# What is the phase sequence of a balanced three-phase circuit for which V an = V and V cn = V? Find V bn.

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1 Chter 1, Prblem 1. f b 400 in blnced Y-cnnected three-hse genertr, find the hse vltges, ssuming the hse sequence is: () bc (b) cb Chter 1, Slutin 1. () f b 400, then 400 n bn cn (b) Fr the cb sequence, 0 10 b b n bn 1 1+ j - 0 i.e. in the cb sequence, Hence, if 400, then n bn cn Chter 1, Prblem. b b lgs n by 0. Wht is the hse sequence f blnced three-hse circuit fr which n nd cn ? Find bn. Chter 1, Slutin. Since hse c lgs hse by 10, this is n cb sequence. bn 160 ( ) PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

2 Chter 1, Prblem. Determine the hse sequence f blnced three-hse circuit in which bn nd cn Obtin n. Chter 1, Slutin. Since bn leds cn by 10, this is n bc sequence. n 08 ( ) Chter 1, Prblem 4. three-hse system with bc sequence nd 00 feeds Y-cnnected ld with Z 40 0 Ω. Find the line currents. Chter 1, Slutin n 00 < < 0 Z x40< 0 b Y < < 150 c < < 90 Chter 1, Prblem 5. Fr Y-cnnected ld, the time-dmin exressins fr three line-t-neutrl vltges t the terminls re: v N 150 cs (ω t + º) v BN 150 cs (ω t 88º) v CN 150 cs (ω t + 15º) Write the time-dmin exressins fr the line-t-line vltges v N, v BC, nd v C. Chter 1, Slutin 5. B < 0 x150 < < 6 Thus, 60cs( ωt+ 6 ) vb Using bc sequence, v 60cs( ωt 58 ) BC vc 60cs( ωt+ 18 ) PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

3 Chter 1, Prblem 6. Fr the Y-Y circuit f Fig. 1.41, find the line currents, the line vltges, nd the ld vltges. Figure 1.41 Fr Prb Chter 1, Slutin 6. Z Y 10 + j The line currents re Z n Y b c The line vltges re b 0 0 bc c The ld vltges re N Z Y n BN bn CN cn PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

4 Chter 1, Prblem 7. Obtin the line currents in the three-hse circuit f Fig. 1.4 n the next ge. Figure 1.4 Fr Prb Chter 1, Slutin 7. This is blnced Y-Y system Z Y 6 j8 Ω Using the er-hse circuit shwn bve, j b c PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

5 Chter 1, Prblem 8. n blnced three-hse Y-Y system, the surce is n bc sequence f vltges nd n rms. The line imednce er hse is j1. Ω, while the er-hse imednce f the ld is 10 + j14 Ω. Clculte the line currents nd the ld vltges. Chter 1, Slutin 8. Cnsider the er hse equivlent circuit shwn belw. Z l n + _ Z n 100 < < 5.1 Z + Z j15. l b c < < < < Z ( j.10)(10 + j14) < b c < < < < PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

6 Chter 1, Prblem 9. blnced Y-Y fur-wire system hs hse vltges n cn bn The ld imednce er hse is 19 + j1 Ω, nd the line imednce er hse is 1 + j Ω. Slve fr the line currents nd neutrl current. Chter 1, Slutin 9. Z n + Z Y j b c s blnced system, n 0 PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

7 Chter 1, Prblem 10. Fr the circuit in Fig. 1.4, determine the current in the neutrl line. Figure 1.4 Fr Prb Chter 1, Slutin 10. Since the neutrl line is resent, we cn slve this rblem n er-hse bsis. Fr hse, Fr hse b, Fr hse c, b c n Z + 7 j bn Z + B cn Z j C The current in the neutrl line is n -( + b + c ) r - n + b + c - n ( j.654) + (-5 j8.667) + ( j16.78) n j PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

8 Chter 1, Prblem 11. n the Y- system shwn in Fig. 1.44, the surce is sitive sequence with n 10 0 nd hse imednce Z j Ω. Clculte the line vltge nd the line current. Figure 1.44 Fr Prb Chter 1, Slutin 11. < 0 (10) < 0 B b x b B B Z < 0 j < 0 x10 B < j8.07 j j PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

9 Chter 1, Prblem 1. Slve fr the line currents in the Y- circuit f Fig Tke Z Ω. Figure 1.45 Fr Prb Chter 1, Slutin 1. Cnvert the delt-ld t wye-ld nd ly er-hse nlysis Z Y Z Y Z 0 45 Ω b c PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

10 Chter 1, Prblem 1. n the blnced three-hse Y- system in Fig. 1.46, find the line current nd the verge wer delivered t the ld. Figure 1.46 Fr Prb PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

11 Chter 1, Slutin 1. Cnvert the delt ld t wye s shwn belw rms + Ω Z Y rms Ω N + Z Y Z Y rms Ω + 1 ZY Z j Ω We cnsider the single hse equivlent shwn belw. Ω rms + _ j Ω < j 0.4 S Z Y (0.4) ( j) j5 P Re(S) 744 W. PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

12 Chter 1, Prblem 14. Obtin the line currents in the three-hse circuit f Fig n the next ge Figure 1.47 Fr Prb PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

13 Chter 1, Slutin 14. We ly mesh nlysis. 1+ j Ω + Z Z - n 1 B C Z 1 + j1ω c b 1+ j Ω Fr mesh, 1+ j Ω (14 + j16) (1 + j) (1 + j1) r 1 ( 14 + j16) 1 (1 + j) (1 + j1) j j86.6 (1) Fr mesh, (1 + j) (1 + j1) + (14 + j16) 0 r ( 1+ j) 1 + (14 + j16) (1 + j1) 50 j j86.6 j17. () Fr mesh, ( 1 + j 1) 1 (1 + j1) + (6 + j6) 0 () Slving (1) t () gives j19., j16.749, j bb cc PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

