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

At an airport, a person is made to walk through the doorway of a metal detector, for security reasons. If she/he is carrying anything made of metal, the metal detector emits a sound. On what principle does this detector work?

In the free oscillations of an LC circuit, the sum of energies stored in the capacitor and the inductor is:

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

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

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.\(1.11 \times 10^{4} \ rad/s\)

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

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