Alternating Current

9 JEE Main questions · Physics

LCR and power

PhysicsJEE Main 21 Jan 2026, Shift 2·Q4·MCQ·Moderate
Open
A capacitor C is first charged fully with potential difference of $V_0$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In t s 25% of the initial energy in the capacitor is transferred to the inductor. The value of t is s.
1. (1) $\dfrac{\pi\sqrt{LC}}{3}$
2. (2) $\dfrac{\pi\sqrt{LC}}{6}$
3. (3) $\dfrac{\pi\sqrt{LC}}{2}$
4. (4) $\pi\sqrt{\dfrac{LC}{2}}$
PhysicsJEE Main 23 Jan 2026, Shift 1·Q23·Numerical·Easy–moderate
Open
Using a variable-frequency a.c. voltage source, the maximum current measured in the given LCR circuit is 50 mA for $V = 5\sin(100t)$ . The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is $\mu$ F.
PhysicsJEE Main 24 Jan 2026, Shift 1·Q9·MCQ·Easy–moderate
Open
For the series LCR circuit connected with 220 V, 50 Hz a.c source as shown in the figure, the power factor is $\dfrac{\alpha}{10}$ . The value of $\alpha$ is
1. (1)4
2. (2)10
3. (3)6
4. (4)8
PhysicsJEE Main 2 Apr 2026, Shift 2·Q17·MCQ·Moderate
Open
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 ( $\phi$ ) between the current and source voltage is $30^\circ$ and phase difference is $60^\circ$ when $S_2$ is closed keeping $S_1$ open. The value of $(3L_1 - L_2)$ is H.
1. (1) $\dfrac92$
2. (2) $\dfrac29$
3. (3) $\dfrac13$
4. (4)3
PhysicsJEE Main 4 Apr 2026, Shift 1·Q25·Numerical·Easy–moderate
Open
An inductor, a capacitor and a resistor of $100\ \Omega$ 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 capacitance reactance is $\sqrt3\,\alpha\ \Omega$ . The value of $\alpha$ is .
We corrected a printing error in the original paper
Source printed “An inductor of 10 mH, capacitor of $0.1\ \mu$ F and a resistor of $100\ \Omega$ are connected in series aross”; corrected to the intended “An inductor, a capacitor and a resistor of $100\ \Omega$ are connected in series across” (10 mH and $0.1\ \mu$ F at 70 Hz give a power factor of about 0.004, contradicting the stated 0.5 on which the key rests).
PhysicsJEE Main 5 Apr 2026, Shift 1·Q19·MCQ·Moderate
Open
An a.c. source of angular frequency $\omega$ 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 $\omega/4$ , (keeping the voltage unchanged) the current is found to be $I/3$ . The ratio of resistance to reactance at frequency $\omega$ is
1. (1) $\sqrt{\dfrac{6}{7}}$
2. (2) $\sqrt{\dfrac{3}{5}}$
3. (3) $\sqrt{\dfrac{7}{8}}$
4. (4) $\sqrt{\dfrac{3}{4}}$
PhysicsJEE Main 5 Apr 2026, Shift 2·Q23·Numerical·Easy–moderate
Open
A series LCR circuit with $R = 20\ \Omega$ , $L = 1.6$ H and $C = 40\ \mu\mathrm{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is $\Omega$ .
PhysicsJEE Main 6 Apr 2026, Shift 1·Q20·MCQ·Easy–moderate
Open
A LCR series circuit driven with $E_{\mathrm{rms}} = 90$ V at frequency $f_d = 30$ Hz has resistance $R = 80\ \Omega$ , an inductance with inductive reactance $X_L = 20.0\ \Omega$ and capacitance with capacitive reactance $X_C = 80.0\ \Omega$ . The power factor of the circuit is .
1. (1)0.8
2. (2)0.64
3. (3)0.9
4. (4)0.5

AC basics and single elements

PhysicsJEE Main 28 Jan 2026, Shift 1·Q2·MCQ·Easy–moderate
Open
The electric current in the circuit is given as $i = i_0(t/T)$ . The r.m.s current for the period $t = 0$ to $t = T$ is
1. (1) $\dfrac{i_0}{\sqrt2}$
2. (2) $i_0$
3. (3) $\dfrac{i_0}{\sqrt6}$
4. (4) $\dfrac{i_0}{\sqrt3}$