JEE Main 2026 Jan 28 Shift 1, Physics Q2: Introduction to Alternating Currents and Circuits

JEE Main2026Jan 28, Shift 1Physics

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

A
$\frac{i _{0}}{2}$
B
$i_{0}$
C
$\frac{i _{0}}{6}$
D
$\frac{i _{0}}{3}$

Solution

By definition: $i_{rms}^{2} = \frac{1}{T} \int_{0}^{T} i^{2} d t = \frac{1}{T} \int_{0}^{T} \frac{i _{0}^{2} t ^{2}}{T ^{2}} d t = \frac{i _{0}^{2}}{T ^{3}} \cdot \frac{T ^{3}}{3} = \frac{i _{0}^{2}}{3}$ .

$∴ i_{rms} = \frac{i _{0}}{3}$ . Option (4).

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JEE Main 2026 Jan 28 Shift 1, Physics Q2: Introduction to Alternating Currents and Circuits

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