In an ac circuit,the r.m.s. value of current, | vedclass

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(B) The $r.m.s.$ (root mean square) value of an alternating current is defined as the square root of the mean of the squares of the instantaneous curr

Vedclass · Accepted Answer

$I_{rms} = \frac{1}{\sqrt{2}} I_0$

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(B) The $r.m.s.$ (root mean square) value of an alternating current is defined as the square root of the mean of the squares of the instantaneous currents over one complete cycle.For a sinusoidal alternating current given by $I = I_0 \sin(\omega t)$,the $r.m.s.$ value is calculated as:$I_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} I^2 dt} = \sqrt{\frac{1}{T} \int_{0}^{T} I_0^2 \sin^2(\omega t) dt}$Solving this integral over one period $T$ gives:$I_{rms} = \frac{I_0}{\sqrt{2}}$Therefore,the correct relation is $I_{rms} = \frac{1}{\sqrt{2}} I_0$.

In an $ac$ circuit,the $r.m.s.$ value of current,$I_{rms}$ is related to the peak current,$I_0$ by the relation:

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