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In an a.c. circuit, the instantaneous e.m.f. and current are given by e = 100 sin 30 t and i = 20 sin (30 t - π/4). In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively:
- 50, 10
- 1000/√2, 10
- 50/√2, 0
- 50, 0
Correct answer: 1000/√2, 10
Solution
With E0=100, I0=20, phi=pi/4: P_avg = (1/2)(100)(20)cos45 = 1000/sqrt(2) W. Wattless (reactive) current = I_rms sin(phi) = (20/sqrt(2))(1/sqrt(2)) = 10. So (1000/sqrt(2), 10).
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