# Physics Class 12 NCERT Solutions: Chapter 7 Alternating Current Part 8 (For CBSE, ICSE, IAS, NET, NRA 2022)

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Q: 19. Suppose the circuit in Exercise has a resistance of . Obtain the average power transferred to each element of the circuit, and the total power absorbed.

Average power transferred to the resistor

Average power transferred to the capacitor

Total power absorbed by the circuit

Inductance of inductor

Capacitance of capacitor,

Resistance of resistor,

Potential of voltage supply,

Frequency of signal,

Angular frequency of signal,

The elements are connected in series to each other. Hence, impedance of the circuit is given as:

Current flowing in the circuit,

Average power transferred to resistance is given as:

Average power transferred to capacitor, Average power transferred to inductor,

Total power absorbed by the circuit:

Hence, the total power absorbed by the circuit is .

Q: 20. A series LCR circuit with is connected to a variable frequency supply.

(A) What is the source frequency for which current amplitude is maximum. Obtain this maximum value.

(B) What is the source frequency for which average power absorbed by the circuit is maximum. Obtain the value of this maximum power.

(C) For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency? What is the current amplitude at these frequencies?

(D) What is the factor of the given circuit?

Inductance,

Capacitance,

Resistance,

Supply voltage,

Peak voltage is given as:

(A) Current flowing in the circuit is given by the relation,

Where,

Maximum at resonance

At resonance, we have

Where,

Resonance angular frequency

∴ Resonant frequency,

And, maximum current

(B) Maximum average power absorbed by the circuit is given as:

Hence, resonant frequency is .

(C) The power transferred to the circuit is half the power at resonant frequency.

Frequencies at which power transferred is half,

Where,

Hence, change in frequency,

And,

Hence, at and frequencies, the power transferred is half.

At these frequencies, current amplitude can be given as:

(D) Q-factor of the given circuit can be obtained using the relation,

Hence, the Q-factor of the given circuit is .

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