14 Chter 1, Prblem 15. The circuit in Fig is excited by blnced three-hse surce with line vltge f 10. f Z l 1 + j1 Ω, Z 4 j0ω, nd Z Y 1 + j5 Ω, determine the mgnitude f the line current f the cmbined lds. Figure 1.48 Fr Prb Chter 1, Slutin 15. Cnvert the delt ld, Z, t its equivlent wye ld. Z Ye Z 8 j10 Z Z Z T Z T (1 + j5)(8 j10) Z Y Z Ye j j.047 Z + Z j1.047 We nw use the er-hse equivlent circuit. Z + Z, where ( ) PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

15 Chter 1, Prblem 16. blnced delt-cnnected ld hs hse current C () Determine the three line currents ssuming tht the circuit ertes in the sitive hse sequence. (b) Clculte the ld imednce if the line vltge is B Chter 1, Slutin 16. () 10 ( ) C - C This imlies tht B b c BC B B (b) Z B Ω Chter 1, Prblem 17. blnced delt-cnnected ld hs line current Find the hse currents B, BC, nd C. Chter 1, Slutin B < B < < 5 < 0 < < 115 BC C B < < 15 B PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

16 Chter 1, Prblem 18. f n in the netwrk f Fig. 1.49, find the ld hse currents B, BC, nd C. Figure 1.49 Fr Prb Chter 1, Slutin ( )( 0 ) B n Z 1 + j B B Z BC B C B PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

17 Chter 1, Prblem 19. Fr the - circuit f Fig. 1.50, clculte the hse nd line currents. Figure 1.50 Fr Prb Chter 1, Slutin 19. Z 0 + j The hse currents re b 17 0 B Z BC B C B The line currents re - 0 B C B b c PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

18 Chter 1, Prblem 0. Refer t the - circuit in Fig Find the line nd hse currents. ssume tht the ld imednce is Z 1 + j9 Ω er hse. Figure 1.51 Fr Prb Chter 1, Slutin 0. Z 1 + j The hse currents re 10 0 B BC B C B The line currents re B b c PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

19 Chter 1, Prblem 1. Three 0- genertrs frm delt-cnnected surce tht is cnnected t blnced delt-cnnected ld f Z 10 + j8 Ω er hse s shwn in Fig () Determine the vlue f C. (b) Wht is the vlue f b? Figure 1.5 Fr Prb Chter 1, Slutin () C (rms) 10 + j rms (b) bb BC + B BC B j j j j j rms PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

20 Chter 1, Prblem. Find the line currents, b, nd c in the three-hse netwrk f Fig. 1.5 belw. Tke Z 1 j15ω, Z Y 4 + j6 Ω, nd Z l Ω Figure 1.5 Fr Prb. 1.. Chter 1, Slutin. Cnvert the -cnnected surce t Y-cnnected surce. 08 n Cnvert the -cnnected ld t Y-cnnected ld. Z (4 + j6)(4 j5) Z Z Y (4 + j6) (4 j5) 8 + j Z 5.7 j0.15 Z n + Z n Z + Z 7.7 j b c PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

21 Chter 1, Prblem. three-hse blnced system with line vltge f 0 rms feeds delt-cnnected ld with Z 5 60 Ω. () Find the line current. (b) Determine the ttl wer sulied t the ld using tw wttmeters cnnected t the nd C lines. Chter 1, Slutin. () B B Z B (b) P P1 + P csθ 0 (0) cs kw PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

22 Chter 1, Prblem 4. blnced delt-cnnected surce hs hse vltge b nd sitive hse sequence. f this is cnnected t blnced delt-cnnected ld, find the line nd hse currents. Tke the ld imednce er hse s 60 0 Ω nd line imednce er hse s 1 + j1 Ω. Chter 1, Slutin 4. Cnvert bth the surce nd the ld t their wye equivlents. Z Z Y j10 b n We nw use er-hse nlysis. 1 + j Ω n Ω n (1 + j) + (17. + j10) b c But - 0 B B BC B C B PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

23 Chter 1, Prblem 5. n the circuit f Fig. 1.54, if b , bc , c , find the line currents. Figure 1.54 Fr Prb Chter 1, Slutin 5. Cnvert the delt-cnnected surce t n equivlent wye-cnnected surce nd cnsider the single-hse equivlent. 440 (10 0 ) Z Y where Z + j + 10 j8 1 j Y ( ) b c PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

24 Chter 1, Prblem 6. Fr the blnced circuit in Fig. 1.55, b Find the line currents, bb, nd cc. Figure 1.55 Fr Prb Chter 1, Slutin 6. Trnsfrm the surce t its wye equivlent. n Nw, use the er-hse equivlent circuit. n Z, Z 4 j bb 10 cc.55 1 PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

25 Chter 1, Prblem 7. -cnnected surce sulies wer t Y-cnnected ld in three-hse blnced system. Given tht the line imednce is + j1 Ω er hse while the ld imednce is 6 + j4 Ω er hse, find the mgnitude f the line vltge t the ld. ssume the surce hse vltge b 08 0 rms. Chter 1, Slutin 7. Since Z nd Z l re in series, we cn lum them tgether s tht ZY + j+ 6+ j4 8+ j5 P < 0 08 < 0 ZY (8+ j5) 08(0.866 j0.5)(6 + j4) (6 + j4) j4.54 (8+ j5) Chter 1, Prblem 8. The line-t-line vltges in Y-ld hve mgnitude f 440 nd re in the sitive sequence t 60 Hz. f the lds re blnced with Z 1 Z Z 5 0, find ll line currents nd hse vltges. Chter 1, Slutin r P 440/ b Fr reference, let N 54 0 which leds t BN nd CN The line currents re fund s fllws, P N /Z Y 54/ This leds t, b nd c PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

