For which of the following reasons are LC oscillations not sustainable for long?

1.	Every inductor has some resistance.
2.	The effect of resistance is to introduce a damping effect on the charge & current in the circuit and the oscillations finally die away.
3.	Even if the resistance is zero, the total energy of the system is radiated away from the system in the form of electromagnetic radiation.
4.	All of the above

A charged 30 µF capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit?

1. \(1.11 \times 10^{3} \ rad/s\)
2.\(2.11 \times 10^{3} \ rad/s\)
3.\(1.11 \times 10^{2} \ rad/s\)
4.\(1.11 \times 10^{4} \ rad/s\)

An LC circuit contains a 20 mH inductor and a 50 µF capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be t = 0. What is the total energy stored initially? 

1. 1.0 J
2. 2.0 J
3. 2.2 J
4. 3.3 J

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)

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?

$1.$ $\frac{\mathrm{\pi }}{\mathrm{160 }}s$

$2.$ $\frac{3\mathrm{\pi }}{\mathrm{160 }}s$

$3.$ $\frac{5\mathrm{\pi }}{\mathrm{160 }}s$

4. All of these

What is the value of the power factor for a parallel LC circuit at a frequency less than the resonance frequency?

1. Zero

2. 1

3. > 1

4.< 1

In LC oscillation, what is the current in the circuit when the total energy is stored in the form of magnetic energy?
(q₀ is the maximum charge stored by the capacitor)

$1.$ $Zero$ $$
$2.$ $\frac{q_0}{\sqrt{Lc}}$ $$
$3.$ $\frac{q_0}{LC}$ $$
$4.$ $q_0\sqrt{LC}$

The natural frequency of the circuit shown in the figure is:
    

1. $\frac{1}{2\mathrm{\pi }\sqrt{\mathrm{LC}}}$

2. $\frac{1}{\mathrm{\pi }\sqrt{\mathrm{LC}}}$

3. $\frac{2}{\mathrm{\pi }\sqrt{\mathrm{LC}}}$

4. None of these

To reduce the resonant frequency in an LCR series circuit with a generator:

A condenser of capacity C is charged to a potential difference of V₁. The plates of the condenser are then connected to an ideal inductor of inductance L. The current through the inductor, when the potential difference across the condenser reduces to V₂ is:

1. $\frac{C\left(V_1^2-V_2^2\right)}{L}$

2. $\frac{C\left(V_1^2+V_2^2\right)}{L}$

3. ${\left(\frac{C\left(V_1^2-V_2^2\right)}{L}\right)}^{1/2}$

4. ${\left(\frac{C{\left(V_1-V_2\right)}^2}{L}\right)}^{1/2}$