At time t = 0 , terminal A in the circuit shown in the figure is connected to B by a key and an alternating current I t = I 0 cos ω t , with I 0 = 1 A and ω = 500 rad s - 1 starts flowing in it with the initial direction shown in the figure. At t = 7 π 6 ω , the key is switched from B to D. Now onwards only A and D are connected. A total charge Q flows from the battery to charge the capacitor fully. If C = 20 μ F , R = 10 Ω and the battery is ideal with of 50 V , identify the correct statement(s).

Magnitude of the maximum charge on the capacitor before t = 7 π 6 ω is 1 × 10 - 3 C .

The current in the left part of the circuit just before t = 7 π 6 ω is clockwise.

EASY

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The resonance frequency of $L C$ circuit is

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Important Questions on Electromagnetic Induction

EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

An oscillating

LC

circuit consists of a

75 mH

inductor and a

1.2 µ F

capacitor. If the maximum charge to the capacitor is

2.7 µ C

. The maximum current in the circuit will be

_______mA

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

In an oscillating

L C

circuit,

L = 3.00 mH

and

C = 2.70 μ F

. At

t = 0

the charge on the capacitor is zero and the current is

2.00 A

. The maximum charge that will appear on the capacitor will be

EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

A capacitor of capacitance

500 μ F

is charged completely using a DC supply of

100 V

. It is now connected to an inductor of inductance

50 mH

to form an LC circuit. The maximum current in LC circuit will be _____

A

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

At time

t = 0

, terminal

A

in the circuit shown in the figure is connected to

B

by a key and an alternating current

I (t) = I_{0} \cos (ω t)

, with

I_{0} = 1 A

and

ω = 500 rad s^{- 1}

starts flowing in it with the initial direction shown in the figure. At

t = \frac{7 π}{6 ω}

, the key is switched from B to D. Now onwards only A and D are connected. A total charge

Q

flows from the battery to charge the capacitor fully. If

C = 20 μ F, R = 10 Ω

and the battery is ideal with of

50 V

, identify the correct statement(s).

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

A fully charged capacitor

C

with initial charge

q_{0}

is connected to a coil of self-inductance

L

t = 0 .

The time at which the energy is stored equally between the electric and the magnetic fields is:

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

In the figure below, the switches

S_{1} a n d S_{2}

are closed simultaneously at

t = 0

and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current I in the middle wire reaches its maximum magnitude

I_{m a x}

time

t = τ

. Which of the following statements is (are) true?

EASY

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

L C

oscillations are similar and analogous to the mechanical oscillations of a block attached to a spring. The electrical equivalent of the force constant of the spring is

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

In the circuit shown, initially there is no charge on capacitors and keys

S_{1}

and

S_{2}

are open. The values of the capacitors are

C_{1} = 10 μ F, C_{2} = 30 μ F

and

C_{3} = C_{4} = 80 μ F .

Which of the statement(s) is/are correct?

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

An LCR circuit is equivalent to a damped pendulum. In an LCR circuit the capacitor is charged to

Q_{0}

and then connected to the L and R as shown below:

If a student plots graphs of the square of maximum charge

(Q_{M a x}^{2})

on the capacitor with time (t) for two different values

L_{1}

and

L_{2} (L_{1} > L_{2})

of L then which of the following represents this graph correctly? (plots are schematic and not drawn to scale)

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

At a certain moment, the switch shown in the figure is disconnected. The energy of the oscillations immediately after the switch $S$ is disconnected and at time $0.1 \sec$ from the time switch is disconnected are, respectively

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

In the circuit shown,

L = 1 μ H, C = 1 μ F a n d R = 1 k Ω .

They are connected in series with an a.c. source

V = V_{0} \sin ω t

as shown. Which of the following options is/are correct?

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

L C R

circuit behaves like a clamped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant

' b^{'},

the correct equivalence would be:

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

A source of constant voltage

V

is connected to a resistance

R

and two ideal inductors

L_{1}

and

L_{2}

through a switch

S

as shown. There is no mutual inductance between the two inductors. The switch

S

is initially open. At

t = 0

, the switch is closed and current begins to flow. Which of the following options is/are correct?

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

In the circuit shown below, the key is pressed at time $t = 0$ . Which of the following statement(s) is(are) true?

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

The instantaneous voltages at three terminals marked

X, Y

and

Z

are given by

V_{X} = V_{0} \sin ω t

V_{Y} = V_{0} \sin (ω t + \frac{2 π}{3})

and

V_{Z} = V_{0} \sin (ω t + \frac{4 π}{3}) .

An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points

X

and

Y

and then between

Y

and

Z

. The reading(s) of the voltmeter will be

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

In a circuit shown in the figure, the capacitor $C$ is initially uncharged and the key $K$ is open. In this condition, a current of $1 A$ flows through the $1 Ω$ resistor. The key is closed at time $t = t_{0}$ . Which of the following statement(s) is(are) correct?

[Given : $e^{- 1} = 0.36$ ]

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

400 Ω

resistor, a

250 mH

inductor and a

2.5 μ F

capacitor are connected in series with an

AC

source of peak voltage

5 V

and angular frequency

2 kHz

. What is the peak value of the electrostatic energy of the capacitor?

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

In an LC circuit connected to an ac supply, the resonant frequency is

200 MHz

when a dielectric of thickness

8 mm

and dielectric constant

6

is fully inserted between the plates of the capacitor. The resonant frequency becomes

198 MHz

when a stress of

995

bar is applied between the plates of the capacitor. The Young's modulus of the dielectric material in

{Nm}^{- 2}

is nearly

HARD

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

L C

circuit the inductance

L = 40 mH

and capacitance

C = 100 μF .

If a voltage

V (t) = 10 s i n (314 t)

is applied to the circuit, the current in the circuit is given as:

MEDIUM

Physics>Electricity and Magnetism>Electromagnetic Induction>LC Oscillations

An oscillator circuit contains an inductor

0.05 H

and a capacitor of capacity

80 μF

. When the maximum voltage across the capacitor is

200 V

, the maximum current (in amperes) in the circuit is

The resonance frequency of LC circuit is

Important Questions on Electromagnetic Induction

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The resonance frequency of $L C$ circuit is