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A time-varying current is given by I = I0 + I1*sin(omega*t). What is its rms value?

1. sqrt(I0² + 0.5*I1²)
2. sqrt(I0² + 0.5*I0²)
3. 0
4. I0/sqrt(2)

Correct answer: sqrt(I0² + 0.5*I1²)

Solution

I² = I0² + 2*I0*I1*sin(wt) + I1²*sin²(wt). Averaging over a cycle: <sin(wt)> = 0 and <sin²(wt)> = 1/2. So <I²> = I0² + I1²/2. The rms value is sqrt(<I²>) = sqrt(I0² + 0.5*I1²).

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