Question

An alternating voltage of amplitude 40 V and frequency 4 kHz is applied directly across the capacitor of 12 μF. The maximum displacement current between the plates of the capacitor is nearly:

• A. 13 A
• B. 8 A
• C. 10 A
• D. 12 A

Answer 1

Answer: (D)

12 A

Answer 2

The displacement current in a capacitor is the same as the conduction current. The capacitive reactance $X_c$ is given by:

$X_c = \frac{1}{\omega C} = \frac{1}{2 \pi f C}$

Substituting the given values:

$X_c = \frac{1}{2 \pi \times 4 \times 10^3 \, \text{Hz} \times 12 \times 10^{-6} \, \text{F}} \approx 3.317 \, \Omega$

The current $I$ is given by:

$I = \frac{V}{X_c} = \frac{40 \, \text{V}}{3.317 \, \Omega} \approx 12 \, \text{A}$