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


 Berniece Hodges
 3 years ago
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1 Chter 1, Prblem 1. f b 400 in blnced Ycnnected threehse 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 threehse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
2 Chter 1, Prblem. Determine the hse sequence f blnced threehse 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. threehse system with bc sequence nd 00 feeds Ycnnected 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 Ycnnected ld, the timedmin exressins fr three linetneutrl 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 timedmin exressins fr the linetline 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
3 Chter 1, Prblem 6. Fr the YY 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
4 Chter 1, Prblem 7. Obtin the line currents in the threehse circuit f Fig. 1.4 n the next ge. Figure 1.4 Fr Prb Chter 1, Slutin 7. This is blnced YY system Z Y 6 j8 Ω Using the erhse circuit shwn bve, j b c PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
5 Chter 1, Prblem 8. n blnced threehse YY system, the surce is n bc sequence f vltges nd n rms. The line imednce er hse is j1. Ω, while the erhse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
6 Chter 1, Prblem 9. blnced YY furwire 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 erhse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 deltld t wyeld nd ly erhse nlysis Z Y Z Y Z 0 45 Ω b c PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
10 Chter 1, Prblem 1. n the blnced threehse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
12 Chter 1, Prblem 14. Obtin the line currents in the threehse circuit f Fig n the next ge Figure 1.47 Fr Prb PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 threehse 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 erhse equivlent circuit. Z + Z, where ( ) PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
15 Chter 1, Prblem 16. blnced deltcnnected 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 deltcnnected 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
19 Chter 1, Prblem 1. Three 0 genertrs frm deltcnnected surce tht is cnnected t blnced deltcnnected 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 threehse 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 Ycnnected surce. 08 n Cnvert the cnnected ld t Ycnnected 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
21 Chter 1, Prblem. threehse blnced system with line vltge f 0 rms feeds deltcnnected 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
22 Chter 1, Prblem 4. blnced deltcnnected surce hs hse vltge b nd sitive hse sequence. f this is cnnected t blnced deltcnnected 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 erhse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 deltcnnected surce t n equivlent wyecnnected surce nd cnsider the singlehse equivlent. 440 (10 0 ) Z Y where Z + j + 10 j8 1 j Y ( ) b c PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 erhse equivlent circuit. n Z, Z 4 j bb 10 cc.55 1 PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
25 Chter 1, Prblem 7. cnnected surce sulies wer t Ycnnected ld in threehse 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 linetline vltges in Yld 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
26 Chter 1, Prblem 9. blnced threehse 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 erhse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 erhse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
28 Chter 1, Prblem 1. blnced deltcnnected ld is sulied by 60Hz threehse 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 deltcnnected 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
29 Chter 1, Prblem. blnced Yld is cnnected t 60Hz threehse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
30 Chter 1, Prblem. threehse surce delivers 4800 t wyecnnected 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 Ycnnected ld,, S S 4800 ()(08) Chter 1, Prblem 4. blnced wyecnnected ld with hse imednce f 10 j16 Ω is cnnected t blnced threehse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
31 Three equl imednces, 60 + j0 Ω ech, re deltcnnected t 0 rms, threehse 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 threehse system nd we cn use er hse equivlent circuit. The deltcnnected ld is cnverted t its wyecnnected 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
32 400, threehse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
33 The ttl wer mesured in threehse system feeding blnced wyecnnected 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 Ycnnected ld,. Z S (1 j16) 10 ()(55.51) Z 1.98 j1. 71 Ω Chter 1, Prblem 8. PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 threehse system, we cn use the erhse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 8Ω resistr is P1 1 (8) j.551 (8) The verge wer bsrbed by the 4Ω resistr is P (4) (6.8571) (4) W The verge wer bsrbed by the 10Ω 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
37 Chter 1, Prblem 40. Fr the threehse circuit in Fig. 1.59, find the verge wer bsrbed by the deltcnnected ld with Z 1+ j4ω. Figure 1.59 Fr Prb Chter 1, Slutin 40. Trnsfrm the deltcnnected ld t its wye equivlent. Z Z Y 7 + j8 Using the erhse equivlent circuit bve, (1 + j0.5) + (7 + j8) Fr wyecnnected ld, S Z ()(8.567) (7 + j8) Re( S) ()(8.567) (7) kw P PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
