Question

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:

• A. $I _{ d }= V _{0} \omega C \cos \omega t$
• B. $I_{d}=\frac{V_{0}}{\omega C} \cos \omega t$
• C. $I _{ d }=\frac{ V _{0}}{\omega C } \sin \omega t$
• D. $I _{ d }= V _{0} \omega C \sin \omega t$

Answer 1

Answer: (A)

$I _{ d }= V _{0} \omega C \cos \omega t$

Answer 2

The displacement current is given by
$I _{ d }= C \frac{ dV }{ dt }$
$= C \frac{ d }{ dt }\left[ V _{0} \sin \omega t \right]$
$= CV _{0} \omega \cos \omega t$
$I _{ d }= V _{0}(\omega C ) \cos \omega t$