26 Chter 1, Prblem 9. blnced three-hse Y- system hs n 10 0 rms nd Z 51+ j45ω. f the line imednce er hse is j1. Ω, find the ttl cmlex wer delivered t the ld. Chter 1, Slutin 9. We cn relce the delt ld with wye ld, Z Y Z / 17+j15Ω. The er-hse equivlent circuit is shwn belw. Z l n + _ Z Y n < Z + Z 17 + j j1. Y l S S Z + j + j Y (5.0475) (17 15) k PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

27 Chter 1, Prblem 0. n Fig. 1.56, the rms vlue f the line vltge is 08. Find the verge wer delivered t the ld. Figure 1.56 Fr Prb Chter 1, Slutin 0. Since this blnced system, we cn relce it by er-hse equivlent, s shwn belw. - + Z S S, * Z (08) S * Z 0 45 P S cs θ 1.0 kw k PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

28 Chter 1, Prblem 1. blnced delt-cnnected ld is sulied by 60-Hz three-hse surce with line vltge f 40. Ech ld hse drws 6 kw t lgging wer fctr f 0.8. Find: () the ld imednce er hse (b) the line current (c) the vlue f ccitnce needed t be cnnected in rllel with ech ld hse t minimize the current frm the surce Chter 1, Slutin 1. () PP P 6,000, csθ 0.8, S 6 / k csθ Q S P sin θ 4.5 kr S S (6 + j4.5) 18 + j1.5 k Fr delt-cnnected ld, 40 (rms). But S * (40) Z, Z j4. 608Ω * P Z S (18 + j1.5) x10 (b) P 6000 cs x40x0.8 θ (c ) We find C t bring the wer fctr t unity Q c Q Qc k C ω rms πx60x µ F PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

29 Chter 1, Prblem. blnced Y-ld is cnnected t 60-Hz three-hse surce with b The ld hs f 0.5 lgging nd ech hse drws 5 kw. () Determine the ld imednce Z Y. (b) Find, b, nd c. Chter 1, Slutin. 40 () b n < f 0.5 csθ θ 60 P 5 P Scsθ S 10 k csθ 0.5 Q S sinθ 10sin S 5+ j8.66 k But * SP Z * j Z S (5 + j8.66) x10 Z j1.66 Ω n < 0 (b) 7.17 < 90 ZY j1.667 b < < 10 < < 0 c PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

30 Chter 1, Prblem. three-hse surce delivers 4800 t wye-cnnected ld with hse vltge f 08 nd wer fctr f 0.9 lgging. Clculte the surce line current nd the surce line vltge. Chter 1, Slutin. S θ S S Fr Y-cnnected ld,, S S 4800 ()(08) Chter 1, Prblem 4. blnced wye-cnnected ld with hse imednce f 10 j16 Ω is cnnected t blnced three-hse genertr with line vltge f 0. Determine the line current nd the cmlex wer bsrbed by the ld. Chter 1, Slutin Z (10 j16) Y 6.7 S θ S 159. j175 Chter 1, Prblem 5. PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

31 Three equl imednces, 60 + j0 Ω ech, re delt-cnnected t 0- rms, three-hse circuit. nther three equl imednces, 40 + j10 Ω ech, re wyecnnected crss the sme circuit t the sme ints. Determine: () the line current (b) the ttl cmlex wer sulied t the tw lds (c) the wer fctr f the tw lds cmbined Chter 1, Slutin 5. () This is blnced three-hse system nd we cn use er hse equivlent circuit. The delt-cnnected ld is cnverted t its wye-cnnected equivlent '' 1 Z y Z (60 + j0) / 0 + j Z y Z y '' Z y Z' y // Z y (40 + j10) //(0 + j10) j j5.5 j5.5 (b) S * s.61+ j1.68 k (c ) f P/S Chter 1, Prblem 6. PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

32 400-, three-hse trnsmissin line hs n imednce f 4 + j10 Ω er hse. f it sulies ld f 1 M t 0.75 wer fctr (lgging), find: () the cmlex wer (b) the wer lss in the line (c) the vltge t the sending end Chter 1, Slutin 6. () S 1 [ sin(cs ) ] j M 6 * * S ( j0.6614) x10 (b) S j5. 49 x400 P Rl (79.6) (4) 5.19 kw (c) s + (4 + j) j0.1 k k Chter 1, Prblem 7. PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

33 The ttl wer mesured in three-hse system feeding blnced wye-cnnected ld is 1 kw t wer fctr f 0.6 leding. f the line vltge is 08, clculte the line current nd the ld imednce Z Y. Chter 1, Slutin 7. P 1 S 0 f 0.6 S S θ 0 θ 1 j16 k But S θ S Z Fr Y-cnnected ld,. Z S (1 j16) 10 ()(55.51) Z 1.98 j1. 71 Ω Chter 1, Prblem 8. PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

34 Given the circuit in Fig belw, find the ttl cmlex wer bsrbed by the ld. Figure 1.57 Fr Prb Chter 1, Slutin 8. s blnced three-hse system, we cn use the er-hse equivlent shwn belw (1 + j) + (9 + j1) 10 + j (110) S Z Y (9 + j1) ( ) The cmlex wer is (110) S S (9 + j1) 96 S j75.81 Chter 1, Prblem 9. PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