38 Chter 1, Prblem 41. blnced deltcnnected ld drws 5 kw t wer fctr f 0.8 lgging. f the threehse 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 threehse genertr delivers 7. kw t wyecnnected 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 Ycnnected lds S ( )(1.66) (7.81 j.047) S 4.7 j1.145 k Chter 1, Prblem 44. threehse line hs n imednce f 1 + j Ω er hse. The line feeds blnced deltcnnected 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
40 Chter 1, Prblem 45. blnced wyecnnected 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) (8445 )( ) j k Nte, this is nt nrmlly exerienced in rctice since trnsfrmers re use which cn significntly reduce line lsses. PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
41 Chter 1, Prblem 46. threehse ld cnsists f three 100 Ω resistrs tht cn be wye r deltcnnected. Determine which cnnectin will bsrb the mst verge wer frm threehse surce with line vltge f 110. ssume zer line imednce. Chter 1, Slutin 46. Fr the wyecnnected ld,, Z * S * Z Z S Z * ( 110) W Fr the deltcnnected ld,,, Z * S * Z Z ()(110) S 6 W 100 * * This shws tht the deltcnnected ld will deliver three times mre verge wer thn the wyecnnected ld. This is ls evident frm Y Z Z. PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
42 Chter 1, Prblem 47. The fllwing three rllelcnnected threehse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
43 Chter 1, Prblem 48. blnced, sitivesequence wyecnnected surce hs n 40 0 rms nd sulies n unblnced deltcnnected 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. 18j1 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 threehse lds re deltcnnected (b) the lds re wyecnnected Chter 1, Slutin 49. () Fr the deltcnnected ld, Z 0 + j10ω, 0 (rms), S Z * x (0 j10) r 5.808kW j k (b) Fr the wyecnnected ld, Z 0 + j10ω, /, S x k r kw * Z (0 j10) Chter 1, Prblem 50. blnced threehse surce with 40 rms is sulying 8 k t 0.6 wer fctr lgging t tw wyecnnected 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
47 Chter 1, Prblem 5. furwire wyewye 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 erhse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
48 Chter 1, Prblem 5. n the YY 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
50 Chter 1, Prblem 54. blnced threehse Ysurce with P 10 rms drives Ycnnected threehse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
51 Chter 1, Prblem 55. threehse suly, with the line vltge 40 rms sitively hsed, hs n unblnced deltcnnected 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
54 Chter 1, Prblem 57. Determine the line currents fr the threehse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
58 Chter 1, Prblem 60. Use PSice t determine in the singlehse, threewire 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
63 Chter 1, Slutin 6. Becuse f the deltcnnected 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 threehse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
67 PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
68 Chter 1, Prblem 65. blnced threehse 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 deltcnnected 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
70 Chter 1, Prblem 66. threehse, furwire 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 threewttmeter 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 threehse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
72 Chter 1, Prblem 67. * s shwn in Fig. 1.7, threehse furwire 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
74 Chter 1, Prblem 68. Meter redings fr threehse wyecnnected 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 wyecnnected ld, (d) PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
75 Chter 1, Prblem 69. certin stre cntins three blnced threehse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
76 Chter 1, Prblem 70. The twwttmeter methd gives P W nd P 400 W fr threehse mtr running n 40 line. ssume tht the mtr ld is wyecnnected 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
78 Chter 1, Slutin 71. () f 08 0, 0810, 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 deltcnnected 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 060 P (0)(0) cs( )  57 W PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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[ (4060 )( ] Re ) 60 W * P [ ] Re[ (4010 )( ] Re ) W PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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[ (0860 ))( ] * P Re ) W W PROPRETRY MTER. 007 The McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
85 Chter 1, Prblem 77. threehse 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. threehse 440, 51kW, 60k 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
86 Chter 1, Prblem 79. blnced threehse genertr hs n bc hse sequence with hse vltge n The genertr feeds n inductin mtr which my be reresented by blnced Ycnnected 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 erhse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
87 Chter 1, Prblem 80. blnced threehse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
88 Chter 1, Prblem 81. rfessinl center is sulied by blnced threehse surce. The center hs fur blnced threehse 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 McGrwHill Cmnies, nc. ll rights reserved. N rt ermitted by McGrwHill fr their individul curse rertin. f yu re student using this Mnul,
Copyright Paul Tobin 46
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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