CHAPTER 17. Exercises. Using the expressions given in the Exercise statement for the currents, we have

Transcription

1 CHATER 7 Execie E7. F Equtin 7.5, we hve B gp Ki ( t ) c( θ) + Ki ( t ) c( θ 0 ) + Ki ( t ) c( θ 40 b c ) Uing the expein given in the Execie tteent f the cuent, we hve B gp K c( ωt )c( θ ) + K c( ωt 40 )c( θ 0 ) + K c( ωt 0 )c( θ 40 ) Then uing the identity f the pduct f cine, we btin B gp K [c( ωt θ ) + c( ωt + θ ) + c( ωt θ 0 + c( ωt + θ 360 ) + c( ωt θ + 0 ) + c( ωt + θ 360 )] ) Hweve we cn wite c( ωt θ) + c( ωt θ 0 ) + c( ωt θ + 0 ) 0 c( ω t + θ 360 ) c( ωt + θ) c( ω t + θ 360 ) c( ωt + θ) Thu we hve Bgp 3 K c( ω t + θ) which cn be ecgnized flux ptten tht tte clckwie. E7. At 60 Hz, ynchnu peed f fu-ple chine i: n ( ) 0f The lip i given by: n n n p.778% The fequency f the t cuent i the lip fequency. F Equtin 575

2 7.7, we hve ω ω. F fequencie in the Hz, thi bece: lip f f Hz lip n the nl nge f petin, lip i ppxitely pptinl t utput pwe nd tque. Thu t hlf pwe, we etite tht %. Thi cepnd t peed f 775 p. E7.3 Fllwing the lutin t Exple 7., we hve: 800 p n n n 800 n The pe phe equivlent cicuit i: 0.0 ( j 0.8) Z j j + j j j pwe fct c % V ( ) lgging A Z F delt-cnnected chine, the gnitude f the line cuent i line A nd the input pwe i 3 V cθ in 7.43 kw 576

3 Next, we cpute V nd. V x x ( j 0.8) j 50 j j j V Vx j A The cppe le in the tt nd t e: nd 3R 3(.)( 5.98) 99.3 W 3R ( ) 3( 0.6)( 3.54) W Finlly, the develped pwe i: ( ) dev 3 R 3( 9.4)( 3.54) 6.7 kw ut dev t 5.7 kw The utput tque i: ut Tut 8.66 newtn ete ω The efficiency i: ut η 00% in 87.6% 577

4 E7.4 The equivlent cicuit i: ( + j 0.8) j 50. Z eq Req + jxeq.6 + j j j 0.8 The ipednce een by the uce i: Z. + j + Z eq. + j j Thu, the tting phe cuent i V 440 0, tting Z , tting A nd f delt cnnectin, the line cuent i line,tting , tting A The pwe cing the i gp i (thee tie) the pwe deliveed t the ight f the dhed line in the equivlent cicuit hwn elie. ( ) R kw g 3 eq, tting 578

5 Finlly, the tting tque i fund uing Equtin g T dev, tting ω π newtn ete E7.5 Thi execie i iil t pt (c) f Exple 7.4. Thu, we hve in δ3 3 in δ in δ 3 00 in which yield the new tque ngle δ E ein cntnt in gnitude, thu we hve E V 3 V E A jx j.4 The pwe fct i c (.045 ) 99.98% lgging. E7.6 We fllw the ppch f Exple 7.5. Thu in the exple, we hve dev A cθ V θ ( ) ( 0.85) c A E V jx V The ph dig i hwn in Figue 7.4 F 90% leding pwe fct, the pwe ngle i θ The new vlue f the cuent gnitude i dev 5. 3 c( θ ) A V nd the ph cuent i A 3 Thu we hve E V jx V c (0.9)

6 The gnitude f E i pptinl t the field cuent, we hve: E A dc f 3 f E 46. E7.7 The ph dig f δ 90 i hwn in Figue 7.7. The develped pwe i given by x 3V c( θ) Hweve f the ph dig, we ee tht E c(θ ) X Subtituting, we hve VE 3 x X The tque i T ω x x 3V E ω X ble 7.* F Tble 7., we ee tht f peed f 850 p the next getet ynchnu peed i 900 p cepnding t 8 ple t. The lip i given by Equtin 7.6 : n n % n F Equtin 7.4, we hve: Synchnu Speed in p Nube f le 50 Hz 400 Hz The vltge induced in the t cnduct e given by Equtin 7.5 which tte v c Blu. When the t tun t ynchnu peed, the eltive peed between the field nd the cnduct i u 0, eulting 580