35 Find the rel wer bsrbed by the ld in Fig Figure 1.58 Fr Prb Chter 1, Slutin 9. Cnsider the system shwn belw. 5 Ω c b 1 5 Ω 8 Ω B -j6 Ω 10 Ω 4 Ω j Ω C 5 Ω Fr mesh 1, Fr mesh, Fr mesh, 100 (18 j6) (1) 1 5 (8 j6) () 0 -(8 j6) () ( j) T eliminte, strt by multilying (1) by, 00 (6 j1) 1 10 (16 j1) (4) Subtrcting () frm (4), PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

36 00 (44 j18) (5) 1 (8 j15) Multilying () by 5 4, (6) 1 5 dding (1) nd (6), 87.5 j1.65 (16.75 j6) (10.5 j6 (7) n mtrix frm, (5) nd (7) becme j j j6 1 ) j j j6.5, j95., 110. j j j We btin frm (6), (-.5 j4.) + (1.104 j1.059) + ( j8.71 The verge wer bsrbed by the 8-Ω resistr is P1 1 (8) j.551 (8) The verge wer bsrbed by the 4-Ω resistr is P (4) (6.8571) (4) W The verge wer bsrbed by the 10-Ω resistr is P (10) j.019 (10) Thus, the ttl rel wer bsrbed by the ld is P P + P W 1 P W j.47) 78.1 W PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

37 Chter 1, Prblem 40. Fr the three-hse circuit in Fig. 1.59, find the verge wer bsrbed by the delt-cnnected ld with Z 1+ j4ω. Figure 1.59 Fr Prb Chter 1, Slutin 40. Trnsfrm the delt-cnnected ld t its wye equivlent. Z Z Y 7 + j8 Using the er-hse equivlent circuit bve, (1 + j0.5) + (7 + j8) Fr wye-cnnected ld, S Z ()(8.567) (7 + j8) Re( S) ()(8.567) (7) kw P PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

38 Chter 1, Prblem 41. blnced delt-cnnected ld drws 5 kw t wer fctr f 0.8 lgging. f the three-hse system hs n effective line vltge f 400, find the line current. Chter 1, Slutin 41. P 5 kw S 6.5 k f 0.8 But S S Chter 1, Prblem 4. blnced three-hse genertr delivers 7. kw t wye-cnnected ld with imednce 0 j40 Ω er hse. Find the line current nd the line vltge. Chter 1, Slutin 4. The ld determines the wer fctr. 40 tn θ 1. θ f csθ 0.6 (leding) 7. S 7. j (0.8) 7. j9.6 k 0.6 But S Z S Z (7. j9.6) 10 ()(0 j40) S (8.944) PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

39 Chter 1, Prblem 4. Refer t Fig Obtin the cmlex wer bsrbed by the cmbined lds. Chter 1, Slutin 4. S Z, fr Y-cnnected lds S ( )(1.66) (7.81 j.047) S 4.7 j1.145 k Chter 1, Prblem 44. three-hse line hs n imednce f 1 + j Ω er hse. The line feeds blnced delt-cnnected ld, which bsrbs ttl cmlex wer f 1 + j5 k. f the line vltge t the ld end hs mgnitude f 40, clculte the mgnitude f the line vltge t the surce end nd the surce wer fctr. Chter 1, Slutin 44. Fr -cnnected ld,, t the surce, S S (1 + 5 ) 10 (40) + Z ' ' (1.7)(1 + ' j9.819 ' ls, t the surce, ' ' S * j) ' S ( j9.819)(1.7) θ tn f csθ PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

40 Chter 1, Prblem 45. blnced wye-cnnected ld is cnnected t the genertr by blnced trnsmissin line with n imednce f j Ω er hse. f the ld is rted t 450 kw, wer fctr lgging, 440- line vltge, find the line vltge t the genertr. Chter 1, Slutin 45. S θ - θ S P , S 65.6 k f (65.6) - θ t the surce, (0.5 + j) (84-45 )( ) j k Nte, this is nt nrmlly exerienced in rctice since trnsfrmers re use which cn significntly reduce line lsses. PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

41 Chter 1, Prblem 46. three-hse ld cnsists f three 100- Ω resistrs tht cn be wye- r delt-cnnected. Determine which cnnectin will bsrb the mst verge wer frm three-hse surce with line vltge f 110. ssume zer line imednce. Chter 1, Slutin 46. Fr the wye-cnnected ld,, Z * S * Z Z S Z * ( 110) W Fr the delt-cnnected ld,,, Z * S * Z Z ()(110) S 6 W 100 * * This shws tht the delt-cnnected ld will deliver three times mre verge wer thn the wye-cnnected ld. This is ls evident frm Y Z Z. PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

42 Chter 1, Prblem 47. The fllwing three rllel-cnnected three-hse lds re fed by blnced threehse surce: d 1: 50 k, 0.8 f lgging d : 00 k, 0.95 f leding d : 450 k, unity f f the line vltge is 1.8 k, clculte the line current nd the wer fctr f the surce. ssume tht the line imednce is zer. Chter 1, Slutin (lgging) θ cs (0.8) j150 k f -1 S (leding) θ cs (0.95) j9.65 k f -1 S -1 f 1.0 θ cs (1) 0 S 450 k S T S1 + S + S 95 + j k S T ( ) 9.19 rms f csθ cs(.45 ) (lgging) PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

