The r.m.s. value of the given current I = I_0 | vedclass

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(B) The $r.m.s.$ value of a current is defined as $I_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} I^2 dt}$.Given $I = I_0 + I_1 \sin \omega t$,we have $I^2

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$\sqrt{I_0^2 + \frac{I_1^2}{2}}$

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(B) The $r.m.s.$ value of a current is defined as $I_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} I^2 dt}$.Given $I = I_0 + I_1 \sin \omega t$,we have $I^2 = I_0^2 + I_1^2 \sin^2 \omega t + 2 I_0 I_1 \sin \omega t$.Integrating over one complete time period $T = \frac{2\pi}{\omega}$:$I_{rms}^2 = \frac{1}{T} \int_{0}^{T} (I_0^2 + I_1^2 \sin^2 \omega t + 2 I_0 I_1 \sin \omega t) dt$.Since the average value of $\sin \omega t$ over a full cycle is $0$,the term $\int_{0}^{T} 2 I_0 I_1 \sin \omega t dt = 0$.The average value of $\sin^2 \omega t$ over a full cycle is $\frac{1}{2}$.Thus,$I_{rms}^2 = I_0^2 + I_1^2 \left( \frac{1}{2} \right) + 0 = I_0^2 + \frac{I_1^2}{2}$.Therefore,$I_{rms} = \sqrt{I_0^2 + \frac{I_1^2}{2}}$.

The $r.m.s.$ value of the given current $I = I_0 + I_1 \sin \omega t$ is

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