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Grade 12th passElectric Current

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

Aman

7 Years agoGrade 12th pass

1 Answer

Kapil Khare

7 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

₀∫^T I²dt = ₀∫^TI₀² + I₁²sin² $\omega$ t + 2 I₀I₁sin( $\omega$ t)

= I₀²T + 2 I₀I₁[-cos( $\omega$ t)] + ₀∫^T I₁²[1 – cos( $\omega$ t)]/2

= I₀²T + [(I₁²T)/2]

I_rms = {{I₀²T + [(I₁²T)/2]}/T}^1/2

I_rms = {I₀² + [(I₁²)/2]}^1/2

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