction f s+le coil or conc5trat$ w9d+4 ,illu/ration3 ,,fig4 #a1ebe4--,vector diagram ( pressures induc$ 9 ! s+le phase multi-coil or di/ribut$ w9d+ %[n 9 diagram 9 fig4 #a1ebd4 ,,table ,,( ,,relative ,,effectiv5ess ,,( ,,w9d+s ---------------------------------------- ------------------------ ,slots w\nd ,pressure across ,w9d+ ,quantity ( 9 s]ies coils coeffici5t copp] 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 ,:at o!r advantage besides obta9+ a s9e wave is secur$ by di/ribut+ a coil8 ,ans4 ,!re is less heat+ because ( ! bett] v5tilation4 ,illu/ration3 ,,fig4 #a1ebf4--;,develop$ diagram ( a s+le phase monotoo? or "o slot b> w9d+2 x is suitable only = op]ation at l[ voltage4 ,s+le ,phase ,w9d+s4--,!re are v>i\s k9ds ( s+le phase w9d+1 su* z1 conc5trat$1 di/ribut$1 hemitropic1 etc4 ,fig4 #a1ebg %[s ! simple type ( s+le phase w9d+4 ,x is a "o slot w9d+1 t is1 conc5trat$ coils are us$4 ,! armature has ! same numb] ( tee? z !re are poles1 ! conc5trat$ coils be+ arrang$ z %[n4 ,9 design+ su* a w9d+1 ! ma*9e1 = example1 may be requir$ to g5]ate1 say1 #c1jjj volts1 frequ5cy #de1 revolutions #ijj p] m9ute4 ,^! conditions require #gbj inductors 9 s]ies 9 ! armature circuit1 & z ! armature is divid$ into six slots correspond+ to ! six poles1 !re w be #abj inductors p] slot1 & ! coil surr\nd+ ea* ( ! six tee? on ! surface ( ! armature w consi/ ( #fj turns4 ,! connections mu/ be su* z to give alt]nate clockwise & c\nt]-clockwise w9d+ proce$+ ar\nd ! armature4 ,illu/ration3 ,,fig4 #a1ebg4--;,diagram ( six pole s+le phase revolv+ armature alt]nator1 ) monotoo? or conc5trat$ :ole coil w9d+4 ,= #c1jjj volts at #ijj revolutions p] m9ute1 #abj inductors are requir$4 ,& 9 ! case ( a conc5trat$ or monotoo? w9d+ !y may be arrang$ 9 :ole coils z above or 9 half coils 7hemitropic7 z 9 fig4 #a1ebh4 ,ques4 ,9 :at o!r way c\ld ! inductors be arrang$ 9 conc5trat$ coils8 ,ans4 ,!y c\ld be gr\p$ 9 ?ree coils ( #abj turns ea*1 z %[n 9 fig4 #a1ebh4 ,:5 ?us gr\p$ ! arrangem5t is call$ a hemitropic w9d+1 z previ\sly expla9$4 ,illu/ration3 ,,fig4 #a1ebh4--;,diagram ( six pole s+le phase alt]nator ) conc5trat$ half coil or hemitropic w9d+ ( same capacity z 9 fig4 #a1ebg4 ,!re are an equal numb] ( inductors1 b 9 ?is case arrang$ 9 ?ree in/ead ( six coils4 ,9 ?is w9d+ ! direction ( w9d+ is alt]nately rev]s$ s t ! induc$ pressures d n oppose "o ano!r4 ,ques4 ,:at is ! advantage1 if any1 ( a half coil w9d+8 ,ans4 ,9 s+le phase ma*9es a half coil w9d+ is equival5t1 electrically1 to a monotoo? w9d+1 &1 !re=e1 is n ( any p>ticul> advantage2 b 9 ?ree phase ma*9es1 x has a decid$ advantage1 z 9 su*1 a conc5trat$ w9d+ yields a high] pressure ?an a di/ribut$ w9d+4 ,illu/ration3 ,,fig4 #a1ebi4--,two phase conc5trat$ :ole coil w9d+4 ,9 ?is /yle w9d+ ! total numb] ( slots is twice ! numb] ( poles1 or "o slot p] pole p] phase4 ,x comprises two w9d+s id5tical ) fig4 #a1ebg1 be+ spac$ #ij pol> degrees z %[n4 ,! two circuits are indep5d5t1 ! w9d+s t]m9at+ at ! f\r collector r+s4 ,illu/ration3 ,,fig4 #a1ecj4--,two phase w9d+ 9 two slots p] pole p] phase4 ,?is /amp+ di/ributes ! coils ( ea* phase into two sections1 z ,a & ,b4 ,! coils are ( ! :ole type & ) six poles ! total numb] ( slots is #d #f #bd1 uni=mly spac$ z %[n4 ,two ,phase ,armature ,w9d+s4--,?is type ( w9d+ c be made f any s+le phase w9d+ by provid+ ano!r set ( slots displac$ along ! surface ( ! armature to ! ext5t ( "o-half ! pole pit*1 plac+ !re9 a duplicate w9d+4 ,illu/ration3 ,,figs4 #a1eca & #a1ecb4--;,develop$ diagram ( ! s+le phase monotoo? w9d+s %[n 9 figs4 #a1ebg & #a1ebh4 ,= in/ance3 ,if ! six pole monotoo?1 s+le phase w9d+1 %[n 9 fig4 #a1ebg1 be ?us duplicat$1 ! result w be ! "o slot two-phase w9d+ %[n 9 fig4 #a1ebi1 :i* w h twelve slots1 & w require f\r slip r+s1 or two r+s = ea* phase4 ,by connect+ up ! two w9d+s 9 s]ies1 ! ma*9es c\ld be us$ z a s+le phase1 ) an increase ( voltage 9 ! ratio ( #a4da to #a4 ,illu/ration3 ,,fig4 #a1ecc4--,two phase w9d+ 9 ?ree slots p] pole p] phase4 ,! coils ( ea* phase are ( ! p>tially di/ribut$ type1 ea* coil be+ made up ( ?ree sections z %[n4 ,! direction ( w9d+ is alt]nately rev]s$4 ,illu/ration3 ,,fig4 #a1ecd4--,section ( two phase w9d+ %[+ %ap+ ( ! coil ends4 ,e o!r coil is flat1 :ile ! alt]nates h _! ends b5t d[n z %[n4 ,) respect to ! %ap+ ( ! coil ends1 x is call$ a two range w9d+4 ,ques4 ,h[ mu/ ! coils be con/ruct$ = two phase w9d+s8 ,ans4 ,!y mu/ be made ( two diff]5t %apes1 "o b5t up out ( ! way ( ! o!r1 z 9 fig4 #a1ecd4 ,!re are num]\s k9ds ( two phase w9d+s2 ! coils may be conc5trat$ or di/ribut$1 half coil or :ole coil1 etc4 ,fig4 #a1ecj %[s a two phase w9d+ ) f\r slots p] pole1 & fig4 #a1ecc "o ) six slots p] pole4 ,illu/ration3 ,,fig4 #a1ece4--,section ( ,triumph armature %[+ me?od ( arrang+ ! ?ree phase w9d+4 ,?ree ,phase ,armature ,w9d+s4--,on ! same g5]al pr9ciple applicable to two phase w9d+s1 a ?ree phase w9d+ c be made f any s+le phase w9d+1 by plac+ ?ree id5tical s+le phase w9d+s spac$ out successively along ! surface ( ! armature at int]vals equal to "o-?ird & two-?irds1 respectively1 ( ! d\ble pole pit*1 ! unit 9 t]ms ( :i* ! spac+ is express$1 be+ t pit*1 :i* corresponds to "o :ole p]iod4 ,illu/ration3 ,,fig4 #a1ecf4--,?ree phase w9d+ ) di/ribut$ coils--w\nd 9 f\r slots p] pole p] phase2 diagram %[+ placem5t ( ! coils4 ,illu/ration3 ,,fig4 #a1ecg4--,treatm5t ( coil ends 9 two phase1 two range w9d+s4 ,9 ?is arrangem5t /raight out 7,b7 & b5t up 7,a7 coils are us$ :i* are plac$ on ! armature z is cle>ly %[n 9 ! illu/ration4 ,illu/ration3 ,,fig4 #a1ech4--,?ree phase1 #aj pole1 #cj slot w9d+ 9 two ranges4 ,9 ?is w9d+ p]fect symmetry occurs aft] e f\r poles4 ,accord+ly 9 ! case ( an odd numb] ( pairs ( pole1 "o ( ! coils mu/ necess>ily be askew go+ f ! inn] to ! out] range z at ,m4 ,ea* ( ! ?ree individual w9d+s mu/ be conc5trat$ into n>r[ belts s z to leave suffici5t space = ! o!r w9d+s betwe5 !m4 ,?is limits ! bread? or space occupi$ by ! w9d+ ( any "o phase to "o-?ird ( ! pole pit*4 ,illu/ration3 ,,fig4 #a1eci4--,?ree phase #aj pole #cj slot w9d+ 9 ?ree ranges4 ,! coils ( ea* phase are alike1 ^? ( ! ,a phase be+ all 9 ! /raight out range1 ^? 9 ! ,b phase1 9 a b5t up range1 & ^? 9 ! ,c phase 9 a b5t d[n range4 ,?is arrangem5t has ! disadvantage1 t by reason ( ! ?ird range1 ! field magnet _c be )drawn4 ,?is treatm5t ( ! coil ends is m cle>ly %[n 9 fig4 #a1edj4 ,ques4 ,h[ are ?ree phase coil ends treat$8 ,ans4 ,!y may be arrang$ 9 two ranges1 z 9 fig4 #a1ech1 or 9 ?ree ranges1 z 9 fig4 #a1eci4 ,ques4 ,:at k9d ( coil mu/ be us$ = ?ree phase w9d+s 9 ord] t ! ends may be arrang$ 9 only two ranges8 ,ans4 ,hemitropic or half coils2 t is1 ! numb] ( coil p] phase mu/ be equal to "o-half ! numb] ( pole4 ,illu/ration3 ,,figs4 #a1edj & #a1eda4--,treatm5t ( coil ends 9 ?ree phase1 ?ree range w9d+s4 ,fig4 #a1edj1 inadmissible arrangem5t 9 :i* ! field magnet _c be )drawn2 fig4 #a1eda1 admissible arrangem5t 9 :i* ! armature segm5ts c be divid$4 ,?is enables ! top half ( armature to be remov$ by disconnection )\t unw9d+ any coil4 ,gr\p+ ( ,phases4--,9 ! prec$+ diagrams1 ! g5]al arrangem5t ( ! coils on ! armature surface are %[n = ! num]\s classes ( w9d+4 ,9 polyphase alt]nators ! sep>ate w9d+s ( ! v>i\s phases may be gr\p$ 9 two ways3 #a4 ,/> connection2 #b4 ,me% connection4 ,illu/ration3 ,,fig4 #a1edb4--,?ree phase w9d+ ) half coils4 ,! advantage ( employ+ half coils is t ! ends may be arrang$ 9 two ranges z %[n4 ,!re is "o slot p] phase p] pole1 t is1 total numb] ( slots #c numb] ( poles4 ,illu/ration3 ,,fig4 #a1edc4--,?ree phase w9d+ ) :ole coils4 ,two sides ( adjac5t coils come 9 "o slot4 ,numb] ( coils p] phase numb] ( poles p] phase4 ,total numb] ( slots #c multipli$ by numb] ( poles p] phase4 ,:ole coils require ! ends arrang$ 9 ?ree ranges z indicat$4 ,! coils are conc5trat$4 ,ques4 ,describe ! two phase /> connection4 ,ans4 ,9 ?is me?od ( gr\p+1 ! middle po9ts ( ea* ( ! two phases are unit$ to a common junction ,m1 & ! f\r ends are br\ght out to f\r t]m9als a1 a'1 b1 b'1 z %[n 9 fig4 #a1edd1 or 9 ! case ( revolv+ armatures1 to f\r slip r+s4 ,illu/ration3 ,,fig4 #a1edd4--;,diagram ( two phase /> gr\p+4 ,ques4 ,:at does ?is arrangem5t give8 ,ans4 ,x is practically equival5t to a f\r phase sy/em4 ,illu/ration3 ,,fig4 #a1ede4--;,diagram ( two phase me% gr\p+4 ,ques4 ,h[ is ! two phase me% connection