43 Chter 1, Prblem 48. blnced, sitive-sequence wye-cnnected surce hs n 40 0 rms nd sulies n unblnced delt-cnnected ld vi trnsmissin line with imednce + j Ω er hse. () Clculte the line currents if Z B 40 + j15 Ω, Z BC 60 Ω, Z C 18 j1ω. (b) Find the cmlex wer sulied by the surce. Chter 1, Slutin 48. () We first cnvert the delt ld t its equivlent wye ld, s shwn belw. 18-j1 Ω 40+j15 Ω Z Z B Z C C B C B 60 Ω Z (40 + j15)( j j1) j1.9 60(40 + j15). Z B j j Z C 60( j1) j 8.99 j6.0 PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

44 The system becmes tht shwn belw. +j + 40<0 Z Z B Z C 40<10 40< j c b B C +j We ly K t the ls. Fr mesh 1, (Z l + Z + Z B ) ( Z B + Z l ) 0 r ( j 11.1) 1 (.5 + j10.105) 60 + j07.85 (1) Fr mesh, ( Z B + Z l ) + (Z l + Z B + Z C ) 0 r (.5 + j10.105) 1 + (.51+ j6.775) j () Slving (1) nd () gives 1.75 j5.8, j , 1 bb cc (b) S ( S 40 0 )( ) ( S b )( ) ( S b )( ) S + S b + S c j0.55 k k PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

45 Chter 1, Prblem 49. Ech hse ld cnsists f 0- Ω resistr nd 10- Ω inductive rectnce. With line vltge f 0 rms, clculte the verge wer tken by the ld if: () the three-hse lds re delt-cnnected (b) the lds re wye-cnnected Chter 1, Slutin 49. () Fr the delt-cnnected ld, Z 0 + j10ω, 0 (rms), S Z * x (0 j10) r 5.808kW j k (b) Fr the wye-cnnected ld, Z 0 + j10ω, /, S x k r kw * Z (0 j10) Chter 1, Prblem 50. blnced three-hse surce with 40 rms is sulying 8 k t 0.6 wer fctr lgging t tw wye-cnnected rllel lds. f ne ld drws kw t unity wer fctr, clculte the imednce er hse f the secnd ld. Chter 1, Slutin 50. S S 1 + S 8(0.6 + j0.8) j6.4 k, S 1 k Hence, S S S But Z j * Z 6.4 k. Z S, S * * * 40 Z Ω j S (1.8 + j6.4) x10 PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

46 Chter 1, Prblem 51. Cnsider the - system shwn in Fig Tke Z i 8 + j6 Ω, Z 4. j. Ω, Z 10 + j0ω. () Find the hse current B, BC, C. (b) Clculte line currents, bb, nd cc Z Z 1 b + c C Z B Figure 1.60 Fr Prb Chter 1, Slutin 51. This is n unblnced system. 40 < 0 40 < 0 B 19.-j14.4 Z 8+ j j BC j7.09 Z C 1 j0.78 Z 10 t nde, (19. j14.4) ( 1 j0.78) 1. + j j6.8 B C ( j7.08) (19. j14.4) j41.48 bb b BC B cc c C BC j41.48 ( 1 j0.78) ( j7.08) 0.76 j j47.86 PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

47 Chter 1, Prblem 5. fur-wire wye-wye circuit hs n 10 10, bn 10 0 cn f the imednces re Z N 0 60, Z BN 0 0 Z cn 40 0 Ω find the current in the neutrl line. Chter 1, Slutin 5. Since the neutrl line is resent, we cn slve this rblem n er-hse bsis. n Z 0 60 b c N bn Z 0 0 BN cn Z 40 0 CN Thus, n b c - n n ( + j5.196) + (4) + (-.598 j1.5) - n j n PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

48 Chter 1, Prblem 5. n the Y-Y system shwn in Fig. 1.61, lds cnnected t the surce re unblnced. () Clculte, b, nd c. (b) Find the ttl wer delivered t the ld. Tke 40 rms. Figure 1.61 Fr Prb Chter 1, Slutin 5. lying mesh nlysis s shwn belw, we get. + _ P 0 100Ω 1 P 10 P 10 80Ω + + b 60 Ω c PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

49 40 < < 0 + x j07.84 (1) < < j415.7 () n mtrix frm, (1) nd () becme j j415.7 Using MTB, we get, >> Z[160,-60;-60,140] Z >> [( i);-415.7i] 1.0e+00 * i i >> inv(z)* i i j0.07 nd j b j c S Z x W (.69) b b b (.454) c c c (.0957) S Z x W S Z x W P P + P b + P c.05 kw PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

50 Chter 1, Prblem 54. blnced three-hse Y-surce with P 10 rms drives Y-cnnected three-hse ld with hse imednce Z 80 Ω, Z B 60 + j90ω, nd Z C j80 Ω. Clculte the line currents nd ttl cmlex wer delivered t the ld. ssume tht the neutrls re cnnected. Chter 1, Slutin 54. Cnsider the ld s shwn belw. N N b B C c 10 < b j c 10 < 0.65 < 90 j80 S 10x * * 10 S b b 6.15 j9. Z 60 j90 + S c * c * b 10 Z j80 j551.5 S S + S + S j b c PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

51 Chter 1, Prblem 55. three-hse suly, with the line vltge 40 rms sitively hsed, hs n unblnced delt-cnnected ld s shwn in Fig Find the hse currents nd the ttl cmlex wer. Figure 1.6 Fr Prb Chter 1, Slutin 55. The hse currents re: B 40/j C / BC / The cmlex wer in ech hse is: S Z (9.6) j5 j04 B B B S Z < C C C (6) S Z < + j The ttl cmlex wer is, BC BC BC (8) S S + S + S j64.10+j.64 k B C BC PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

