A bulb is rated at \(100\) V, \(100\) W, and is treated as a resistor. The inductance of an inductor (choke coil) that should be connected in series with the bulb to operate the bulb at its rated power with the help of an AC source of \(200\) V and \(50\) Hz is:
1. \(\dfrac{\pi }{\sqrt{3}}~\text{H}\)
2. \(100~\text{H}\)
3. \(\dfrac{\sqrt{2}}{\pi }~\text{H}\)
4. \(\dfrac{\sqrt{3}}{\pi }~\text{H}\)

What is the phase difference between potential difference across the inductor and potential difference across the capacitor in a series LCR circuit?

1. Zero

$2.<mspace\; width="1em"></mspace>\frac{\pi }{4}$
$3.<mspace\; width="1em"></mspace>\frac{\pi }{4}$
$4.<mspace\; width="1em"></mspace>\pi$

What is the reading of the A.C voltmeter in the network as shown in the figure?

1. zero

2. 100 V

3. 200 V

4. 400 v

When an alternating voltage is given as; \(E = (6 \sin\omega t - 2 \cos \omega t)~\text V,\) what is its RMS value?
1. \(4 \sqrt 2 ~\text V\) 
2. \(2 \sqrt 5 ~\text V\) 
3. \(2 \sqrt 3 ~\text V\) 
4. \(4 ~\text V\) 

An LC circuit contains an inductor (L=25 mH) and a capacitor (C=25 mF) with an initial charge of Q₀. At what time will the circuit have an equal amount of electrical and magnetic energy?

$1.$ $\frac{\mathrm{\pi }}{\mathrm{160<mspace\; width="1em"></mspace>}}s$

$2.$ $\frac{3\mathrm{\pi }}{\mathrm{160<mspace\; width="1em"></mspace>}}s$

$3.$ $\frac{5\mathrm{\pi }}{\mathrm{160<mspace\; width="1em"></mspace>}}s$

4. All of these

In which of the following circuits can the power factor be zero?

1. LC circuit

2. LCR circuit

3. Purely resistive circuit

4. Both (1) & (2)

In the given circuit, switch S is closed at t=0. After a long time, the iron rod is withdrawn from the inductor L. Then, the bulb

1. Glow with the same brightness

2. Glows more brightly

3. Gets dimmer

4. Stops glowing

LCR series circuit is connected with an alternating emf source. If the peak current and voltage are $l_{0<mspace\; width="1em"></mspace>}and<mspace\; width="1em"></mspace>V_0$ respectively then at resonance the value of wattless current is

$1.<mspace\; width="1em"></mspace>l_0$
$2.<mspace\; width="1em"></mspace>\frac{l_0}{\sqrt{2}}$
$3.<mspace\; width="1em"></mspace>\sqrt{2}{l}_0$
$4.<mspace\; width="1em"></mspace>zero<mspace\; width="1em"></mspace>$

The value of quality factor ( Q-value) of the series resonant circuit with inductance L = 2.0 H, capacitance C= 32 $\mu F$ and resistance R = 10 $\Omega$, is

1. 25

2. 250

3. 0.25

4. 2.5

Given below are two statements: