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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Select the correct phasor diagram of the circuit having only resistance.

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Important Questions on Alternating Current

EASY

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

What is meant by Wattless current? Clarify.

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

At very high frequencies, the effective impedance of the given circuit will be _________

Ω .

HARD

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

Derive an expression for average or mean value of alternating current for half cycle.

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

Using

P = V_{r m s} I_{r m s} \cos δ

, discuss any two special cases for power consumed in an AC circuit.

EASY

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

When the rms voltages

V_{L}, V_{C}

and

V_{R}

are measured respectively across the inductor

L,

the capacitor

C

and the resistor

R

in a series

L C R

circuit connected to an

A C

source, it is found that the ratio

V_{L} : V_{C} : V_{R} = 1 : 2 : 3.

If the rms voltage of the

A C

source is

100 V,

then

V_{R}

is close to :

EASY

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

The phaser diagram of the alternating voltage across an unknown device $X$ and current flowing through it are shown below.

Question Image

Draw the graphical variation of current and voltage with $ωt$ through this device.

HARD

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

Assuming expression for impedance in a parallel resonant circuit, state the conditions for parallel resonance. Define resonant frequency and obtain an expression for it.

EASY

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

A parallel combination of pure inductor and capacitor is connected across a source of alternating EMF $e$ . The currents flowing through an inductor and capacitor are $i_{L}$ and $i_{C}$ respectively. In this parallel resonant circuit, the condition for currents $i$ $, i_{L}$ and $i_{C}$ is ( $i =$ net RMS current in the circuit)

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

An alternating voltage

V (t) = 220 \sin (100 π t)

volt is applied to a purely resistive load of

50 Ω

. The time taken for the current to rise from half of the peak value to the peak value is:

EASY

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

AC

circuit has

R = 100 Ω, C = 2 μ F

and

L = 80 mH,

connected in series. The quality factor of the circuit is :

HARD

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

Show that the voltage and current are always in phase when a resistance is connected across an A.C. source. Draw the phasor diagram for it. To tune a radio over a frequency range of

800 k H z t o 1200 k H z

, inductance ‘L’ is kept constant and the corresponding capacitance is varied from

C_{1} t o C_{2}

. Compare

C_{1} t o C_{2}

EASY

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

An alternating emf source of

100 V

50 Hz

is connected to a circuit of resistance

(10 π) Ω

and inductance of

0.173 H

. What is the phase difference between current and emf

EASY

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

A small signal voltage

V (t) = V_{0} \sin ω t

is applied across an ideal capacitor

C

EASY

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

The phase difference between current and voltage in an ac circuit containing resistance only is

HARD

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

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).
Question Image

EASY

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

An alternating voltage

V = 200 \sqrt{2} \sin (100 t) V

is connected to a

1 μ F

capacitor through an AC ammeter. The reading of the ammeter is

EASY

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

A sinusoidal voltage with a frequency of

50 Hz

is applied to a series

L C R

circuit with a resistance of

5 Ω

, inductance of

20 mH

and a capacitance of

500 μ F

. The magnitude of impedance of the circuit is close to

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

100 W

bulb is connected to an

AC

source of

220 V, 50 Hz

. Then the current flowing through the bulb is

EASY

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

Out of the following graphs, which graph shows the correct relation (graphical representation) for LC Parallel resonant circuit?

HARD

Physics>Electricity and Magnetism>Alternating Current>Representation of AC Current and Voltage By Rotating Vectors-Phasors

If the input voltage $V_{i}$ to the circuit below is given by $V_{i} (t) = A \cos (2 π f t),$ the output voltage is given by $V_{o} (t) = B \cos (2 π f t + ϕ)$ .

Question Image

Which one of the following four graphs best depict the variation of $ϕ$ vs $f$ ?

Select the correct phasor diagram of the circuit having only resistance.

Important Questions on Alternating Current

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