Question

The variation of charge \( q \) with time \( t \) on a parallel plate capacitor is given by \( q = q_0 \cos(\omega t) \). The displacement current through the capacitor is:

• A. \( q_0 \sin(\omega t) \)
• B. \( -q_0 \sin(\omega t) \)
• C. \( -q_0 \omega \sin(\omega t) \)
• D. \( q_0 \omega \sin(\omega t) \)

Hint:

The displacement current in a capacitor is given by the rate of change of charge: \( I_d = \frac{dq}{dt} \).

Answer 1

The Correct Option is C

The displacement current is given by: \[ I_d = \frac{dq}{dt} \] Since \( q = q_0 \cos(\omega t) \), we differentiate with respect to time: \[ I_d = \frac{d}{dt}(q_0 \cos(\omega t)) = -q_0 \omega \sin(\omega t) \] Thus, the displacement current is \( -q_0 \omega \sin(\omega t) \).