A transistor-oscillator using a resonant circuit with an inductance \(L\) (of negligible resistance) and a capacitance \(C\) has a frequency \(f.\) If \(L\) is doubled and \(C\) is changed to \(4C,\) the frequency will be:
1. \(f/4\)
2. \(8f\)
3. \(f/2\sqrt2\)
4. \(f/2\)

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.

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

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)

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

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

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

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)

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

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