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Physics Part-I

Alternating Current

A series LCR circuit with L = 0.12 H. C = 480 nF, R = 23 is c

Physics Part-I

Class 12

NCERT

Chapter 1: Electric Charges and Fields

47 questions

Chapter 2: Electrostatic Potential and Capacitance

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Chapter 3: Current Electricity

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Chapter 4: Moving Charges and Magnetism

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Chapter 5: Magnetism and Matter

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Chapter 6: Electromagnetic Induction

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Chapter 7: Alternating Current

37 questions

Suppose the circuit in Exercise 7.18 has a resistance of 15 Ω. Obtain the average power transferred to each element of the circuit, and the total power absorbed.

A series LCR circuit with L = 0.12 H. C = 480 nF, R = 23

Ω

is connected to a 230 V 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 Q-factor of the given circuit?

Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H,

C = 27 μ F

, and

R = 7.4Ω

. It is desired to improve the sharpness of the resonance of the circuit by reducing its 'full width at half maximum' by a factor of 2. Suggest a suitable way.

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A series LCR circuit with L = 0.12 H. C = 480 nF, R = 23 $Ω$ is connected to a 230 V 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 Q-factor of the given circuit?

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Updated on: Jul 25, 2022

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Physics Part-I (NCERT)

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A series LCR circuit with L = 0.12 H. C = 480 nF, R = 23

Ω

is connected to a 230 V 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 Q-factor of the given circuit?

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

(a)

V_{o} = 2 V = 325.2 v o lt s

Tt resonance,

ω_{R} L = 1/ (ω_{R} C)

We know that,

\Rightarrow ω_{R} = 1/ L C = 4166.67 r a d / s

Resonant frequency,

ν_{R} = ω_{R} /2 π = 663.48 Hz

I_{o} = V_{o} / R = 14.14 A

(b)

Maximum power absorbed

P = \frac{1}{2} I_{o}^{2} R \frac{1}{2} (14.14)^{2} \times 23 \Rightarrow 2299.3 W

(c)

The angular frequencies at which the power would be half of the power at resonant frequency will be:

ω^{'} = ω_{R} \pm Δ ω

Here,

Δ ω = \frac{R}{2 L}

\Rightarrow Δ ω = \frac{23}{2 \times 0.12} ⟹ 95.83 r a d / s

So,

ω_{1}^{'} = 4166.67 + 95.83 = 4262.3 r a d / s

ω_{2}^{'} = 4166.67 - 95.83 = 4070.87 r a d / s

The amplitude of current at these frequencies will be the RMS value.

I = \frac{I _{0}}{2} \Rightarrow \frac{14.14}{1.414} \Rightarrow 10 A

(d)

Q factor is given by

Q = \frac{1}{R} \frac{L}{C} = \frac{1}{23} \frac{0.12}{480 \times 1 0 ^{- 9}} = 21.74

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Practice more questions from Physics Part-I (NCERT)

Suppose the circuit in Exercise 7.18 has a resistance of 15 Ω. Obtain the average power transferred to each element of the circuit, and the total power absorbed.

A series LCR circuit with L = 0.12 H. C = 480 nF, R = 23

Ω

is connected to a 230 V 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 Q-factor of the given circuit?

Obtain the resonant frequency and Q-factor of a series LCR circuit with L = 3.0 H,

C = 27 μ F

, and

R = 7.4Ω

. It is desired to improve the sharpness of the resonance of the circuit by reducing its 'full width at half maximum' by a factor of 2. Suggest a suitable way.

View all

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Question Text	A series LCR circuit with L = 0.12 H. C = 480 nF, R = 23 $Ω$ is connected to a 230 V 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 Q-factor of the given circuit?
Updated On	Jul 25, 2022
Topic	Alternating Current
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 4
Upvotes	364
Avg. Video Duration	11 min

Text solutionVerified

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