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(1) 242 W

(2) 305 W

(3) 210 W

(4) Zero W

**[AIEEE – 2010]**

**Sol.**(1)

(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)

(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)

** [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

(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

(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 $=\frac{\omega_{0} \mathrm{L}}{\mathrm{R}}$

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)

was really interesting