7 in v 0. Becue the induced vltge e ze, the t cuent e c ze. Thu, the fce cting n the t cnduct, given by f i l B, e ze. 7.4 At 60 Hz, ynchnu peed f ix-ple chine i: 0f 0( 60) n 00 p 6 The lip i given by: n n % n 00 f lip The fequency f the t cuent i the lip fequency. F Equtin 7.7, we hve ω ω. F fequencie in the Hz, thi bece: f lip Hz n the nl nge f petin, lip i ppxitely pptinl t utput pwe nd tque. Thu t hlf pwe, we etite tht %. Thi cepnd t peed f 80 p. 7.5 n thi ce the develped tque ppe the diectin f ttin. we i tken f the pie ve nd cnveted t electicl f. Thu the chine ct genet. 58

8 7.6 Fitcnide n i-gp flux given by B B c( ω t + θ ). F t 0, the flux i given by B c( θ ). Thu, the flux cplete tw cplete B cycle θ vie f 0 t 360 chnging diectin fu tie und the peiphey f the i gp. Cnequently, the t h fu ple. Siilly, t tht h B B c( ω t + 3θ ) i ix-ple t. The peed e 500 p nd 000 p, epectively. 7.7* Slip i given by: n n n n n F lip f 4% nd echnicl peed f n 500 p, the ynchnu peed i: n 500 n 604 p 0.96 Slving Equtin 7.4 f fequency, we hve: f n 86.8 Hz 0 0 The blck dig f the yte i hwn belw: The input pwe t the t i: ut, t 746 t η 0.80 in, t 865 W The input pwe t the cnvete i: ut, cnvete 865 in, cnvete 9 W η 0.88 cnvete Finlly, the cuent tken f the 400-V uce i: in, 5.98 A cnvete T cnvet peed in ph t evlutin f the tie pe inute, we hve: 580 n peed in ph 60 0 π 58

9 Thu the peed nge 5 t 70 ph iplie ttinl peed nge f 84.0 t 76 p. We ue negligible lip thi i the nge f ynchnu peed f the t. Slving Equtin 7.4 f fequency, we hve: n f 0 F thi ful, we find tht the nge f fequencie needed i f.8 t 39. Hz. The finl peed f 40 ph cnvet t 7.88 /. The cceletin f the vehicle i: u T The fce needed t ccelete the vehicle i: f newtn Velcity i cceletin tie tie. u. 788t The utput pwe needed f the t i: p t fu t 397t ( ) wtt The pwe equied f the bttey i lge becue f le. p( t ) p bttey 46t wtt Finlly, the cuent tken f the 48-V bttey i: pbttey i ( t ) 88.0t pee A in the lutin t pble 7.8, the nge f fequencie needed nge f.8 t 39. Hz nd the finl peed f 40 ph cnvet t 7.88 /. At peed f 40 ph the kinetic enegy f the vehicle i 3 W u J The vege pwe equied duing cceletin i: W 5.98 kw T Accunting f efficiencie, the pwe equied f the bttey i: ut bttey. kw Finlly, the bttey cuent i: bttey A 583

