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Physics Part-I

Alternating Current

An LC circuit contains a 20 mH inductor and a 50 capacitor wi

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

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?

A coil of inductance 0.50 H and resistance

100Ω

is connected to a 240 V, 50 Hz ac supply.

(a) What is the maximum current in the coil?

(b) What is the time lag between the voltage maximum and the current maximum?

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Chapter 8: Electromagnetic Waves

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Question

Hard

Solving time: 4 mins

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?
(c) At what time is the energy stored
(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?

Uploaded: 2022-05-22T06:00:02.000Z
Duration: 3 min

Views: 5,933 students

Updated on: May 24, 2022

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Physics Part-I (NCERT)

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Sebastian Discussed

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?

15 mins ago

Discuss this question LIVE

15 mins ago

Text solutionVerified

(a)

The energy stored initially in the capacitor is given by:

E = \frac{Q ^{2}}{2 C}

= \frac{( 10 \times 1 0 ^{- 3} ) ^{2}}{2 \times 50 \times 1 0 ^{- 6}} = 1 J

Yes. The energy is conserved. It only gets converted from electrical to magnetic and vice versa.

(b)

Natural frequency of oscillation of the circuit is given by,

ν = 1/2 π L C

ν = 159.24 Hz

(c)

(i) Time period,

T = 1/ f = 6.28 s

total charge on capacitor at time

t = Q^{^{'}} = Q cos (\frac{2 π}{T} t)

For energy stored in electrical, we can write,

Q^{^{'}} = \pm Q

It can be inferred that the energy stored in capacitor is completely electrical at time,

t = 0, T /2, 3 T /2, ...

(ii) Magnetic energy is maximum when the electrical energy is zero. hence,

t = T /4, 3 T /4, 5 T /4, ...

(d)

Q_{1}

is the charge when total energy is equally shared.

\Rightarrow \frac{1}{2} \frac{Q _{1}^{2}}{C} = \frac{1}{2} (\frac{1}{2} \frac{Q ^{2}}{C})

Q_{1} = \pm Q / 2

but,

Q_{1} = Q cos 2 π t / T

\Rightarrow cos 2 π t / T = \pm 1/ 2 \Rightarrow t = (2 n + 1) T /8

so,

t = T /8, 3 T /8, 5 T /8

(e)

The energy stored initially is

E = \frac{Q ^{2}}{2 C} = \frac{( 10 \times 1 0 ^{- 3} ) ^{2}}{2 \times 50 \times 1 0 ^{- 6}} = 1 J

When the resistor is inserted in the circuit, it will dissipate entire 1J in heat.

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Practice more questions from Physics Part-I (NCERT)

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?

A coil of inductance 0.50 H and resistance

100Ω

is connected to a 240 V, 50 Hz ac supply.

(a) What is the maximum current in the coil?

(b) What is the time lag between the voltage maximum and the current maximum?

View all

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Question Text	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? (c) At what time is the energy stored (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?
Updated On	May 24, 2022
Topic	Alternating Current
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 2
Upvotes	255
Avg. Video Duration	5 min

Text solutionVerified

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