The electric current in the circuit is given as i=i o (t / T) . The r.m.s current for the period t=0 to t=T is \ \ \ \

Physics · Alternating Current

JEE Main 2026 — 28 January, Morning Shift — Question 26

The electric current in the circuit is given as $i=i_{\mathrm{o}}(t / T)$ . The r.m.s current for the period $t=0$ to $t=T$ is $\_\_\_\_$

Option A:
$\frac{i_{0}}{\sqrt{2}}$
Option B:
$i_{0}$
Option C:
$\frac{i_{0}}{\sqrt{6}}$
Option D:
$\frac{i_{0}}{\sqrt{3}}$
Correct

Answer: D

Step-by-step solution

$\mathrm{i}_{\mathrm{rms}}^{2}=\frac{\int_{0}^{\mathrm{T}}\left(\mathrm{i}_{0}^{2} \mathrm{t}^{2} / \mathrm{T}^{2}\right) \mathrm{dt}}{\int_{0}^{\mathrm{T}} \mathrm{dt}}=\frac{\mathrm{i}_{0}^{2}}{\mathrm{~T}^{3}} \cdot \frac{\mathrm{~T}^{3}}{3}=\frac{\mathrm{i}_{0}^{2}}{3}$ $\mathrm{i}_{\text {rms }}=\frac{\mathrm{i}_{0}}{\sqrt{3}}$

Answer key and solution verified before publishing.

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Exam: JEE Main 2026
Paper: 28 January, Morning Shift
Subject: Physics
Chapter: Alternating Current
Topic: Average, Peak and RMS value of Alternating Current and Voltage