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Physics Part-I

Alternating Current

Figure shows a series LCR circuit connected to a variable freq

Physics Part-I

Class 12

NCERT

Chapter 1: Electric Charges and Fields

47 questions

Chapter 2: Electrostatic Potential and Capacitance

46 questions

Chapter 3: Current Electricity

33 questions

Chapter 4: Moving Charges and Magnetism

41 questions

Chapter 5: Magnetism and Matter

36 questions

Chapter 6: Electromagnetic Induction

28 questions

Chapter 7: Alternating Current

37 questions

A radio can tune over the frequency range of a portion of MW broadcast band: (800 kHz to 1200 kHz). If its LC circuit has an effective inductance of 200

μ

H, what must be the range of its variable capacitor?

[Hint: For tuning, the natural frequency i.e., the frequency of free oscillations of the LC circuit should be equal to the frequency of the radiowave.]

Figure shows a series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80 μF, R = 40Ω.
(a) Determine the source frequency which drives the circuit in resonance.
(b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.
(c) Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.

An LC circuit contains a 20 mH inductor and a 50

μ

F 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.(a) What is the total energy stored initially? Is it conserved during LC oscillations?

(b) What is the natural frequency of the
circuit?

(i) completely electrical (i.e., stored in the capacitor)?

(ii) completely magnetic (i.e. stored in the inductor)?

(d) At what times is the total energy shared
equally between the inductor and the capacitor?

(e) If a resistor is inserted in the circuit,

how much energy is eventually dissipated as heat?

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Chapter 8: Electromagnetic Waves

20 questions

Question

Medium

Solving time: 4 mins

Figure shows a series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80 μF, R = 40Ω.
(a) Determine the source frequency which drives the circuit in resonance.
(b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency.
(c) Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.

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Updated on: Nov 19, 2023

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Physics Part-I (NCERT)

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Text solutionVerified

(a)

The resonance frequency is given by

ω = \frac{1}{L C} = \frac{1}{5 \times 80 \times 1 0 ^{- 6}} = 50 r a d / s

The resonant frquency is 50 rad/s.

(b)

At resonance, $ω L = 1/ ω C$

$\Rightarrow Z = R = 40Ω$

The peak voltage, $V_{o} = 2 V$

$I_{o} = 2 V / Z$

$I_{o} = 8.13 A$

(c)

Potential drop across inductor,

$V_{L (r m s)} = I \times ω_{R} L$

$I = I_{0} / 2 = 2 V / 2 Z = 23/40 A$

$\Rightarrow V_{r m s} = 1437.5 V$

Potential drop across capacitor,

$(V_{c})_{r m s} = I \times \frac{1}{w _{r} C} = 1437.5 V$

Potential drop across resistor,

$(V_{R})_{r m s} = I \times R = 230 V$

Potential drop across the LC combination

$V_{L C}$ = $I$ ( $X_{L}$ - $X_{C}$ )

at resonance $X_{L}$ = $X_{C}$ $\Rightarrow V_{L C} = 0 V$

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Practice more questions from Physics Part-I (NCERT)

A radio can tune over the frequency range of a portion of MW broadcast band: (800 kHz to 1200 kHz). If its LC circuit has an effective inductance of 200

μ

H, what must be the range of its variable capacitor?

[Hint: For tuning, the natural frequency i.e., the frequency of free oscillations of the LC circuit should be equal to the frequency of the radiowave.]

An LC circuit contains a 20 mH inductor and a 50

μ

(b) What is the natural frequency of the
circuit?

(i) completely electrical (i.e., stored in the capacitor)?

(ii) completely magnetic (i.e. stored in the inductor)?

(d) At what times is the total energy shared
equally between the inductor and the capacitor?

(e) If a resistor is inserted in the circuit,

how much energy is eventually dissipated as heat?

View all

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Question Text	Figure shows a series LCR circuit connected to a variable frequency 230 V source. L = 5.0 H, C = 80 μF, R = 40Ω. (a) Determine the source frequency which drives the circuit in resonance. (b) Obtain the impedance of the circuit and the amplitude of current at the resonating frequency. (c) Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.
Updated On	Nov 19, 2023
Topic	Alternating Current
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 5
Upvotes	581
Avg. Video Duration	10 min

Text solutionVerified

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