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Obtain the readings of wattmeters in lines (a) A and B, (b) B and C. Ans: a 7.52 kW, 24.8 kW; (b) 16.16 kW, 16.16 kW 11.37 Two wattmeters in a three-phase, three-wire system with e ective line voltage 120 V read 1500 W and 500 W. What is the impedance of the balanced -connected load Ans: 16:3 40:98  A three-phase, three-wire, ABC system has e ective line voltage 173.2 V. Wattmeters in lines A and B read 301 W and 1327 W, respectively. Find the impedance of the balanced Y-connected load. (Since the sequence is speci ed, the sign of the impedance angle can be determined.) Ans: 10 708  A three-phase, three-wire system, with a line voltage VBC 339:4 08 V, has a balanced Y-connected load of ZY 15 608 . The lines between the system and the load have impedances 2:24 26:578 . Find the linevoltage magnitude at the load. Ans: 301.1 V Repeat Problem 11.39 with the load impedance ZY 15 608 . By drawing the voltage phasor diagrams for the two cases, illustrate the e ect of load impedance angle on the voltage drop for a given line impedance. Ans: 332.9 V A three-phase generator with an e ective line voltage of 6000 V supplies the following four balanced loads in parallel: 16 kW at pf 0:8 lagging, 24 kW at pf 0:6 lagging, 4 kW at pf 1, and 1 kW at pf 0:1 leading. (a) Find the total average power (P) supplied by the generator, reactive power (Q), apparent power (S), power factor, and e ective value of line current. (b) Find the amount of reactive load Qc to be added in parallel to produce an overall power factor of 0.9 lagging, then nd apparent power and e ective value of line current. Ans: a P 45 kW, Q 34:05 kvar, S 56:43 kVA, pf 0:8 lagging, IL 5:43 A, (b) QC 12:25 kvar, S 50 kVA, IL 5:35 A A balanced -connected load with impedances Z 6 j9  is connected to a three-phase generator with an e ective line voltage of 400 V. The lines between the load and the generator have resistances of 1  each. Find the e ective line current, power delivered by the generator, and power absorbed by the load. Ans: IL 54:43 A, Pg 26666 W, P 17777 W In Problem 11.42, nd the e ective line voltage at the load. Ans: VL 340 V A three-phase generator feeds two balanced loads (9 kW at pf 0:8 and 12 kW at pf 0:6, both lagging) through three cables (0.1  each). The generator is regulated such that the e ective line voltage at the load is 220 V. Find the e ective line voltage at the generator. Ans: 230 V A balanced -connected load has impedances 45 j60 . e ective line voltage of: (a) 400 V, (b) 390 V. Ans: a 3:84 kW, (b) 3.65 kW Find the average power delivered to it at an
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Obtain the change in average power delivered to a three-phase balanced load if the line voltage is multiplied by a factor . Ans: Power is multiplied by the factor 2 A three-phase, three-wire source supplies a balanced load rated for 15 kW with pf 0:8 at an e ective line voltage of 220 V. Find the power absorbed by the load if the three wires connecting the source to the load have resistances of 0.05  each and the e ective line voltage at the source is 220 V. Use both a simpli ed
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approximation and also an exact method. Ans: 14:67 kW (by an approximate method), 14.54 kW (by an exact method) 11.48 In Problem 11.47 determine the e ective value of line voltage such that the load operates at its rated values. Ans: 222.46 V (by an approximate method), 221.98 V (by an exact method) What happens to the quantity of power supplied by a three-phase, three-wire system to a balanced load if one phase is disconnected Ans: Power is halved. A three-phase, three-wire generator with e ective line voltage 6000 V is connected to a balanced load by three lines with resistances of 1  each, delivering a total of 200 kW. Find the e ciency (the ratio of power absorbed by the load to power delivered by the system) if the power factor of the generator is (a) 0.6, (b) 0.9 Ans. (a) 98.5 percent (b) 99.3 percent. A 60-Hz three-phase, three-wire system with terminals labeled 1; 2; 3 has an e ective line voltage of 220 V. To determine if the system is ABC or CBA, the circuit of Fig. 11-35 is tested. Find the e ective voltage between node 4 and line 2 if the system is (a) ABC, (b) CBA. Ans: a 80.5 V; (b) 300.5 V
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