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In the given circuit if switches $S_{3} a n d S_{4}$ are open, keeping $S_{1} a n d S_{2}$ closed, the value of I is $I_{0}$ . If switches $S_{1} a n d S_{2}$ are open, keeping $S_{3} a n d S_{4}$ closed, the value of $I$ is $I_{0}$ sin $ω$ t. Now, if switches $S_{1}$ and $S_{4}$ are open keeping $S_{2}$ and $S_{3}$ closed, the value of rms current through the AC-component, during one complete cycle, is

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$\frac{I_{0}}{\sqrt{2}}$

$I_{0} (1 - \frac{1}{\sqrt{2}})$

$\sqrt{\frac{3}{2}} I_{0}$

$I_{0} (1 + \frac{1}{\sqrt{2}})$

answer is D.

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Detailed Solution

From the given data, one can conclude that the AC-component has to be resistance. Effective current is rms current $= i_{e f f}$
$i_{e f f} = \sqrt{\frac{\int_{0}^{T} {(I_{0} + I_{0} \sin ω t)}^{2} d t}{T}}$

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