CHAP. 10]

10.51

AC POWER

247

pﬃﬃﬃ pﬃﬃﬃ In the circuit of Fig. 10-29, va ¼ 10 2 cos t and ib ¼ 10 2 cos 2t. (a) Find the average power delivered by each source. (b) Find the current in the resistor and the average pﬃﬃﬃﬃﬃ pﬃﬃﬃﬃﬃ power absorbed by it. Ans: ðaÞ Pa ¼ Pb ¼ 80 W; ðbÞ iR ¼ 2 10 cos ðt  26:58Þ þ 2 10 cos ð2t  63:48Þ, PR ¼ 160 W

Fig. 10-29

10.52

A single-phase AC source having eﬀective value 6 kV delivers 100 kW at a power factor 0.8 lagging to two parallel loads. The individual power factors of the loads are pf1 ¼ 0:7 lagging and pf2 ¼ 0:1 leading. (a) Find powers P1 and P2 delivered to each load. (b) Find the impedance of each load and their combination. Ans: ðaÞ P1 ¼ 97:54 kW, P2 ¼ 2:46 kW, (b) Z1 ¼ 0:244 84:26 , Z2 ¼ 0:043 45:57 , Z ¼ 0:048 36:87 

10.53

A practical voltage source is modeled by an ideal voltage source Vg with an open-circuited eﬀective value of 320 V in series with an output impedance Zg ¼ 50 þ j100 . The source feeds a load Z‘ ¼ 200 þ j100 . See Fig. 10-30. ða) Find the average power and reactive power delivered by Vg . (b) Find the average power and reactive power absorbed by the load. (c) A reactive element jX is added in parallel to Z‘ . Find the X such that power delivered to Z‘ is maximized. Ans: ðaÞ Pg ¼ 250 W and Qg ¼ 200 var, (b) P‘ ¼ 200 W and Q‘ ¼ 100 var, (c) X ¼ 100 

Fig. 10-30

Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An
Mahmood_Nahvi_eBook_Schaum_s_Outlines_Theory_An