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Important Questions on Electromagnetic Induction and Alternating Currents

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

A series R-C circuit is connected to an alternating voltage source. Consider two situations:

i. When capacitor is air filled.

ii. When capacitor is mica filled.

Current through resistor is

i

and voltage across capacitor is

V

then:

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

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In the above circuit, $C = \frac{\sqrt{3}}{2} μ F, R_{2} = 20 Ω, L = \frac{\sqrt{3}}{10} H$ and $R_{1} = 10 Ω .$ Current in $L - R_{1}$ path is $I_{1}$ and in $C - R_{2}$ path it is $I_{2} .$ The voltage of AC source is given by, $V = 200 \sqrt{2} \sin (100 t)$ volts. The phase difference between $I_{1}$ and $I_{2}$ is:

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

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?

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor

C^{'}

, when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor

C^{'}

, must have been connected in:
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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

An inductor

20 mH

, a capacitor

50 μ F

and a resistor

40 Ω

are connected in series across a source of emf

V = 10 \sin 340 t

. The power loss in

AC

circuit is:

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

In the given circuits

(a)

and

(b)

, switches

S_{1}

and

S_{2}

are closed at

t = 0

and kept close for a long time. The variation of currents in the two circuits for

t \geq 0

are shown in the options. (Figures are schematic and not drawn to scale.)
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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

A series

A C

circuit containing an inductor

(20 mH),

a capacitor

(120 μ F)

and a resistor

(60 Ω)

is driven by an

A C

source of

24 V / 50 Hz .

The energy dissipated in the circuit in

60 s

is:

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

The potential differences across the resistance, capacitance, and inductance are

80 V, 40 V

and

100 V

, respectively in an LCR circuit. The power factor of this circuit is

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

An infinite line charge of uniform electric charge density

λ

lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled with a material of permittivity

ε

and electrical conductivity

σ

. The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density j(t) at any point in the material?

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

In the circuit shown below, the key is pressed at time $t = 0$ . Which of the following statement(s) is(are) true?
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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

The AC voltage across a resistance can be measured using a:

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

An inductor $(L = 0.03 H)$ and a resistor $(R = 0.15 kΩ)$ are connected in series to a battery of $15 V$ E.M.F. in a circuit shown below. The key $K_{1}$ has been kept closed for a long time. Then at $t = 0$ , $K_{1}$ is opened and key $K_{2}$ is closed simultaneously. At $t = 1 ms$ , the current in the circuit will be : $(Take, e^{5} \approx 150)$

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

An alternating voltage

V = V_{0} s i n ω t

is connected to a capacitor of capacity

C

through an A.C. ammeter of zero resistance. The reading of ammeter is

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

In an

LCR

circuit as shown below both switches are open initially. Now switch

S_{1}

is closed,

S_{2}

kept open. (

q

is charge on the capacitor and

τ = RC

is capacitive time constant). Which of the following statement is correct?
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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

A resistance

R

draws power

P

when connected to an

AC

source. If an inductance is now placed in series with the resistance, such that the impedance of the circuit becomes

Z

, the power drawn will be:

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

In the following circuit the switch $S$ is closed at $t = 0$ . The charge on the capacitor $C_{1}$ as a function of time will be given by $(C_{e q} = \frac{C_{1} C_{2}}{C_{1} + C_{2}})$

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

Which of the following combinations should be selected for better tuning of an LCR circuit used for communication?

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Physics>Electricity and Magnetism>Electromagnetic Induction and Alternating Currents>RC, LR and LC Circuits with D.C. and A.C. Sources

In the figure shown, a circuit contains two identical resistors with resistance $R = 5 Ω$ and an inductance with $L = 2 m H .$ An ideal battery of $15 V$ is connected in the circuit. What will be the current through the battery long after the switch is closed?

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