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# An AC current is given by I = I0 + I1 sin ωt, its rms value will be

Kapil Khare
80 Points
2 years ago
Current = I = I0 + I1sin($\omega$t)
Let the time period be T
then $\omega$T = 2$\pi$
RMS value = [(∫ I2dt)/T]1/2

0T I2dt   =   0I02 + I12sin2$\omega$t + 2 I0I1sin($\omega$t)
= I02T + 2 I0I1[-cos($\omega$t)] +  0T I12[1 – cos($\omega$t)]/2
= I02T + [(I12T)/2]
Irms = {{I02T + [(I12T)/2]}/T}1/2
Irms = {I02 + [(I12)/2]}1/2