This set of Class 12 Physics Chapter 7 Multiple Choice Questions & Answers (MCQs) focuses on “Alternating Current – LC Oscillations”.

1. LED lights of chargers glow even after it is switched off. Which of the following causes this situation?

a) LC Oscillations

b) Phasors

c) Power of the AC circuit

d) Eddy currents

View Answer

Explanation: This situation is caused due to LC Oscillations. These circuits consist capacitors and inductors, thus the energy keeps oscillating in the circuit even after the electric connection is disconnected. The combination of a capacitor and an inductor constitutes an LC oscillator circuit.

2. Find the true statement.

a) When a resistor is connected to an inductor, the electric current in the circuit undergoes LC oscillations

b) When a resistor is connected to a capacitor, the electric current in the circuit undergoes LC oscillations

c) When a charged capacitor is connected to an inductor, the electric current in the circuit and charge on the capacitor undergoes LC oscillations

d) When a charged capacitor is connected to an inductor, only the electric current in the circuit undergoes LC oscillations

View Answer

Explanation: When we are connecting a charged capacitor to an inductor, the electric current in the circuit and charge on the capacitor undergoes LC oscillations. All the others are incorrect statements regarding LC Oscillations.

3. A capacitor of capacitance 5μF is charged to a potential difference of 20V. After that, it is connected across an inductor of inductance 0.5 mH. What is the current flowing in the circuit at a time when the potential difference across the capacitor is 10 V?

a) 1 A

b) 2 A

c) 5 A

d) 0.5 A

View Answer

Explanation: Given: V

_{2}= 10 V; V

_{1}= 20 V; C = 5 μF; Inductance (I) = 0.5 mH

Initial charge on the capacitor (q

_{1}) = C × V

_{1}= 5 × 10

^{-6}× 20 ……………….1

q

_{1}= 10

^{-4}C …………..B

The instantaneous charge on the capacitor as the capacitor discharges through the inductor ➔ q

_{2}

q

_{2}= q

_{1}cos (ωt) ➔ \(\frac {q_2}{q_2}\) = cos (ωt) ………………..A

Also, q

_{2}= C × V

_{2}= 5 × 10

^{-6}× 10 …………………….2

q

_{2}= 0.5 × 10

^{-4}C

From 1 and 2 ➔ \(\frac {q_2}{q_2} = \frac {V_2}{V_1}\) ➔ \(\frac {q_2}{q_2}\) = 0.5 = \(\frac {1}{2}\)

From equation A, we can equate as follows ➔ cos (ωt) = \(\frac {1}{2}\)

ωt = \(\frac {\pi }{2}\) rad ………………..3

For an LC circuit ➔ ω=\(\frac {1}{\sqrt {LC}}\)

ω=20000\(\frac {rad}{s}\) …………………….4

The current through the circuit is given as:

Current (I)=-\(\frac {dq}{dt}\)

Charge decreases with respect to time, so, \(\frac {dq}{dt}\) obtained will be negative and this is why we add a negative sign to make a current positive.

Current = q

_{1}ω sinωt

Considering 3, 4 and B

Current = 10

^{-4}× 20000 × sin (\(\frac {\pi }{2}\))

Current = 2 A [Sin(\(\frac {\pi }{2}\)) = 1]

Therefore, the current flowing through the circuit is 2 A.

4. LC oscillations only continues at a definite frequency.

a) True

b) False

View Answer

Explanation: No, this statement is false. The process of LC oscillations, caused when we connect a charged capacitor to an inductor, continues at a definite frequency. But when the resistance in the LC circuit is zero, the LC oscillations continue at indefinite frequency. Therefore, indefinite frequency is also possible.

5. What is the most common application of LC oscillators?

a) Radio transmitters

b) Switches

c) Torch

d) Fans

View Answer

Explanation: The most common application of LC oscillators is radio transmitters and receivers. LC oscillators have good phase noise characteristics as well as offer ease of implementation. Due to these factors, LC oscillators are most commonly used in radio-frequency circuits.

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