52 Chter 1, Prblem 56. Refer t the unblnced circuit f Fig Clculte: () the line currents (b) the rel wer bsrbed by the ld (c) the ttl cmlex wer sulied by the surce Figure 1.6 Fr Prb Chter 1, Slutin 56. () Cnsider the circuit belw b + 1 B j10 Ω -j5 Ω Ω c C Fr mesh 1, j10( 1 ) 0 (440)(1.5 + j0.866) (1) j10 Fr mesh, ( ) 0 (440)( j1.7) j8.1 () 0 PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

53 Fr mesh, j10( 1) + 0( ) j5 Substituting (1) nd () int the equtin fr mesh gives, (440)( j0.866) () j5 Frm (1), j Frm (), 1 j j b j c (b) S S (j10) B 1 (0) BC j58.08 k 9.04 k S C (-j5) (15.4) (-j5) -j k S S + S + S B BC C 9.04 j58.08 k Rel wer bsrbed 9.04 kw (c) Ttl cmlex sulied by the surce is S 9.04 j58.08 k PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

54 Chter 1, Prblem 57. Determine the line currents fr the three-hse circuit f Fig et 110 0, b , c Figure 1.64 Fr Prb Chter 1, Slutin 57. We ly mesh nlysis t the circuit shwn belw. c j 0Ω b + + b 80 + j 50Ω 60 j40ω c ( j80) 1 (0 + j0) b j95.6 (1) ( 0 + j0) 1 + (80 j10) b c j190.5 () j0.6084, j Slving (1) nd () gives , 1 b 0.58 j c PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

55 Chter 1, Prblem 58. Slve Prb using PSice. Chter 1, Slutin 58. The schemtic is shwn belw. PRNT is inserted in the neutrl line t mesure the current thrugh the line. n the C Swee bx, we select Ttl Ptss 1, Strt Freq , nd End Freq fter simultin, the utut file includes FREQ M(_PRNT4) P(_PRNT4) 1.59 E E E+01 i.e. n PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

56 Chter 1, Prblem 59. The surce in Fig is blnced nd exhibits sitive hse sequence. f f 60 Hz, use PSice t find N, BN, nd CN. Figure 1.65 Fr Prb PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

57 Chter 1, Slutin 59. The schemtic is shwn belw. n the C Swee bx, we set Ttl Pts 1, Strt Freq 60, nd End Freq 60. fter simultin, we btin n utut file which includes FREQ M(1) P(1) E E E+01 FREQ M() P() E E E+01 FREQ M() P() E E E+01 i.e. N , BN , CN PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

58 Chter 1, Prblem 60. Use PSice t determine in the single-hse, three-wire circuit f Fig et Z 1 15 j10ω, Z 0 + j0 Ω, nd Z 1 + j5 Ω. Figure 1.66 Fr Prb PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

59 Chter 1, Slutin 60. The schemtic is shwn belw. PRNT is inserted t give. We select Ttl Pts 1, Strt Freq 0.159, nd End Freq in the C Swee bx. Un simultin, the utut file includes FREQ M(_PRNT4) P(_PRNT4) 1.59 E E E+0 frm which, PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

60 Chter 1, Prblem 61. Given the circuit in Fig. 1.67, use PSice t determine currents nd vltge BN. Figure 1.67 Fr Prb PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

61 Chter 1, Slutin 61. The schemtic is shwn belw. Pseudcmnents PRNT nd PRNT re inserted t mesure nd BN. n the C Swee bx, we set Ttl Pts 1, Strt Freq 0.159, nd End Freq Once the circuit is simulted, we get n utut file which includes frm which FREQ M() P() 1.59 E E E+0 FREQ M(_PRNT) P(_PRNT) 1.59 E E E , BN PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

62 Chter 1, Prblem 6. The circuit in Fig ertes t 60 Hz. Use PSice t find the surce current b nd the line current bb. Figure 1.68 Fr Prb PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

63 Chter 1, Slutin 6. Becuse f the delt-cnnected surce invlved, we fllw Exmle 1.1. n the C Swee bx, we tye Ttl Pts 1, Strt Freq 60, nd End Freq 60. fter simultin, the utut file includes FREQ M(_PRNT) P(_PRNT) E E E+01 FREQ M(_PRNT1) P(_PRNT1) E E E+0 Frm which b 7.x , bb PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

64 Chter 1, Prblem 6. Use PSice t find currents nd C in the unblnced three-hse system shwn in Fig et Z + j, Z j0 Ω, Z 50 j0ω, Z 5 Ω Figure 1.69 Fr Prb PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

65 Chter 1, Slutin 6. 1 et ω 1 s tht X/ ω 0 H, nd C 0.0 F ωx The schemtic is shwn belw. When the file is sved nd run, we btin n utut file which includes the fllwing:. FREQ M(_PRNT1)P(_PRNT1) 1.59E E E+0 FREQ M(_PRNT)P(_PRNT) 1.59E E E+0 Frm the utut file, the required currents re: , C Chter 1, Prblem 64. PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

66 Fr the circuit in Fig. 1.58, use PSice t find the line currents nd the hse currents. Chter 1, Slutin 64. We fllw Exmle 1.1. n the C Swee bx we tye Ttl Pts 1, Strt Freq 0.159, nd End Freq fter simultin the utut file includes frm this we btin FREQ M(_PRNT1) P(_PRNT1) 1.59 E E E+01 FREQ M(_PRNT) P(_PRNT) 1.59 E E E+0 FREQ M(_PRNT) P(_PRNT) 1.59 E E E+00 FREQ M(_PRNT4) P(_PRNT4) 1.59 E E E+01 FREQ M(_PRNT5) P(_PRNT5) 1.59 E E E+01 FREQ M(_PRNT6) P(_PRNT6) 1.59 E E E , bb , cc B , C , BC PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

