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 After a long time, the iron rod is withdrawn from the inductor L. Then, the bulb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: 

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R): 

In the light of the above statements choose the correct answer from the options given below:
 

A: When the frequency of the AC source in a series LCR circuit equals to the resonant frequency, the reactance of the circuit is zero.

R: There is maximum current through the inductor as well as a capacitor at resonance.

1. If both Assertion & Reason are true and the reason is the correct explanation of the assertion, then mark (1)

2. If both Assertion & Reasons are true but the reason is not the correct explanation of the assertion, then mark (2)

3. If Assertion is a true statement but the reason is false, the mark (3)

4. If both Assertion and Reason are false statements, then mark (4)

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. \(4 ~\text V\) 

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