Question

Choose the correct answer from the alternatives given.
The charge on a parallel plate capacitor varies as $q=q_{0}cos2\pi \nu t$. The plates are very large and close together (area = A, separation = d). The displacement current through the capacitor is then

• A. $3q_{0}2\pi \nu sin2\pi \nu t$
• B. $-q_{0}2\pi \nu sin2\pi \nu t$
• C. $4q_{0}2\pi sin2\pi \nu t$
• D. $5q_{0}2\pi sin2\pi \nu t$

Answer 1

The correct option is B $-q_{0}2\pi \nu sin2\pi \nu t$

Given: The charge on the parallel plate capacitor varies as $q=q_{0}cos2\pi \nu t$

To find: The displacement current through the capacitor.

The displacement current in a capacitor is equal to the conduction current of the capacitor.

Displacement current, $I_D=I_C$

The conduction current in a capacitor is given by:
$I_C=\frac{dq}{dt}$

$⟹\frac{d}{dt}\left[q_{0}cos2\pi \nu t\right]$

$=-q_{0}2\pi \nu sin2\pi \nu t$

Option $\left(B\right)$ is correct.