10 7.0* A fequency i educed, the ectnce X, X, nd X f the chine bece lle. (Recll tht X ωl.) Thu the pplied vltge ut be educed t keep the cuent f becing t lge, eulting in gnetic tutin nd veheting. 7. The ttl field in the chine i the u f the field pduced by the epte winding. Thu, B B + B Ki t c θ + Ki t c θ 90 b ( ) ( ) ( ) ( ) Subtituting the expein given f the cuent, we hve: B K c ωt c θ + K c ωt 90 c θ 90 b ( ) ( ) ( ) ( ) Uing the tignetic identity A c B [ c( A B ) + c( A + B )] we hve: c, K ( ωt θ) + [ c( ωt + θ) + c( ωt + 80 )] B K c θ c ωt + θ + c ωt + θ 80 becue the Hweve, we cn wite ( ) ( ) 0 tw te e ut f phe. Thu, we hve: B K c ωt θ ( ) Accding t thi eult, the xiu flux ccu f θ ωt, which iplie ttin f the field in the cunteclckwie diectin t n ngul peed f ω. The xiu flux denity i B K x. 7. With the cnnectin t the b-winding eveed the cuent bece i ( t ) c ωt nd ( ) ( ω t 90 ) c( ω + ) i ( t ) c t 90 b A befe, the ttl field in the chine i the u f the field pduced by the epte winding. Thu, B B + B Ki t c θ + Ki t c θ 90 b ( ) ( ) ( ) ( ) Subtituting the expein given f the cuent, we hve: b ( ωt ) c( θ) + K c( ωt + 90 ) c( 90 ) B K c θ c, Uing the tignetic identity A c B [ c( A B ) + c( A + B )] we hve: K ( ωt + θ) + [ c( ωt θ) + c( ωt 80 )] B K c θ + c ωt θ + c ωt θ + 80 becue the Hweve, we cn wite ( ) ( ) 0 584

11 tw te e ut f phe. Thu, we hve: B K c ω t + θ ( ) Accding t thi eult, the xiu flux ccu f θ ωt, which iplie ttin f the field in the clckwie diectin t n ngul peed f ω. Thi i the ppite t the diectin fund in ble 7.. Thu the diectin f ttin f tw-phe inductin t cn be eveed by eveing the cnnectin t ne f the tw winding. 7.3* The gnetic field i peidic with the e fequency the uce f ll chine. n tw-ple chine the gnetic field ke ne cycle und the i gp (f nth t uth nd bck t nth). n fuple chine the gnetic field ke tw cycle und the i gp. Siilly the field f the ix-ple chine h thee cycle. Thu the expein f the field e: B c ωt θ nd Bfu-ple Bix-ple B c t ( ) ( ω 3θ ) 7.4 With ze eitnce f the t cnduct, Equtin 7.9 f the t cuent bece Vc c jωl c Thu the t cuent c lg the induced t vltge V c by 90. Thu, δ bece ze (efe t Figue 7.9 in the bk), nd the t ple lie exctly unde the tt ple. Then the develped tque i ze t ll peed. Thu uing upecnduct f the t cnduct i nt gd ide. 7.5 The tw bic type f t cntuctin f inductin t e the quiel cge t in which the cnduct cnit f b f luinu tht e ct int lt cut int the t nd the wund t in which inulted wie e wund int lt in the t. Often extenl cnnectin e de t the winding f the wund t f pupe f peed cntl. The quiel cge i the e ugged f the tw type. 7.6* The ynchnu peed f the chine i given by: ω π60 0f ω 88.5 d by n 800 p 4 ( ) 585

12 Typiclly, lip i but 5% t full ld. Thu, the full-ld peed i: n p full -ld ω d, full-ld The full-ld tque i: T -ld ω full, full-ld 0.8 newtn ete Typiclly the tting tque i.5 tie the full-ld tque nd the pullut tque i tie the full-ld tque. Thu, ketch f the tque-peed chcteitic i hwn belw. We etite the efficiency f typicl chine uch thi 80%. Theefe, the input pwe t full ld i: ut in 466 W η 0.80 Typiclly the pwe fct i 75% nd the line cuent i in 466 line 6.3 A 3V cθ ( )( ) Typiclly the tting cuent i 5 t 7 tie the full-ld cuent, we etite: A tting 7.7 Beide lw ct, we uully wuld pefe n inductin t with:. High pwe fct.. High tting tque. 3. High efficiency. 4. Lw tting cuent. 5. High pull-ut tque. 586

