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

The Correct Option is D

In a capacitor, the displacement current equals the conduction current. The capacitive reactance \(X_c\) is calculated as:

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

Using the provided 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 determined by:

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