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

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(C) The given current is $i = 3 + 4 \sin \omega t$.To find the $RMS$ value,we first calculate the mean square value $i^2_{rms} = \overline{i^2}$.$i^2

Vedclass · Accepted Answer

$\sqrt{17}$

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(C) The given current is $i = 3 + 4 \sin \omega t$.To find the $RMS$ value,we first calculate the mean square value $i^2_{rms} = \overline{i^2}$.$i^2 = (3 + 4 \sin \omega t)^2 = 9 + 16 \sin^2 \omega t + 24 \sin \omega t$.Taking the average over a full cycle:$\overline{i^2} = \overline{9} + 16 \overline{\sin^2 \omega t} + 24 \overline{\sin \omega t}$.We know that $\overline{\sin^2 \omega t} = 1/2$ and $\overline{\sin \omega t} = 0$ over a full cycle.Therefore,$i^2_{rms} = 9 + 16(1/2) + 0 = 9 + 8 = 17$.The $RMS$ value is $i_{rms} = \sqrt{\overline{i^2}} = \sqrt{17}$.

$A$ current in a circuit is given by $i = 3 + 4 \sin \omega t$. Then the effective value ($RMS$ value) of the current is:

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