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

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

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

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)

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

In an ideal parallel LC circuit, the capacitor is charged by connecting it to a dc source which is then disconnected. The current in the circuit will:
1. Become zero instantaneously.
2. Grow monotonically.
3. Decay monotonically.
4. Oscillate instantaneously.

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

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 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)