arrang$8 ,ans4 ,9 ?is /yle ( gr\p+1 ! two phases are divid$ into two p>ts1 & ! f\r p>ts are connect$ up 9 cyclic ord]1 ! end ( "o to ! beg9n+ ( ! next1 s z to =m a squ>e1 ! f\r corn]s ( :i* are connect$ to ! f\r t]m9als a1 b1 a'1 b'1 z %[n 9 fig4 #a1ede1 or 9 ! case ( revolv+ armatures1 to f\r slip r+s4 ,ques4 ,describe a ?ree phase /> connection8 ,ans4 ,9 ?ree phase /> gr\p+1 "o end ( ea* ( ! ?ree circuits is br\ght to a common junction ,m1 usually insulat$1 & ! ?ree o!r ends are connect$ to ?ree t]m9als a1 b1 c1 z %[n 9 fig4 #a1edf1 or 9 ! case ( revolv+ armatures to ?ree slip r+s4 ,illu/ration3 ,,fig4 #a1edf4--;,diagram ( ?ree phase /> gr\p+1 commonly call$ ,y gr\p+ ow+ to its resemblance ( ! lett] ,y4 ,! curr5t 9 ea* ma9 is obvi\sly equal to ! curr5t 9 ea* phase w9d+1 b ! t]m9al pressure is ! vector sum ( ! pressures 9 ! compon5t phase w9d+s1 t is1 #c multipli$ by ! pressure 9 "o phase4 ,ques4 ,:at o!r "n is giv5 to ?is connection1 & :y8 ,ans4 ,x is commonly call$ a ,y connection or gr\p+ ow+ to ! resemblance ( its diagrammatic repres5tation to ! lett] ,y4 ,illu/ration3 ,,fig4 #a1edg4--,radial diagram ( ?ree phase1 "o slot w9d+ ) ,y connection4 ,illu/ration3 ,,fig4 #a1edh4--,radial diagram ( ?ree phase "o slot w9d+ ) delta connection4 ,ques4 ,h[ is a ?ree phase me% connection arrang$8 ,ans4 ,! ?ree circuits are connect$ up toge!r 9 ! =m ( a triangle1 ! ?ree corn]s are connect$ to ! ?ree t]m9als1 a1 b1 c1 z %[n 9 fig4 #a1edi1 or 9 ! case ( revolv+ armatures to ?ree slip r+s4 ,illu/ration3 ,,fig4 #a1edi4--;,diagram ( ?ree phase me% gr\p+1 commonly call$ delta gr\p+ ow+ to its resemblance to ! ,greek lett] 4 ,! voltage at ! t]m9als is equal to ! voltage 9 "o phase1 & ! curr5t 9 ea* l9e is equal to ! vector sum ( ! curr5ts 9 two phases1 t is1 x is equal to #c multipli$ by ! curr5t 9 "o phase4 ,ques4 ,:at o!r "n is giv5 to ?is /yle ( connection1 & :y8 ,ans4 ,x is commonly call$ a delta gr\p+ on acc\nt ( ! resemblance ( its diagrammatic repres5tation to ! ,greek lett] 4 ,illu/ration3 ,,fig4 #a1eej4--,?ree phase w9d+ ) %ort coils4 ,! use ( %ort coils z "h %[n1 9 :i* ! coil bread? pole pit*1 avoids ! necessity ( ov]lapp+4 ,9 polyphase work+1 x is evid5t t by ! use ( f\r equal indep5d5t w9d+s on ! armature1 connect$ to eight t]m9als or slip r+s1 a two phase alt]nator c be built to supply curr5ts ( equal voltage to f\r indep5d5t circuits4 ,likewise1 by ! use ( ?ree equal indep5d5t w9d+s1 connect$ to six t]m9als or slip r+s1 a ?ree phase alt]nator c be made to supply ?ree indep5d5t circuits4 ,?is is n ! usual me?od employ$ 9 ei!r case1 h[ev]1 z ! /> gr\p+ or me% gr\p+ me?ods ( connection n only gives ! same results1 b also1 9 /> gr\p+1 a great] plurality ( voltages = ! same ma*9e1 & a high] voltage betwe5 its ma9 t]m9als4 ,radial diagrams ( ! arrangem5t & connections ( ,y gr\p+ ( lap w9d+s & wave w9d+s = ?ree phase alt]nators are %[n by figs4 #a1eea & #a1eeb4 ,illu/ration3 ,,fig4 #a1eea4--,radial diagram ( ?ree phase lap w9d+ ) /> connection4 ,ques4 ,9 ?ree phase /> gr\p+1 :at is ! po9t :]e ! phases jo91 call$8 ,ans4 ,! /> po9t4 ,ques4 ,9 a ?ree phase /> connect$ alt]nator :at is ! voltage betwe5 any two collector r+s8 ,ans4 ,x is equal to ! voltage g5]at$ p] phase multipli$ by #c or #a4gcb4 ,illu/ration3 ,,fig4 #a1eeb4--,radial diagram ( ?ree phase wave w9d+ ) /> connection4 ,ques4 ,9 a ?ree phase /> connect$ alt]nator :at is ! value ( ! curr5t 9 ea* l9e8 ,ans4 ,! same z ! curr5t 9 ea* phase w9d+4 ,illu/ration3 ,,figs4 #a1eec & #a1eed4--;,gramme r+ armatures %[+ ?ree phase /> & me% connections1 respectively1 ) direction ( curr5ts 9 ! coils4 ,9 ! figures1 ! coils ,a1 ,b1 ,c1 are spac$ at equidi/ant positions on ! r+ core4 ,! arr[ heads repres5t ! directions ( ! induc$ pressures or curr5ts = ! position %[n1 ! rotation be+ clockwise4 ,9 coil ,a ! pressure is increas+1 9 coil ,b x is dim9i%+1 b is 9 ! same direction z 9 ,a1 :]eas 9 coil ,c x is also dim9i%+1 b is 9 ! opposite direction to :at x is 9 coils ,a & ,b4 ,z ! r+s rotate ! ?ree coils h simil> alt]nations ( pressure induc$ 9 !m1 b diff] 9 phase4 ,if a1 b & c be jo9$ to collector r+s ?ree phase curr5ts c be suppli$ to ! out] circuits4 ,9 fig4 #a1eec at ! in/ant repres5t$ a & b are giv+ _! curr5t to _! l9es1 :ile c is receiv+ f its l9e a curr5t equal to ! sum ( a & b4 ,9 fig4 #a1eed1 at ! in/ant repres5t$1 ! curr5ts s5t out f a w be equal to ! sum ( ! curr5ts 9 x & y1 & int]m$iate betwe5 !m 9 phase4 ,! curr5t f b w be equal to ! diff]5ce ( ! curr5ts 9 z & y1 & ( int]m$iate phase1 :ile simil>ly ! curr5t receiv$ by c w be equal to ! sum ( ! curr5ts 9 x & z4 ,ques4 ,:at is ! value ( ! total output 9 watts ( a /> connect$ alt]nator8 ,ans4 ,x is equal to ! sum ( ! outputs ( ea* ( ! ?ree phases4 ,:5 work+ on a non-inductive load1 ! total output ( a /> connect$ alt]nator is equal to #c multipli$ by ! product ( ! l9e curr5t & l9e voltage4 ,ques4 ,:at is ! value ( ! l9e voltage 9 a ?ree phase delta connect$ alt]nator8 ,ans4 ,x is equal to ! voltage g5]at$ 9 ea* phase4 ,ques4 ,:at is ! value ( ! l9e curr5t 9 a ?ree phase delta connect$ alt]nator8 ,ans4 ,x is equal to ! curr5t 9 ea* phase multipli$ by #c4 ,ques4 ,:at is ! total output ( a ?ree phase delta connect$ alt]nator work+ on a non-inductive load8 ,ans4 ,! total watts is equal to #c multipli$ by ! product ( ! l9e curr5t & ! l9e voltage4 ,illu/ration3 ,,figs4 #a1eee to #a1eeg4--,sep>ate coils1 & section ( ,allis-,*alm]s alt]nator ) coils 9 place4 ,num]\s op5+s are provid$ 9 ! frame ?r\gh :i* air curr5ts1 set up by ! revolv+ field1 c pass freely & c>ry (f heat4 ,%ields are provid$ to protect ! armature coils :]e !y project beyond ! core4 ,9 assembl+ ! core spac+ segm5ts are plac$ at int]vals to =m v5tilat+ ducts4 ,aft] ! coils h be5 cov]$ ) insulat+ mat]ials & treat$ ) insulat+ comp\nd1 ! p>ts t are to lie 9 ! slots are press$ to exact size 9 /eam heat$ m\lds4 ,?is runs ! insulat+ mat]ial into all ! small spaces 9 ! coil s z to exclude moi/ure1 x also makes ! coil /ructure firm & solid4 ,! project+ ends ( ! coils are heavily tap$1 suitable supports be+ provid$ = ! coil connections s t !y _c become displac$ on acc\nt ( /resses due to %ort circuits or o!r causes4 ,on high pressure ma*9es ! armature t]m9als are arrang$ s t x is impossible = an att5dant to make accid5tal contact ) !m4 ,ques4 ,:at are ! features ( ! /> connection8 ,ans4 ,x gives a high] l9e voltage ?an ! delta connection = ! same pressure g5]at$ p] phase1 h5ce x is suit$ = ma*9es ( high voltage & mod]ate curr5t4 ,! delta connection gives a l[] l9e voltage ?an ! />#e connection = ! pressure g5]at$ p] phase1 & cuts d[n ! curr5t 9 ! inductors2 s9ce ! inductors1 on ?is acc\nt1 may be r$uc$ 9 size1 ! delta connection is adapt$ to ma*9es ( l>ge curr5t output4 #e ,,note4--,9 ! /> connect$ armature ! prop] ends to connect to ! common t]m9al or /> po9t are det]m9$ z foll[s3 ,assume t ! inductor opposite ! middle ( a pole is c>ry+ ! maximum curr5t1 & m>k its direction by an arr[4 ,!n ! curr5t 9 ! inductors on ei!r side ( & adjac5t to x w be 9 ! same direction4 ,z ! maximum curr5t mu/ be com+ f ! common t]m9al1 ! end t[>d :i* ! arr[ po9ts mu/ be connect$ to "o ( ! r+s1 :ile ! o!r end is connect$ to ! common t]m9al4 ,! curr5t 9 ! two adjac5t inductors evid5tly mu/ be fl[+ into ! common t]m9al1 h5ce ! ends t[>d :i* ! arr[s po9t mu/ be connect$ to ! common t]m9al1 :ile _! o!r ends are connect$ to ! rema9+ two r+s4 ,illu/ration3 ,,fig4 #a1eeh4--;,diagram ( ,we/+h\se two phase composite w\nd alt]nator1 %[+ connections betwe5 two phase armature & a s+le phase rectifi$ & composite field w9d+4 ,! arrangem5t makes use ( a s]ies trans=m]1 m\nt$ on ! spokes ( ! armature4 ,by means ( ?is s]ies trans=m] ! voltage deliv]$ to ! rectify+ commutator & ! fields is mu* less ?an t g5]at$ by ! ma*9e4 ,! armature ( ?is ma*9e is ( ! clos$ coil s+le w9d+ type1 all ! armature inductors be+ connect$ ) ea* o!r to =m a clos$ circuit :i* resembles to a c]ta9 ext5t ! ord9>y drum w9d+ ( a multipol> direct curr5t ma*9e4 ,?is w9d+ is tapp$ out at two po9ts p] pole j z is ! cont9u\s w9d+ ( a two phase rot>y conv]t]1 ^! taps runn+ to collector r+s ?r\gh :i* ! curr5ts are deliv]$ to ! outside circuits4 ,on acc\nt ( ?is connection ( bo? phases to "o w9d+ !re is a def9ite voltage set up betwe5 ! inductors ( phase ,a1 & ( phase ,b1 ?is voltage be+ %[n by ! figures giv5 9 ! diagram4 ,! arrangem5t is adapt$ = two phase "w by fitt+ ! s]ies trans=m] = ! auxili>y field excitation ) two prim>ies connect$ respectively 9 "o leg ( ea* ( ! two phases2 ?us ! trans=m] is excit$ by two curr5ts normally p]iod out ( phase ) ea* o!r4 ,! result ^u ! second>y is a comb9ation ( ! effects ( ! two prim>y curr5ts1 ! voltage deliv]$ by ! second>y be+ int]m$iate 9 phase betwe5 ^? pressures :i* w\ld be sep>ately set up by ! two prim>ies4 ,?is comb9ation effect is %[n 9 ! small diagram 9 ! upp] "r h& corn] ( ! illu/ration4 ,if ,,oa be ! effect set up 9 ! second>y ( ! s]ies trans=m] by ! prim>y curr5t ( phase ,a1 & ,,ob be ! effect set up by ! prim>y curr5t ( phase ,b1 ,,oc repres5ts 9 magnitude & phase relation ! resultant effect ^u ! second>y4 ,x is readily se5 t ?is resultant is n equal to ! ari?metical sum ( ! two compon5ts s9ce1 to a c]ta9 ext5t1 !y "w at cross purposes4 ,h[ev]1 if ei!r "o ( !m increase ! resultant effect increases1 al?\gh n 9 exact proportion4 ,if ! load rema9 balanc$1 ! two compon5ts rema9+ equal to ea* o!r1 ! resultant ,,oc v>ies 9 exact proportion to any *anges 9 ! compon5ts4 ,if ! load become unbalanc$1 ! resultant sw+s ar\nd m ne>ly into phase ) ! l>g] load2 ?us if ,,ob become great]1 ,,oa rema9+ ! same1 ,,oc sw+s ar\nd1 becom+ m ne>ly horizontal4 ,?is requires a readju/m5t ( ! position ( ! bru%es on ! commutator to set !m prop]ly = m9imum sp>k+1 an adju/m5t exactly simil> to t requir$ :5 ! p[] factor ( ! load *anges4 ,illu/ration3 ,,fig4 #a1eei4--;,diagram ( ,we/+h\se ?ree phase composite w\nd alt]nator4 ,! armature inductors are ( ! clos$ coil or delta connect$ type1 b are tapp$ at ?ree po9ts p] pair or poles to ! ?ree collector r+s4 ,all ?ree connections betwe5 ! armature coils & ! collector r+s run ?r\gh prim>y circuits ( ! s]ies trans=m] )9 ! armature1 ^! ?ree prim>ies ea* giv+ _! own effect ^u ! second>y4 ,s9ce ! resultant ( ?ree equal alt]nat+ electromotive =ces #abj ap>t is z]o1 s t "s special arrangem5t mu/ be adopt$ to make ^! electromotive =ces act ) in/ead ( aga9/ ea* o!r4 ,! arrangem5t is a rev]sal ( ! connections ( "o ( ! prim>ies ( ! s]ies trans=m]4 ,?is is %[n 9 ! case ( ! l[e/ prim>y indicat$ 9 ! diagram4 ,! comb9ation ( ! effects ( ! ?ree prim>ies is aga9 indicat$ 9 ! small vector diagram 9 ! upp] "r h& corn]4 ,"h ,,oa is ! effect ( "o prim>y1 ,,ob t ( ano!r ( a p]iod displac$ f ! =m] 9 phase1 & ,,oc t :i* ! ?ird w\ld ex]t 7 x n rev]s$1 b ! rev]sal br+s ! effect ( ?is ?ird coil into ! phase relation ,,od1 s t ! ?ree are only #fj ap>t4 ,! comb9ation ( ,,oa & ,,ob is equal to ,,oc1 :i* comb9$ aga9 ) ,,od gives a resultant effect1 ,,oe4 ,9 ?is case1 z 9 ! o!r1 ! effect ^u ! s]ies field does n rema9 exactly proportional to ! load unless ! latt] is balanc$2 9 fact1 an increas$ curr5t ?r\gh ! "o leg repres5t$ by ,,od1 affects ! s]ies field z mu* z an equal increase 9 ea* ( ! o!r legs put toge!r4 ,practically1 h[ev]1 any increase ( ! load--di/ribut$ z x mu/ be 9 two legs at lea/--increases ! field excitation s t prop] regulation is secur$4 ,ques4 ,h[ is ! pa? & value ( curr5ts 9 a delta connect$ armature det]m9$8 ,ans4 ,/>t+ ) ! inductors ( "o phase opposite ! middle ( ! poles1 assume ! maximum curr5t to be induc$ at ?is mom5t2 !n b "o-half ( ! same value ( curr5t w be induc$ at ! same mom5t 9 ! o!r two phases1 & its pa? & value w be/ be %[n by aid ( fig4 #a1efj1 9 :i* ,x may be tak5 z ! middle collector r+1 & ! maximum curr5t to be fl[+ f ,x t[>d ,z4 ,x w be se5 t no curr5t is com+ 9 ?r\gh ! l9e ,y1 b "p ( ! curr5t at ,z w h be5 induc$ 9 ! bran*es b & c4 ,illu/ration3 ,,fig4 #a1efj4--;,diagram %[+ det]m9ation ( pa? & value ( curr5t fl[+ 9 delta connect$ armature4 ,ques4 ,s9ce mo/ ?ree phase w9d+s c be connect$ ei!r ,y or delta1 :at %\ld be not$ z to ! effects produc$8 ,ans4 ,) ! same w9d+1 ! delta connection w /& #a4gcb z mu* curr5t z ! ,y connection1 b w give only #a #a4gcb or 4#egg z mu* voltage4 ,illu/ration3 ,,fig4 #a1efa4--,triumph bru%es & bru% hold]4 ,! hold] is ( ! box type provid$ ) an adju/able t5sion spr+1 mak+ ! bru%es self-fe$+4 ,ea* hold] is c>ri$ on insulat$ /uds atta*$ to a ca/ iron yoke :i* is m\nt$ on ! be>+4 ,illu/ration3 ,,fig4 #a1efb4--;,diagram ( ,y connection ) a common return wire4 ,:5 ! ?ree l9es lead+ f a1 b & c are equal 9 resi/ance & reactance1 or 9 o!r words :5 ! sy/em is balanc$1 ! curr5ts ( ! ?ree phases are equal & are #abj ap>t 9 phase 7ea* curr5t lagg+ beh9d its pressure by ! same am\nt z ! o!rs7 & _! sum is at ea* in/ant equal to z]o4 ,9 ?is case ! resultant curr5t be+ equal to z]o !re is no ne$ ( a common return wire4 ,h[ev]1 9 "s cases1 :]e p[] is di/ribut$ f trans=m]s or ?ree wire sy/ems1 ! diff]5t bran*es are liable to become unbalanc$4 ,"u su* circum/ances ! common return wire is sometimes us$1 be+ made l>ge en\gh to take c>e ( ! maximum unbalanc+ t may occur 9 op]ation4 ,! return wire is us$ sometimes on alt]nators t furni% curr5t mo/ly = light+ "w4 ,*a9 or ,basket ,w9d+4--,"o disadvantage 9 ord9>y two-range w9d+s is t two or ?ree sep>ate %apes ( coil are requir$4 ,! co/ ( mak+1 w9d+1 & supply+ sp>es w\ld be less if "o %ape ( coil c\ld be made to d = all phases4 ,"o way ( accompli%+ ?is is by ! me?od ( *a9 w9d+1 9 :i* ! two sides ( ea* coil are made ( diff]5t l5g?s1 z %[n 9 fig4 #a1efc1 & b5t s t !y c lie beh9d "o ano!r4 ,illu/ration3 ,,fig4 #a1efc4--;,diagram %[+ *a9 w9d+4 ,9 ?is me?od ( w9d+ ! coils are all simil> ) long & %ort sides4 ,x obviates ! extra co/ ( mak+ coils ( sev]al diff]5t %apes4 ,! diagram repres5ts a w9d+ = "o slot p] pole p] phase4 ,illu/ration3 ,,fig4 #a1efd4--;,g5]al ,electric t]m9al bo>d %[+ cables lead+ to ?ree phase w9d+4 ,9 ! case ( op5 slots ! coils may be =m] w\nd & aft]w>ds w$g$ into _! places4 ,9 *a9 w9d+ ! adjac5t coils l9k "o ano!r z 9 a *a9 7h5ce1 ! "n72 ! w9d+ is simil> to a skew coil w9d+4 ,?is plan ( w9d+ is suppos$ to h "s advantage 9 keep+ coils ( diff]5t phases fur!r sep>at$ ?an ! two range plan4 ,illu/ration3 ,,fig4 #a1efe4--,section ( armature w9d+ ( ,allis-,*alm]s #ejj kw4 ?ree phase wat] :eel alt]nator4 ,! coils are ( ! conc5trat$ half type4 ,ea* coil is completely insulat$ be=e be+ plac$ on ! core & no insulation is plac$ 9 ! slot itself4 ,! ends ( ! coils :]e !y project beyond ! slots are heavily tap$4 ,:]e necess>y suitable supports are provid$ = ! coil connections s t !y _c become displac$ on acc\nt ( /resses due to %ort circuits or o!r causes4 ,! w9d+ is ( ! *a9 type4 ,?is is %[n by ! way ! coils are connect$ toge!r at ! "r4 ,! armature t]m9als are ei!r provid$ ) insulat$ connectors or are l$ to a m>ble t]m9al bo>d on :i* ! t]m9als are s m\nt$ & protect$ t x is impossible = an att5dant to make accid5tal contact ) !m4 ,! position ( ! illu/ration w\ld indicate a horizontal alt]nator b ! ma*9e is ( ! v]tical type2 ! lug on ! "r %[s ?is1 be+ us$ = adju/+ ! alt]nator on ! f\ndation4 ,skew ,coil ,w9d+4--,9 ?is type ( w9d+ ! object is to %ape ! coils s t all may be ( "o patt]n4 ,?is is accompli%$ by mak+ ! ends skew %ape z %[n 9 figs4 #a1eff to #a1efh4 ,illu/ration3 ,,figs4 #a1eff to #a1efh4--,views ( a section ( skew coil w9d+2 s call$ on acc\nt ( ! skew %ape giv5 to ! coil ends 9 ord] t all ! coils may be ( "o %ape4 ,f$-9 ,w9d+4--,?is "n is giv5 to a type ( w9d+ possible ) op5 or only p>tially clos$ slots1 9 :i* coils previ\sly =m$ are introduc$1 only a few inductors at a "t if necess>y4 ,!y are ins]t$ into ! slots f ! top1 ! slot be+ provid$ ) a l9+ ( horn fibre or o!r suitable mat]ial1 :i* is f9ally clos$ ov] & secur$ 9 place by means ( a w$ge1 or by "s o!r suitable means4 ,an example ( a f$-9 w9d+ is %[n 9 figs4 #a1eff & #a1efh4 ,imbricat$ ,w9d+4--,?is is a species ( spiral coil w9d+ 9 :i* ! end connections are built up "o above ! o!r1 ei!r 9 a radial1 or 9 a horizontal direction4 ,! w9d+ is us$ especially on ! armatures ( turb9e alt]nators & dynamos4 ,spiral ,w9d+4--,?is is a w9d+ 9 :i* spiral coils1 z %[n 9 fig4 #a1efi1 are us$4 ,! spiral =m ( coil is v ext5sively us$ = armature w9d+s ( alt]nators4 ,illu/ration3 ,,fig4 #a1efi4--;,diagram %[+ a spiral coil4 ,?is type ( coil is "o 9 :i* ea* successive turn lies entirely )9 ! previ\s turn1 />t+ ) ! out]mo/ turn ( ! coil4 ,! successive turns ( a spiral coil are ?us n ( ! same size1 & are n ov]lapp+ z 9 a lap coil4 ,mummifi$ ,w9d+4--,! ^w mummifi$ z appli$ to a w9d+ is us$ to express ! treatm5t ! coils ( ! w9d+ receive 9 ! mak+2 t is1 :5 a w9d+1 aft] be+ cov]$ ) tape or o!r absorb5t mat]ial1 is saturat$ 9 an insulat+ comp\nd & bak$ until ! :ole is solidifi$1 x is said to be mummifi$4 ,%uttle ,w9d+4--,?is type ( w9d+ consi/s ( a s+le coil hav+ a l>ge numb] ( turns1 w\nd 9 two slots spac$ #ahj ap>t4 ,x 0 orig9ally us$ on ,siem5s' armature & is n[ us$ on magnetos1 z %[n 9 figs4 #a1dei to #a1dfa4 ,illu/ration3 ,,fig4 #a1egj4--;,frame & armature w9d+ ( ,we/+h\se p$e/al be>+ alt]nator4 ,armature frames are ( ca/ iron & v5tilat$4 ,int]ior transv]se ribs /r5g!n ! frame & support ! core lam9ations4 ,! armature core is built up ( anneal$ & japann$ pun*$ lam9ations4 ,armature slots are op54 ,armature coils are =m w\nd1 impregnat$1 & int]*angeable2 !y are held 9 place ) fib] w$ges4 ,v5tilat+ spaces are provid$ at int]vals 9 ! armature core & also betwe5 all coil ends4 ,creep+ ,w9d+4--,ano!r species ( w9d+1 kn[n z a creep+ w9d+ is applicable to p>ticul> cases4 ,if ?ree adjac5t coils1 ea* hav+ a pit* ( #abj electrical degrees1 be set side by side1 !y w occupy ! same bread? z #d poles1 &1 by repetition1 w s]ve = any ma*9e hav+ a multiple ( #d poles1 b _c be us$ = ma*9es ) #f1 #aj or #ad poles4 ,fig4 #a1ega %[s ?is example4 ,illu/ration3 ,,figs4 #a1ega & #a1egb4--;,diagram ( creep+ w9d+s4 ,fig4 #a1ega1 ?ree coils subt5d+ f\r poles2 fig4 #a1egb1 n9e coils subt5d+ eight poles4 ,9 ! same way #i coils1 ea* ( #afj electrical degrees1 w occupy ! same angul> bread? z #h poles4 ,fur!r1 #i coils ( #bjj electrical degrees w occupy ! same angul> bread? z #aj poles4 ,n[ ( ^! #i coils1 any ?ree contigu\s ones are ne>ly 9 phase1 if w\nd alt]nately clockwise & c\nt]-clockwise4 ,= ! #h pole ma*9e1 ! phase diff]5ce betwe5 adjac5t coils is #bj degrees4 ,= ! #aj pole ma*9e1 ! phase diff]5ce is also #bj degrees4 ,! cos9e ( #bj degrees is 4#icig1 consequ5tly1 if #c adjac5t coils be unit$ 9 s]ies1 _! jo9t pressure w be #b4hig multipli$ by t ( ! middle "o ( ! ?ree4 ,! #i coils may !re=e be jo9$ up 9 ?ree gr\ps ( #c adjac5t coils1 = ! ?ree phases4 ,by repetition1 ! same gr\p+ w suit = any ma*9e hav+ a multiple ( #h or ( #aj poles4 ,^! two cases are illu/rat$ 9 figs4 #a1egb & #a1egc4 ,9 ! figures1 ! coils are repres5t$ z occupy+ two slots ea*1 b !y might be fur!r di/ribut$4 ,illu/ration3 ,,fig4 #a1egc4--;,develop$ diagram ( creep+ w9d+3 n9e coils subt5d+ t5 poles4 ,illu/ration3 ,,fig4 #a1egd4--,triumph p$e/al & bru% rigg+ = l>ge revolv+ field alt]nators4 ,c>bon bru%es are us$1 c>ri$ 9 box type bru% hold]s4 ,! /& or p$e/al "h %[n is ! k9d us$ ) ! eng9e & fly :eel types ( alt]nator4 ,! bru% /uds are m\nt$ on ! /& 9 su* a mann] t ! bru%es are easily accessible4 ,! latt] c>ry only ! l[ voltage direct curr5t necess>y = excit+ ! field4 ,turb9e ,alt]nator ,w9d+4--,= ! reason t /eam turb9es run at s mu* high] spe$ ?an /eam eng9es1 ! con/ruction ( armatures & w9d+s = alt]nators int5d$ to be direct connect$ to turb9es mu/ be q diff]5t f ^? driv5 by /eam eng9es4 ,accord+ly1 9 ord] t ! frequ5cy be n too high1 turb9e driv5 alt]nators mu/ h v few poles--usually two or f\r1 b r>ely six4 ,illu/ration3 ,,figs4 #a1ege & #a1egf4--,we/+h\se turb9e alt]nator armature con/ruction4 ,fig4 #a1ege4 ,view %[+ dovetail grooves 9 armature ca/+2 fig4 #a1egf1 lam9 assembl$ 9 dovetail grooves ( armature ca/+4 ,! foll[+ table w %[ ! relation betwe5 ! revolutions & frequ5cies = ! numb]s ( poles j designat$4 ,,table ,,( ,,frequ5cy ,,& ,,revolutions -------------------------------------- ,,revolutions ,frequ5cy -------------------------- #b pole #d pole #f pole ----------------------------------- #be #a1ejj #gej #ejj #fj #c1fjj #a1hjj #a1bjj #ajj #f1jjj #c1jjj #b1jjj ----------------------------------- ,illu/ration3 ,,fig4 #a1egg4--;,armature ( ,we/+h\se turb9e alt]nator ) end bells remov$ %[+ me?od ( brac+ ! coil ends4 ,illu/ration3 ,,fig4 #a1egh4--,/ation>y armature ( ,we/+h\se turb9e alt]nator ) "p ( ! w9d+ 9 place4 ,because ( ! small numb] ( coils 9 a turb9e alt]nator z comp>$ ) a sl[ spe$ ma*9e ( ! same kva4 rat+1 ea* coil c>ries a great am\nt ( p[] on l>ge load1 p>ticul>ly at times ( %ort circuits or gr\nds on ! ext]nal circuit4 ,! ?r[ ( ! coils is