Rankers Physics

Alternating Current: Practice Problem & Solution

5. A capacitor of capacitance 'C', is connected across an ac source of voltage V, given by $V = V_0 \sin \omega t$. The displacement current between the plates of the capacitor, would then be given by: (2021)
$I_d = \frac{V_0}{\omega C} \cos \omega t$
$I_d = -\frac{V_0}{\omega C} \sin \omega t$
$I_d = V_0 \omega C \sin \omega t$
$I_d = V_0 \omega C \cos \omega t$

Solution Explained:

To solve this problem, we apply the core principles of Alternating Current. Understanding the underlying formula is key to arriving at the correct answer below:

The displacement current between the capacitor plates is equal to the conduction current, $I_d = \frac{dq}{dt}$. Since charge on the capacitor is $q = C V = C V_0 \sin \omega t$, we differentiate with respect to time. $I_d = \frac{d}{dt}(C V_0 \sin \omega t) = V_0 \omega C \cos \omega t$.

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