An alternating current is given by $I={I}_{A}\sin \omega t+{I}_{B}\cos \omega t$. The r.m.s current will be

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Correct answer: d) $\sqrt{\frac{{I}_{A}^{2}+{I}_{B}^{2}}{2}}$. Given the current as $I={I}_{A}\sin \omega t+$ ${I}_{B}\cos \omega t$, the r.m.s. current is calculated by integrating the square of the current over time, then taking the square root. i.e., ${i}_{ms}=\sqrt{\frac{\int {I}^{2}dt}{\int dt}}\ {I}_{rms}=\sqrt{\frac{{I}_{A}^{2}+{I}_{B}^{2}}{2}}$

An alternating current is given by \(I={I}_{A}\sin \omega t+{I}_{B}\cos \omega t\). The r.m.s current will be

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