Alternating Current – JEE Main Previous Year Questions with Solutions

JEE Main Previous Year Question of Physics with Solutions are available here. Practicing JEE Main Previous Year Papers Questions of Physics will help all the JEE aspirants in realizing the question pattern as well as help in analyzing their weak & strong areas.

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Q. In a series LCR circuit R = $200 \Omega$ and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lages behind the voltage by $30^{\circ}$. On taking out the inductor from the circuit the current leads the voltage by $30^{\circ}$. The power dissipated in the LCR circuit is :

(1) 242 W

(2) 305 W

(3) 210 W

(4) Zero W

[AIEEE – 2010]

Sol. (1) Q. A fully charged capacitor C with intial charge $\mathrm{q}_{0}$ is connected to a coil of self inductance L at t = 0. The time at which the energy is stored equally between the electric and the magnetic fields is :-

(1) $2 \pi \sqrt{\mathrm{LC}}$

(2) $\sqrt{1 C}$

(3) $\pi \sqrt{\mathrm{LC}}$

(4) $\frac{\pi}{4} \sqrt{\mathrm{LC}}$

[AIEEE – 2011]

Sol. (4) Q. In an LCR circuit as shown below both switches are open initially. Now switch S1 is closed, $\mathrm{S}_{2}$ kept open, (q is charge on the capacitor and $\tau=\mathrm{RC}$ is Capacitive time constant). Which of the following statement is correct?

(1) Work done by the battery is half of the energy dissipated in the resistor

(2) At t $=\tau, q=C \sqrt{/ 2}$

(3) At $\mathrm{t}=2 \pi, \mathrm{q}=\mathrm{CV}\left(1-\mathrm{e}^{-2}\right)$

(4) At $\mathrm{t}=\frac{\tau}{2}, \mathrm{q}=\mathrm{CV}\left(1-\mathrm{e}^{-1}\right)$ [JEE Main-2013]

Sol. (3) Q. An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to $\mathrm{Q}_{0}$ and then connected to the L and R as shown below. If a student plots graphs of the square of maximum charge on the capacitor with time (t) for two different values $\mathrm{L}_{1}$ and $\mathrm{L}_{2}\left(\mathrm{L}_{1}>\mathrm{L}_{2}\right)$ of L then which of the following represents this graph correctly ? (plots are schematic and not drawn to scale)  [JEE Main-2015]

Sol. (3)

As damping is happening its amplitude would vary as

The oscillations decay exponentially and will be proportional to $\mathrm{e}^{-\gamma t}$ where $\gamma$ depends inversely on L.

So as inductance increases decay becomes slower

 for Q. An arc lamp requires a direct current of 10A at 80V to function. If it is connected to a 220V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to :-

(1) 0.065 H

(2) 80 H

(3) 0.08 H

(4) 0.044 H

[JEE Main-2016]

Sol. (1) As damping is happening its amplitude would vary as

The oscillations decay exponentially and will be proportional to $\mathrm{e}^{-\gamma t}$ where $\gamma$ depends inversely on L.

So as inductance increases decay becomes slower

 for Q. For an RLC circuit driven with voltage of amplitude $\mathrm{v}_{\mathrm{m}}$ and frequency $\mathrm{w}_{0}=\frac{1}{\sqrt{\mathrm{LC}}}$ the current exhibits resonance. The quality factor, Q is given by :

(1) $\frac{\omega_{0} \mathrm{R}}{\mathrm{L}}$

( 2)$\frac{\mathrm{R}}{\left(\omega_{0} \mathrm{C}\right)}$

(3) $\frac{\mathrm{CR}}{\omega_{0}}$

(4) $\frac{\omega_{0} \mathrm{L}}{\mathrm{R}}$

[JEE Main-2018]

Sol. (4)

Quality factor $=\frac{\omega_{0} \mathrm{L}}{\mathrm{R}}$

Q. In an a. c. circuit, the instantaneous e.m.f. and current are given by e = 100 sin 30 t i = 20

sin $\left(30 t-\frac{\pi}{4}\right)$

In one cycle of a.c., the average power consumed by the circuit and the wattless current are, respectively.

(1) $\frac{1000}{\sqrt{2}}, 10$

(2) $\frac{50}{\sqrt{2}}, 0$

(3) 50, 0

(4) 50, 10

[JEE Main-2018]

Sol. (1)  