13 7.8 Refe t Figue 7.3. Neglecting the tt eitnce R nd ttinl le, the nly l i t cppe l given by: ( ) R 3 The develped pwe nd the utput pwe e equl nd given by: ( ) ut dev 3 R Nw the efficiency i given by: ut ut η 0.60 in + ut + η 60% 7.9 Synchnu peed f n 8-ple 60-Hz t i 900 p. Thu, the lip i given by: ω ω n n ω n 900 Of cue, the fequency f the tt cuent i the line fequency 60-Hz. The fequency f the t cuent i the lip fequency given by: f f Hz lip Refe t Figue 7.3. The develped pwe i: W dev ut t Since we hve ( ) ( ) dev 3 R nd 3R we cn wite dev W * Fllwing Exple 7., we find V 0 0, tting Z , tting Becue the chine i delt cnnected, the gnitude f the tting line cuent i 587

14 line,tting A, tting T R ( ) g 3 eq, tting dev, tting kw g 7688 ω π newtn ete Cping thee eult t the f the exple, we ee tht the tting cuent i educed by fct f nd the tting tque i educed by fct f 4. Depending n the tque--peed chcteitic f the ld, the yte y nt tt. 7. F line cuent f 50 3 A, the phe cuent i 50 A. Equivlent cicuit f the chine unde tting cnditin e hwn in Figue 7.5. With the dded eitnce in eie, we hve the cicuit The ttl ipednce gnitude i equied t be: V 440 Z 8. 8Ω ttl 50 Hweve, the ipednce gnitude i Z ( ) + ( + 0. ) R 7943 ttl Slving f the dded eitnce R, we find R Ω A in Exple 7., the pwe cing the i gp i: R ( ) ( )( ) g 3 eq, tting W Finlly, the tting tque i fund uing Equtin g Tdev, tting ω 588

15 4359 π newtn ete Cping thee eult t the f the exple, we ee tht the tting tque i educed by fct f 63./ Depending n the tque--peed chcteitic f the ld, the yte y nt tt. 7. Fllwing the lutin t Exple 7., we hve: n 800 p n n n The pe phe equivlent cicuit i: ( j 0.8) Z j j.5 + j j j pwe fct c % 3 ( ) lgging V 40 0 Z V c θ.80 kw in Next, we cpute V x V nd. x ( j 0.8) j 40 j j j

16 Vx j The cppe le in the tt nd t e: R nd 3 3()( 8.) W 3R ( ) 3( 0.5)( 6.98) 43.5 W Finlly, the develped pwe i: ( ) dev 3 R ( )( ) 0.38 kw ut dev t 0.8 kw The utput tque i: ut Tut 56.5 newtn ete ω The efficiency i: η 00% ut in 86.9% 7.3* Neglecting ttinl le, the lip i ze with n ld, nd the t un t ynchnu peed which i 800 p. Then the equivlent cicuit bece: 590

17 Z R + jx + jx + j.5 j The pwe fct i: c The cuent i: V Z ( ) % Becue the chine i delt cnnected, the line cuent gnitude i line 3 0 A 7.4 Thi i iil t Exple 7.. The equivlent cicuit i: ( j 0.8) j 40 Z eq Req + jxeq j j j 0.8 The ipednce een by the uce i: Z.0 + j.5 + Z eq.0 + j j Thu, the tting cuent i: V 40 0, tting Z , tting Becue the chine i delt cnnected, the gnitude f the tting line cuent i lin,tting , tting A 59

18 The pwe cing the i gp i (thee tie) the pwe deliveed t the ight f the dhed line. R ( ) g 3 eq, tting.7 kw Finlly, the tting tque i fund uing Equtin g Tdev, tting ω 70 π newtn ete 7.5 Thi i iil t ble 7. nd Exple 7.. The pe phe equivlent cicuit i: ( j 0.5) Z j j j j j pwe fct c % Next, we cpute V x V Z ( ) lgging in 3 V cθ kw V nd. x ( j 0.5) j j j j

19 Vx j j.77 The cppe le in the tt nd t e: R nd kw 3 R ( ).70 kw Finlly, the develped pwe i: ( ) dev 3 R kw ut dev t 30.8 kw The utput tque i: ut Tut ω The efficiency i: η 00% 40 newtn ete ut in 90.7% 7.6* Neglecting ttinl le, the lip i ze with n ld, nd the t un t ynchnu peed which i 00 p. Then the equivlent cicuit bece: 593

