A current in a circuit is given by i = 3 + 4 | vedclass

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(C) The given current is $i = I_0 + I_1 \sin \omega t$,where $I_0 = 3$ and $I_1 = 4$.The effective $(RMS)$ value of current is defined as $I_{rms} = \

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$\sqrt{17}$

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(C) The given current is $i = I_0 + I_1 \sin \omega t$,where $I_0 = 3$ and $I_1 = 4$.The effective $(RMS)$ value of current is defined as $I_{rms} = \sqrt{\frac{1}{T} \int_0^T i^2 dt}$.Substituting $i = I_0 + I_1 \sin \omega t$:$I_{rms} = \sqrt{\frac{1}{T} \int_0^T (I_0^2 + I_1^2 \sin^2 \omega t + 2 I_0 I_1 \sin \omega t) dt}$.Using the properties of integration over a full cycle:$\frac{1}{T} \int_0^T dt = 1$,$\frac{1}{T} \int_0^T \sin^2 \omega t dt = \frac{1}{2}$,and $\frac{1}{T} \int_0^T \sin \omega t dt = 0$.Thus,$I_{rms} = \sqrt{I_0^2 + \frac{I_1^2}{2}}$.Substituting the values $I_0 = 3$ and $I_1 = 4$:$I_{rms} = \sqrt{3^2 + \frac{4^2}{2}} = \sqrt{9 + \frac{16}{2}} = \sqrt{9 + 8} = \sqrt{17}$.

$A$ current in a circuit is given by $i = 3 + 4 \sin \omega t$. The effective value of the current is

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