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In an AC circuit the instantaneous emf and current are e = 100*sin(30t) and i = 20*sin(30t - pi/4). Over one full cycle, what are the average power consumed and the wattless current, respectively?

1. 1000/sqrt(2), 10
2. 50/sqrt(2), 0
3. 50, 0
4. 50, 10

Correct answer: 1000/sqrt(2), 10

Solution

Average power = 0.5*100*20*cos45 = 1000/sqrt(2) W. The wattless (reactive) current component is I_rms*sin(phi) = (20/sqrt(2))*(1/sqrt(2)) = 10 A.

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