20 Z R + jx + jx j j The pwe fct i: c The cuent i: V Z ( ) % Becue the chine i delt cnnected, the gnitude f the tting line cuent i line A 7.7 Thi i iil t Exple 7.. The equivlent cicuit i: ( + j 0.5) j Z eq Req + jx eq j j j 0.5 The ipednce een by the uce i: Z j Z Thu, the tting cuent i: V 440, tting Z , tting 778 eq Becue the chine i delt cnnected, the gnitude f the tting line cuent i 594

21 lin,tting A, tting The pwe cing the i gp i (thee tie) the pwe deliveed t the ight f the dhed line. R ( ) g 3 eq, tting 39.7 kw Finlly, the tting tque i fund uing Equtin g dev, tting ω π newtn ete Becue the chine i delt cnnected, the gnitude f the phe cuent i: / line 3 5.7/ A Then we hve 3V cθ ( ) ( ) W in ut W ut efficiency 00% 85.65% in 7.9* Becue the chine i wye cnnected the phe vltge i: V line / 3 440/ V Refe t Figue 7.3. in 3 V cθ kw g in dev g ( ) ( ) kw kw ut dev t kw ut η 00% 9.5% in 7.30 The n-ld peed i ppxitely 800 p. Thu, the ynchnu peed ppe t be 800 p, nd we hve fu-ple t. Stedy-tte petin i t the inteectin f the tque-peed 595

22 chcteitic f the t nd tht f the ld. Thu, we hve T ut 5 newtn ete nd n 400 p. The lip i: n n % n 800 π ω n 46.6 din 60 T ω 3665 W ut ut Since we e uing 0, we hve t dev ut 3 R Al, we hve R Thu, ( ) 3 ( ) ut 047 W 7.3 A n engineeing etite, we tke the diffeence between the t tque nd the ld tque ppxitely 5 newtn ete ve the peed nge f inteet. Thu, the ngul cceletin f the yte i: dω Tt Tld 5 5 din dt ttinl ineti 5 n 000 p cepnd t ω Thu, the tie equied i ppxitely: 04.7 T -up 5 un ecnd 7.3* Fit, the full-ld utput tque i: ut T ut 0.8 newtn ete 3500 π 60 ω ( ) We ue tht the develped tque i pptinl t lip in the nl peting nge. n n T T + T k K ( n n ) dev ut t n Thu t full ld, we hve: T t K (00) () 596

23 At n ld, we hve ut 0 t ( ) T nd ( n n ) T K () Slving Equtin () nd (), we btin: T newtn ete t t Tt ω 76. W. Thu, 7.33 Unde the cnditin given, we hve n n n 800 ut W ut 49 T 750 π 60 ut ω ( ) 8.4 newtn ete A n ppxitin, we ue tht the utput tque i pptinl t lip. Thu, we hve: T ut K Subtituting the bve vlue, we btin K Nw ccding t Equtin 7.34, we hve T g dev ω. Hweve, the i-gp pwe i pptinl t the que f the uce vltge. Thu, the develped tque i pptinl t uce vltge qued. Neglecting ttinl l, the utput tque i equl t the develped tque. Thu, utput tque i pptinl t the que f the uce vltge. Thu f petin t 0 V, we hve: K K ( ) 3 Then the lip i: T K n ut n nd the new peed i ( ) p Tw itutin in which ynchnu t i bette chice thn n inductin t e: 597

24 . A vey cntnt peed i equied the ld vie.. t i deible t tke dvntge f the pwe-fct cectin cpbility f the ynchnu t. 7.35*. Ue n electnic yte t cnvet 60-Hz pwe int thee-phe c f vible fequency. Stt with fequency f ne hetz le nd then gdully incee the fequency.. Ue pie ve t bing the t up t ynchnu peed befe cnnecting the uce. 3. Stt the t n inductin t elying n the tieu cnduct t pduce tque A ynchnu cpcit i n veexcited thee-phe ynchnu t peting with n ld. t ct uce f ective pwe nd cn cect the vell pwe fct f n indutil plnt, theeby educing enegy ct See Figue 7.3 in the text f the V cuve. The ph dig cepnding t the iniu pint f cuve i: 7.38* () Field cuent ein cntnt. The field cicuit i independent f the c uce nd the ld. (b) Mechnicl peed ein cntnt uing tht the pull-ut tque h nt been exceeded. (c) Output tque incee by fct f / (d) Atue cuent incee in gnitude. (e) we fct decee nd bece lgging. (f) Tque ngle incee. 598