l>ge1 leav+ a consid]able "p ( ! w9d+ 9 ! end turns unsupport$ by ! armature core4 ,= ^! reasons great /resses1 :i* are dang]\s1 if effective means be n adopt$ to )/& !m1 may exi/ betwe5 ! coils4 ,! inductors are ( su* cross section t !y c be made rigid & insulat$ satisfactorily4 ,! end turns are giv5 a fan l =m z %[n1 af=d+ v5tilation & effective brac+ z %[n 9 fig4 #a1egg4 ,cord la%+s are1 except 9 ! smalle/ frames1 us$ only = hold+ 9 ! small spac+ blocks betwe5 ! coils4 ,!y are n dep5d$ on to support ! coils4 ,malleable iron braces1 h>d maple blocks1 & brass or /eel bolts ) brass wa%]s are us$ to )/& ! me*anical /resses impos$ on ! armature coils by ext]nal %ort circuits4 ,f ! table1 x is evid5t t a l>ge numb] ( poles is n p]missible1 consid]+ ! high spe$ at :i* ! turb9e mu/ be run4 ,illu/ration3 ,,fig4 #a1egi4--,two pole radial slot field4 ,radial slot fields are us$ on v small & v l>ge alt]nators4 ,! field diamet]s are s small t ! end turns ( ! w9d+ c be effectively b\nd into place1 su* b9d+ be+ necess>y ) a radial slot ma*9e4 ,! %aft & disc are a "o piece =g+ ( /eel4 ,ques4 ,h[ is ! high voltage obta9$ ) s few poles8 ,ans4 ,!re mu/ be ei!r num]\s inductors p] slot or num]\s slots p] pole4 ,illu/ration3 ,,figs4 #a1ehj to #a1ehb4--,we/+h\se two pole p>allel slot field ) ends remov$ %[+ con/ruction4 ,! p>allel slot design ( field con/ruction is us$ 9 ,we/+h\se ma*9es up to #aj1jjj kva4 capacity4 ,9 fig4 #a1eha1 ! l>ge holes at ! end ne> ! circumf]5ce ( ! cyl9d] are = ! accommodation ( ! bolts t hold ! bronze end discs & /ub %afts4 ,9 w9d+1 ! cyl9d] is m\nt$ on a horizontal turntable t rotates 9 a horizontal plane4 ,! copp] /rap field coil w9d+ is w\nd turn by turn "u pressure & /rip insulation is w\nd 9 betwe54 ,:5 complet$ ! turns are held rigidly 9 position ) heavy brass w$ges4 ,an end disc made ( bronze holds ! /ub %aft & is bolt$ to ea* end ( ! /eel c5t]4 ,:5 ! leads are atta*$ to ! collector r+s ! field is complete4 ,ques4 ,:at =m ( armature is g5]ally us$8 ,ans4 ,a /ation>y armature4 ,ques4 ,:at difficulty is exp]i5c$ ) revolv+ armatures8 ,ans4 ,! c5trifugal =ce be+ consid]able on acc\nt ( ! high spe$1 requires specially /rong con/ruction to resi/ x1 consequ5tly clos$ or ne>ly clos$ slots mu/ be us$4 ,ques4 ,h[ is ! design ( ! rotor modifi$ s z to r$uce ! c5trifugal =ce8 ,ans4 ,x is made long & ( small diamet]4 ,"s examples ( revolv+ fields are %[n 9 figs4 #a1egi to #a1ehd4 ,figs4 #a1egg & #a1egh %[ "s con/ruction details ( a /ation>y armature ( turb9e alt]nator4 ,illu/ration3 ,,fig4 #a1ehc4--,we/+h\se two pole p>allel slot turb9e alt]nator field4 ,illu/ration3 ,,fig4 #a1ehd4--,we/+h\se f\r pole p>allel slot turb9e alt]nator field4 ,,hawk9s ,,practical ,,libr>y ,,( ,,electricity ,,9 ,,h&y ,,pocket ,,=m ,,price #a ,,ea* 99 99 99 99 99 ,!y are n only ! be/1 b ! *eape/ "w publi%$ on ,electricity4 ,ea* numb] be+ complete 9 itself4 ,sep>ate numb]s s5t po/paid to any address on receipt ( price4 ,!y are gu>ante$ 9 e way or y\r money w be return$4 ,complete catalog ( s]ies w be mail$ free on reque/4 ,,electrical ,,guide1 ,,no4 #a ,conta9+ ! pr9ciples ( ,elem5t>y ,electricity1 ,magnetism1 ,induction1 ,exp]im5ts1 ,dynamos1 ,electric ,ma*9]y4 ,,electrical ,,guide1 ,,no4 #b ,! con/ruction ( ,dynamos1 ,motors1 ,armatures1 ,armature ,w9d+s1 ,in/all+ ( ,dynamos4 ,,electrical ,,guide1 ,,no4 #c ,electrical ,in/rum5ts1 ,te/+1 ,practical ,managem5t ( ,dynamos & ,motors4 ,,electrical ,,guide1 ,,no4 #d ,di/ribution ,sy/ems1 ,wir+1 ,wir+ ,diagrams1 ,sign ,fla%]s1 ,/orage ,batt]ies4 ,,electrical ,,guide1 ,,no4 #e ,pr9ciples ( ,alt]nat+ ,curr5ts & ,alt]nators4 ,,electrical ,,guide1 ,,no4 #f ,alt]nat+ ,curr5t ,motors1 ,trans=m]s1 ,conv]t]s1 ,rectifi]s4 ,,electrical ,,guide1 ,,no4 #g ,alt]nat+ ,curr5t ,sy/ems1 ,circuit ,break]s1 ,measur+ ,in/rum5ts4 ,,electrical ,,guide1 ,,no4 #h ,alt]nat+ ,curr5t ,swit* ,bo>ds1 ,wir+1 ,p[] ,/ations1 ,in/allation & ,op]ation4 ,,electrical ,,guide1 ,,no4 #i ,telephone1 ,telegraph1 ,wireless1 ,bells1 ,light+1 ,railways4 ,,electrical ,,guide1 ,,no4 #aj ,mod]n ,practical ,applications ( ,electricity & ,ready ,ref]5ce ,index ( ! 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