67 PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

68 Chter 1, Prblem 65. blnced three-hse circuit is shwn in Fig n the next ge. Use PSice t find the line currents, bb, nd cc. Figure 1.70 Fr Prb Chter 1, Slutin 65. Due t the delt-cnnected surce, we fllw Exmle 1.1. We tye Ttl Pts 1, Strt Freq 0.159, nd End Freq The schemtic is shwn belw. fter it is sved nd simulted, we btin n utut file which includes FREQ M(_PRNT1) P(_PRNT1) 1.59E E E+00 FREQ M(_PRNT) P(_PRNT) 1.59E E E+0 FREQ M(_PRNT) P(_PRNT) 1.59E E E+0 Thus, , bb , cc PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

69 Since this is blnced circuit, we cn erfrm quick check. The ld resistnce is lrge cmred t the line nd surce imednces s we will ignre them (lthugh it wuld nt be difficult t include them). Cnverting the surces t Y cnfigurtin we get: n rms nd Z Y 10 j Nw we cn clculte, ( )/( ) Clerly, we hve gd rximtin which is very clse t wht we relly hve. PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

70 Chter 1, Prblem 66. three-hse, fur-wire system erting with 08- line vltge is shwn in Fig The surce vltges re blnced. The wer bsrbed by the resistive wyecnnected ld is mesured by the three-wttmeter methd. Clculte: () the vltge t neutrl (b) the currents 1,,, nd n (c) the redings f the wttmeters (d) the ttl wer bsrbed by the ld Figure 1.71 Fr Prb PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

71 Chter 1, Slutin () 10 (b) Becuse the ld is unblnced, we hve n unblnced three-hse system. ssuming n bc sequence, N () j N j j () j Hence, 1.5,,, N (c) P R (.5) (48) W R () (40) 60 W P R () (60) 40 W P (d) P P + P + P 900 W T 1 PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

72 Chter 1, Prblem 67. * s shwn in Fig. 1.7, three-hse fur-wire line with hse vltge f 10 rms nd sitive hse sequence sulies blnced mtr ld t 60 k t 0.85 f lgging. The mtr ld is cnnected t the three min lines mrked, b, nd c. n dditin, incndescent lms (unity f) re cnnected s fllws: 4 kw frm line c t the neutrl, 15 kw frm line b t the neutrl, nd 9 kw frm line c t the neutrl. () f three wttmeters re rrnged t mesure the wer in ech line, clculte the reding f ech meter. (b) Find the mgnitude f the current in the neutrl line. Figure 1.7 Fr Prb * n sterisk indictes chllenging rblem. PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

73 Chter 1, Slutin 67. () The wer t the mtr is P T Scsθ (60)(0.85) 1 kw The mtr wer er hse is 1 P PT 7.67 kw Hence, the wttmeter redings re s fllws: kw W W b kw W c kw (b) The mtr ld is blnced s tht N 0. Fr the lighting lds, 4, ,000 b ,000 c f we let b c Then, N - N b 00 + (15) j - N 100 j N c + (75) j PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

74 Chter 1, Prblem 68. Meter redings fr three-hse wye-cnnected lterntr sulying wer t mtr indicte tht the line vltges re 0, the line currents re 8.4, nd the ttl line wer is 4.5 kw. Find: () the ld in (b) the ld f (c) the hse current (d) the hse vltge Chter 1, Slutin 68. () S (0)(8.4) 4801 (b) P Scsθ f csθ P S 4500 f (c) Fr wye-cnnected ld, (d) PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

75 Chter 1, Prblem 69. certin stre cntins three blnced three-hse lds. The three lds re: d 1: 16 k t 0.85 f lgging d : 1 k t 0.6 f lgging d : 8 kw t unity f The line vltge t the ld is 08 rms t 60 Hz, nd the line imednce is j0.8 Ω. Determine the line current nd the cmlex wer delivered t the lds. Chter 1, Slutin 69. Fr ld 1, S1 S1csθ 1+ js1sinθ1 f 0.85 csθ1 θ S j8.4 k Fr ld, S 1x0.6 + j1x j9.6 k Fr ld, S 8+ j0 k S S1 + S + S j j18.0 k But S P P * P with P * S (8800 j1800) P + P x j Nte, this is reltive t f we ssume sitive hse rttin nd b 08 0, then n which yields , b , c PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

76 Chter 1, Prblem 70. The tw-wttmeter methd gives P W nd P 400 W fr three-hse mtr running n 40- line. ssume tht the mtr ld is wye-cnnected nd tht it drws line current f 6. Clculte the f f the mtr nd its hse imednce. Chter 1, Slutin 70. P T P1 + P Q 1 T P P QT tn θ - θ -6.4 P 800 T f csθ (leding) Z Z Ω PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

77 Chter 1, Prblem 71. n Fig. 1.7, tw wttmeters re rerly cnnected t the unblnced ld sulied by blnced surce such tht b 08 0 with sitive hse sequence. () Determine the reding f ech wttmeter. (b) Clculte the ttl rent wer bsrbed by the ld. Figure 1.7 Fr Prb PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

78 Chter 1, Slutin 71. () f 08 0, 08-10, 08 10, B BC C b b Z 0 b bc bc Z BC c Z 1.6 C c cc cc B C j C BC P1 b cs( θ b θ ) (08)(0.171) cs( ) P W P cb cc cs( θ cb θ ) cc But cb - bc P (08)(0.64) cs( ) 4808 W (b) PT P1 + P W QT (P P1 ) R S P + jq j840.5 T T T S S 85 T T PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