25 7.39 () Output pwe ein cntnt. (b) Mechnicl peed ein cntnt. (c) Output tque ein cntnt. (d) Atue cuent incee in gnitude nd it phe led the uce vltge. (e) we fct decee nd bece leding. Rective pwe i pduced by the chine. (f) Tque ngle decee Synchnu peed f the chine i: ω π60 ω 5.7 d 6 n T dev ( ) 00 p ω dev 9.68 N Accding t Equtin 7.37, we hve: T KB in δ dev B ttl We define Kt KB B. Then f the initil peting cnditin, we ttl find: Tdev 9.68 K t in δ in 5 ( ) Nw when the tque duble, we hve Tdev 9.68 in δ K t which yield δ The pullut tque ccu f δ 90. Thu we hve: T in newtn x K t dev, x Tx ω ( ) ete 4.8 kw hp 7.4* T ω π60 ω d n 70 p 0 ( ) dev, ted dev, ted ω newtn ete 599

26 Accding t Equtin 7.37, we hve: T KB in δ dev B ttl We define Kt KB B. Then f the ted peting cnditin, we ttl find: Tdev K t 893 in δ in 0 ( ) The pullut tque ccu f δ 90. Thu we hve: T in newtn x K t ( ) ete The tque peed chcteitic i: 7.4 Refe t Figue 7. f the ph dig with cntnt develped pwe nd vible field cuent. The ph dig f the initil peting cnditin i: E X E V c δ E in δ. E 40 c 5 ( )

27 The ph dig f the ecnd petin cnditin i: Ntice tht the veticl cpnent f dig. Nw we cn wite: ( V tn ) ( ) ( ) + X θ + X E ( tnθ ) + ( 64.3) ( 98. ) 6 jx i the e in bth Slving, we find θ 38.5 nd the pwe fct i c θ 78.4% leding. Finlly, we hve: X 64.3 inδ E 98.6 which yield: δ The develped pwe i W. Neglecting le, thi i the input pwe. On pe phe bi, we hve in cθ 40 c 0. Thi yield 5.8 A The ph dig i: V. A ph V 40 E c δ c5 X V tn δ

28 X X Ω The ph dig with the ld eved i: Ntice tht E i cntnt in gnitude. Al with ze develped pwe, the tque ngle i ze. We hve X E V j.4 Thu, θ 90, nd the pwe fct i ze. 7.44* F ze develped pwe, the tque ngle i ze. The ph dig i: E ( 90 ) V jx j T chieve ze tue cuent, we ut hve E V The gnitude f E i pptinl t the field cuent. Thu we hve: E 480 f f A E

29 7.45 () ω π60 ω 5.66 d n 00 p 6 T ( ) dev dev ω 96.8 newtn ete (b) V cθ 3 40( 0.9) in dev Thu, ( ) θ c Thu, ( 5.) E V jx 40 j j j E 5.6 j Thu, the tque ngle i δ (c) T duble the pwe, we ut duble the tque. Accding t Equtin 7.37, the develped tque i pptinl t in δ. Thu, in δ in δ which yield the new tque ngle in gnitude, thu we hve E V E jx δ j 0.5. E ein cntnt The pwe fct i c ( 9.38 ) 98.66% leding Becue the develped pwe include the le, we hve: W 3 V cθ in dev Slving, we hve in V cθ ( 40) c ( 0.85) 3.79 θ.9 A Thu,

30 E V jx 07.9 j The ph dig i: F 00% pwe fct, the ph dig bece: Ntice tht (efe t Figue 7.) the iginy (i.e., veticl) cpnent f E i the e in bth dig. Thu we hve: X E in( 3.99 ) 5. 8 E ( V ) + ( X ) 40 + ( 5.8) The gnitude f E i pptinl t the field cuent, we hve: E 45.5 f f 0.46 A E * () The peed f ynchnu chine i elted t the fequency f the tue vltge by Equtin 7.4: 0f n The fequency f the vltge pplied t the -ple t i 60 Hz nd the peed i 600 p. Thu, the genet i diven t 600 p nd the vltge induced in it tue hve fequency f: ngen fgen 50 Hz

