A capacitor of capacitance 'C', is connected across an ac source of voltage V, given by $V = V_{0} sinωt .$ The displacement current between the plates of the capacitor, would then be given by:

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$I_{d} = V_{0} ωCsin ωt$

$I_{d} = V_{0} ωcos ωt$

$I_{d} = \frac{V_{0}}{ωC} \cos ωt$

$I_{d} = \frac{V_{0}}{ωC} \sin ωt$

answer is B.

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Detailed Solution

The displacement current is given by
$\begin{array}{l} I_{d} = C \frac{dV}{dt} \\ = C \frac{d}{dt} [V_{0} \sin ωt] \\ = {CV}_{0} ωcos ωt \\ I_{d} = V_{0} (ωC) \cos ωt \end{array}$

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