79 Chter 1, Prblem 7. f wttmeters W 1 nd W re rerly cnnected resectively between lines nd b nd lines b nd c t mesure the wer bsrbed by the delt-cnnected ld in Fig. 1.44, redict their redings. Chter 1, Slutin 7. Frm Prblem 1.11, 0 10 nd P 1 B (0)(0) cs( ) 44 W CB cc BC 0-60 P (0)(0) cs( ) - 57 W PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

80 Chter 1, Prblem 7. Fr the circuit dislyed in Fig. 1.74, find the wttmeter redings. Figure 1.74 Fr Prb PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

81 Chter 1, Slutin 7. Cnsider the circuit s shwn belw Z Z Z b c Z 10 + j b c Z c c b c * P [ ] Re[ (40-60 )( ] Re ) 60 W * P [ ] Re[ (40-10 )( ] Re ) W PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

82 Chter 1, Prblem 74. Predict the wttmeter redings fr the circuit in Fig Figure 1.75 Fr Prb PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

83 Chter 1, Slutin 74. Cnsider the circuit shwn belw. Z 60 j0 Ω Z Z Fr mesh 1, Fr mesh, 08 Z Z Z + Z 1 n mtrix frm, 08 Z Z -Z Z 1 Z, 1 (08)(1.5 + j0.866) Z, (08)(j1.7) Z 1 1 (08)(1.5 + j0.866) ()(60 j0) (08)( j1.7) ()(60 j0) * P [ ] Re[ (08)( ] Re ) [ (- ) ] Re[ (08-60 ))( ] * P Re ) W W PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

84 Chter 1, Prblem 75. mn hs bdy resistnce f 600 Ω. Hw much current flws thrugh his ungrunded bdy: () when he tuches the terminls f 1- utbttery? (b) when he sticks his finger int 10- light scket? Chter 1, Slutin () R (b) R m 00 m Chter 1, Prblem 76. Shw tht the R lsses will be higher fr 10- lince thn fr 40- lince if bth hve the sme wer rting. Chter 1, Slutin 76. f bth linces hve the sme wer rting, P, P s Fr the 10- lince, Fr the 40- lince, Pwer lss P R R 10 P R 40 P P. 40 fr the10- lince fr the 40- lince 1 1 Since >, the lsses in the 10- lince re higher PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

85 Chter 1, Prblem 77. three-hse genertr sulied.6 k t wer fctr f 0.85 lgging. f 500 W re delivered t the ld nd line lsses re 80 W er hse, wht re the lsses in the genertr? Chter 1, Slutin 77. P g P P P, f T ld line But P T 600 csθ 600 f 060 P g ()(80) 0 W Chter 1, Prblem 78. three-hse 440-, 51-kW, 60-k inductive ld ertes t 60 Hz nd is wyecnnected. t is desired t crrect the wer fctr t 0.95 lgging. Wht vlue f ccitr shuld be lced in rllel with ech ld imednce? Chter 1, Slutin csθ θ S sin θ (60)(0.568) 1.61 kr Q1 1 1 P P1 51 kw csθ 0.95 θ P S 5.68 k csθ Q S sin θ kr c Q1 Q kr Q Fr ech ld, Q Q 1 Q c1 C ω c c 4.95 kr 4950 (π)(60)(440) 67.8 µ F PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

86 Chter 1, Prblem 79. blnced three-hse genertr hs n bc hse sequence with hse vltge n The genertr feeds n inductin mtr which my be reresented by blnced Y-cnnected ld with n imednce f 1 + j5 Ω er hse. Find the line currents nd the ld vltges. ssume line imednce f Ω er hse. Chter 1, Slutin 79. Cnsider the er-hse equivlent circuit belw. Ω n + Z Y 1 + j5 Ω n N n Z + Y j5 Thus, b c N Z ( )(1.6 ) Y.97 Thus, -10 BN N CN N PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

87 Chter 1, Prblem 80. blnced three-hse surce furnishes wer t the fllwing three lds: d 1: 6 k t 0.8 f lgging d : unknwn d : 8 kw t f leding f the line current is 84.6 rms, the line vltge t the ld is 08 rms, nd the cmbined ld hs 0.8 f lgging, determine the unknwn ld. Chter 1, Slutin S S1 + S + S 6[0.8 + j sin(cs 0.8)] + S + 8( j0.7071) S j.1+ S k (1) But S θ (08)(84.6)(0.8 + j0.6) j18.87 k () Frm (1) nd (), S j k Thus, the unknwn ld is 4.76 k t f lgging. PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

88 Chter 1, Prblem 81. rfessinl center is sulied by blnced three-hse surce. The center hs fur blnced three-hse lds s fllws: d 1: 150 k t 0.8 f leding d : 100 kw t unity f d : 00 k t 0.6 f lgging d 4: 80 kw nd 95 kr (inductive) f the line imednce is j0.05 Ω er hse nd the line vltge t the lds is 480, find the mgnitude f the line vltge t the surce. Chter 1, Slutin 81. f 0.8 (leding) θ S k 1 f 1.0 θ 0 S k f 0.6 (lgging) θ 5. 1 S k S j95 k S S1 + S + S + S 4 S 40 + j k S S Fr the line, S Z ()(54.7) (0.0 + j0.05) S j44.18 k t the surce, S T S + S j09. S k T T S T PROPRETRY MTER. 007 The McGrw-Hill Cmnies, nc. ll rights reserved. N rt ermitted by McGrw-Hill fr their individul curse rertin. f yu re student using this Mnul,

DIT, Kevin St. lectric Circuit Thery DT87/ Mesh Anlysis Summry In this sectin we use the frmt pprch fr slving circuit prblems using mesh nlysis. This technique genertes set f equtins, which cn be slved

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