JEE Main · 2026 · 24 Jan 2026 · Shift 1 · Alternating Current

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

(A)4
(B)10
(C)6✓ Correct
(D)8

Answer: (C)

Solution

For a series LCR circuit the power factor is

cos ϕ = \frac{R}{Z}

with

Z = R^{2} + (X_{L} - X_{C})^{2}

. The circuit gives

R = 60 Ω

X_{L} = 70 Ω

and

X_{C} = 150 Ω

, so

Z = 6 0^{2} + (70 - 150)^{2} = 3600 + 6400 = 100 Ω

. The power factor is

\frac{60}{100} = \frac{6}{10}

, and comparing with

\frac{α}{10}

gives

α = 6

JEE Main · 2026 · 24 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 →
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 ______
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 →