31 Thu, the tw chine cn be ued t cnvet 60-Hz pwe int 50-Hz pwe. (b) 000 p i nt the ynchnu peed f ny 60-Hz t. Thu, we will ty t cnvet 60-Hz int e the fequency f which 000 p i ynchnu peed. The blck dig f thi yte i: The peed f t nd the genet e the e, we hve: f n g The fequencie e the e f the genet nd t, we cn wite: n 000 f 0 0 Subtituting nd enging, we hve: 7 0 g Of cue, the nube f ple n ech chine ut be n even intege. One lutin i: g 0 nd 6 f which f 50 Hz. Anthe lutin i: g 0 6 nd f which f 00 Hz Refeing t the V-cuve hwn in Figue 7.3, we ee tht unity pwe fct ccu when the tue cuent i iniu. Thu, we wuld djut the hett in the field cicuit t btin iniu tue 605

32 cuent. The etting equied wuld chnge with ld The chine h cppe-le in the tue winding nd ttinl le. (We d nt cnide the pwe tht ut be upplied t the field cicuit.) With n ld nd cuent djuted f iniu tue cuent, the chine pete with unity pwe fct. F delt cnnectin, the phe cuent i the line cuent divided by 3. The input pwe i: ( ) kw in, n-ld The cppe l i: ( )( 9.5) 3.5 W cppe, n-ld Thu, the ttinl l i: t in, n-ld cppe, n-ld 3.68 kw We ue tht the ttinl l i independent f the ld. At fullld, we hve ut 00 + t + 3( ) R 3V c( θ) in ( 746) ( ) 3( 480) ( 0.9) Slving f, we hve The pppite t i 7.6 A. Thu, we hve: in 3V c( θ) 65.4 kw ut η 00% 90.% in 7.50* () ut 746 η 0.8 in pwe fct cθ V in 93.5 W ( ) 76.% Of cue, the pwe fct i lgging f n inductin t. (b) Z ( V ) c ( pwe fct) 0 0. c ( 0.76) Ω (c) Since the t un jut unde 800 p, evidently we hve fu-ple t. 606

33 7.5 At full ld, the lip i ( ) % full At n ld, the lip i ( ) % n Thu, we cn wite.0778k K K K 0.5 Slving, we find K 8.95 nd K Nw, f 0. hp ut Finlly, the peed f 0. hp ut i n ( ) p The phe ngle f i θ ctn Thu the phe f need t be θ The iginy pt f Z i 9 tnθ 9 ωc Of cue, ω π60, nd we find C 47.4 µ F 7.53* Unde full ld, the cuent f the t i A full ( ) We etite the tting cuent 6. A tt 6 full Neglecting the ld tht ight be cnnected, the equivlent cicuit i 607

34 Duing tting, the vltge c the t i V j θ ( ) tt t The phe ngle f the tting cuent i unknwn. Hweve, we cn nticipte tht the t ppe inductive nd θ i negtive. n the wt ce, we wuld hve θ tn tt ( ) 45 Then, vltge dp f 40 V t 40 - ( 0.) + ( 0.) 6..4 V when the t tt. The pecentge dp in vltge i 7.33%. Thi wuld cue nticeble enty diing f the light in the fhue T evee the diectin f ttin, evee the cnnectin t eithe the in winding the tting winding (but nt bth). tt 7.55 A univel t wuld be bette thn n inductin t in ptble vcuu clene becue the univel t give highe pwe t weight ti. An inductin t wuld be the bette chice f fn in heting yte becue the life f univel t i eltively ht cped t tht f n inductin t. The inductin t wuld be bette f efiget cpe, gin becue f lnge evice life. F vible peed hnd-held dill, we huld che the univel t becue it give highe pwe f given weight A ketch f teppe t c ectin with 6 tt ple nd 8 t ple i: 608

35 The ttin i 5 pe tep Mny ite deling with teppe t cn be fund n the intenet but the URL chnge ften Cped t cnventinl dc t, the dvntge f buhle dc t e lng evice life with little intnce, feed f di intefeence, bility t pete in explive envinent, nd cpbility f vey high peed. 609