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POLYPHASE CIRCUITS

[CHAP. 11

and the total complex power is their sum, ST ¼ 6205 þ j4224 that is, PT ¼ 6205 W and QT ¼ 4224 var (inductive). To obtain the currents a sequence must be assumed; let it be ABC.

Then, using Fig. 11-7(a),

339:4 1208 ¼ 13:6 308 A 25 908 339:4 08 ¼ 22:6 308 A ¼ 15 308 339:4 2408 ¼ 17:0 2408 A ¼ 20 08

IAB ¼ IBC ICA

The line currents are obtained by applying KCL at the junctions. IA ¼ IAB þ IAC ¼ 13:6 308  17:0 2408 ¼ 29:6 46:78

A

IB ¼ IBC þ IBA ¼ 22:6 308  13:6 308 ¼ 19:7 66:78 A IC ¼ ICA þ ICB ¼ 17:0 2408  22:6 308 ¼ 28:3 173:18 A

11.11 Obtain the readings of wattmeters placed in lines A and B of the circuit of Problem 11.10 (Line C is the potential reference for both meters.)    29:6 WA ¼ Re ðVAC eff IA eff Þ ¼ Re ð240 608Þ pffiffiffi 46:78 2 ¼ Re ð5023 13:38Þ ¼ 4888 W    19:7 WB ¼ Re ðVBC eff IB eff Þ ¼ Re ð240 08Þ pffiffiffi 66:78 2 ¼ Re ð3343 66:78Þ ¼ 1322 W Note that WA þ WB ¼ 6210 W, which agrees with PT as found in Problem 11.10.

11.12 A three-phase, four-wire, ABC system, with line voltage VBC ¼ 294:2 08 V, has a Y-connected load of ZA ¼ 10 08 , ZB ¼ 15 308 , and ZC ¼ 10 308  (Fig. 11-31). Obtain the line and neutral currents.

Fig. 11-31

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An  
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An  
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