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 ______

JEE Main · 2026 · 28 Jan 2026 · Shift 1 · Alternating Current

The electric current in the circuit is given as

i = i_{o} (t / T)

. The r.m.s current for the period

t = 0

t = T

is ______

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

Answer: (D)

Solution

The rms current is defined as:

i_{rms} = \frac{1}{T} \int_{0}^{T} i^{2} d t

Substituting

i = i_{0} (t / T)

i_{rms}^{2} = \frac{1}{T} \int_{0}^{T} \frac{i _{0}^{2} t ^{2}}{T ^{2}} d t = \frac{i _{0}^{2}}{T ^{3}} [\frac{t ^{3}}{3}]_{0}^{T} = \frac{i _{0}^{2}}{T ^{3}} \cdot \frac{T ^{3}}{3} = \frac{i _{0}^{2}}{3}

Therefore:

i_{rms} = \frac{i _{0}}{3}

JEE Main · 2026 · 28 Jan 2026 · Shift 1 · Single correct option

Practise more: all JEE Main PYQs on Alternating Current →

More JEE Main questions on Alternating Current

Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for $V = 5 sin (100 t)$ . The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ______ $μ$ F.
JEE Main 2026View solution →
For the series LCR circuit connected with 220 V, 50 Hz a.c source as shown in the figure, the power factor is $\frac{α}{10}$ . The value of $α$ is
JEE Main 2026View solution →
An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is ______ .
( $π = 3.14$ )
JEE Main 2026View solution →
The figure given below shows an LCR series circuit with two switches $S_{1}$ and $S_{2}$ . When switch $S_{1}$ is closed keeping $S_{2}$ open, the phase difference $(ϕ)$ between the current and source voltage is $3 0^{\circ}$ and phase differe …
JEE Main 2026View solution →
An inductor of 10 mH, capacitor of $0.1 μ F$ and a resistor of $100Ω$ are connected in series across an a.c power supply $220 V, 70 Hz$ . The power factor of the given circuit is 0.5. The difference in the inductive reactance and capacit …
JEE Main 2026View solution →
An a.c. source of angular frequency $ω$ is connected across a resistor R and a capacitor C in series. The current is observed as I. Now the frequency of the source is changed to $ω /4$ , (keeping the voltage unchanged) the current is found to be $I /3$ . The ratio of resist …
JEE Main 2026View solution →