# Physics Class 12 NCERT Solutions: Chapter 7 Alternating Current Part 2

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Q: 6. Obtain the resonant frequency of a series LCR circuit with and . What is the value of this circuit?

Answer: Inductance,

Capacitance,

Resistance,

Resonant frequency is given by the relation,

Now, Q-value of the circuit is given as:

Hence, the Q-Value of this circuit is.

Q: 7. A charged capacitor is connected to a inductor. What is the angular frequency of free oscillations of the circuit?

Answer:

Capacitance,

Inductance,

Angular frequency is given as:

Hence, the angular frequency of free oscillations of the circuit is.

Q: 8. Suppose the initial charge on the capacitor in Exercise is . What is the total energy stored in the circuit initially? What is the total energy at later time?

Answer:

Capacitance of the capacitor,

Inductance of the inductor,

Charge on the capacitor,

Total energy stored in the capacitor can be calculated by the relation,

Total energy at a later time will remain the same because energy is shared between the capacitor and the inductor.

Q: 9. A series LCR circuit with and is connected to a variable-frequency ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle?

Answer:

At resonance, the frequency of the supply power equals the natural frequency of the given LCR circuit.

Resistance,

Inductance,

Capacitance,

AC supply voltage to the LCR circuit,

Impedance of the circuit is given by the relation,

At resonance,

Current in the circuit can be calculated as:

Hence, the average power transferred to the circuit in one complete cycle is,

.