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An AC current is given by I = I 0 + I 1 sin ωt, its rms value will be

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

Grade:12th pass

1 Answers

Kapil Khare
80 Points
2 years ago
Current = I = I0 + I1sin(\omegat)
Let the time period be T
then \omegaT = 2\pi
RMS value = [(∫ I2dt)/T]1/2
 
          0T I2dt   =   0I02 + I12sin2\omegat + 2 I0I1sin(\omegat)
                        = I02T + 2 I0I1[-cos(\omegat)] +  0T I12[1 – cos(\omegat)]/2
                        = I02T + [(I12T)/2]
       Irms = {{I02T + [(I12T)/2]}/T}1/2
      Irms = {I02 + [(I12)/2]}1/2

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