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In an alternating-current circuit, the voltage and current vary with time as e = 100 sin 30t and i = 20 sin(30t - π/4). Over one complete AC cycle, the average power dissipated in the circuit and the wattless current are, respectively:
- 50 W, 10 A
- 1000/√2 W, 10 A
- 50/√2 W, 0
- 50 W, 0
Correct answer: 1000/√2 W, 10 A
Solution
Phase difference phi = pi/4. Average power = (1/2)*100*20*cos45 = 1000/sqrt(2) W. Wattless (reactive) current = Irms*sin45 = (20/sqrt2)*(1/sqrt2) = 10 A.
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