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

Physics · Electromagnetic Waves

JEE Main 2024 — 5 April, Shift 1 — Question 48

An alternating voltage of amplitude 40 V and frequency 4 kHz is applied directly across the capacitor of $12 \mu \mathrm{~F}$ . The maximum displacement current between the plates of the capacitor is nearly:

Option A:
(1) 13 A
Option B:
(8 A)
Option C:
(10A)
Option D:
(12A)
Correct

Answer: D

Step-by-step solution

Displacement current is same as conduction current in capacitor.

\begin{aligned} & X_{C}=\frac{1}{\omega \mathrm{C}}=\frac{1}{2 \pi \mathrm{fC}} & =\frac{1}{2 \pi \times 4 \times 10^{3} \times 12 \times 10^{-6}}=3.317 \Omega \end{aligned}

\mathrm{I}=\frac{\mathrm{V}}{\mathrm{X}_{\mathrm{C}}}=\frac{40}{3.317}=12 \mathrm{~A}

Answer key and solution verified before publishing.

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Exam: JEE Main 2024
Paper: 5 April, Shift 1
Subject: Physics
Chapter: Electromagnetic Waves
Topic: Displacement Current and Equation of EM Waves