A circuit connected to an ac source of emf e = e 0 sin ⁡ 100 t with t in seconds, gives a phase difference of π 4 between the emf e and current i . Which of the following circuits will exhibit this?

R C circuit with R = 1 k Ω and C = 10 μ F

R C circuit with R = 1 k Ω and C = 1 μ F

R L circuit with R = 1 k Ω and L = 1 m H

R L circuit with R = 1 k Ω and L = 10 m H

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

Earn 100

Explain the term: Capacitive reactance.

Important Questions on Alternating Current

HARD

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

An inductance coil has a reactance of

100 Ω

. When an AC signal of frequency

1000 Hz

is applied to the coil, the applied voltage leads the current by

45 °

. The self-inductance of the coil is

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

A series

L R

circuit is connected to a voltage source with

V (t) = V_{0} \sin (ω t)

. After a very large time, current

I (t)

behaves as

(t_{0} ≫ \frac{L}{R})

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

A circuit connected to an ac source of emf

e = e_{0} \sin (100 t)

with

t

in seconds, gives a phase difference of

\frac{π}{4}

between the emf

e

and current

i

. Which of the following circuits will exhibit this?

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

A charged capacitor of capacitance

C

is discharging through a resistor of resistance

R

. At what time the charge on the capacitor is equal to one half of its initial value?

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

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>AC Voltage Applied to a Capacitor

A resistor

R

, an inductor

L

, a capacitor

C

and voltmeters

V_{1}, V_{2}

and

V_{3}

are connected to an oscillator in the circuit as shown in the adjoining diagram. When the frequency of the oscillation is increased, then at the resonant frequency, the voltmeter reading is zero in the case of
Question Image

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

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?
Question Image

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

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)

HARD

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

A sinusoidal voltage of peak value

283 V

and angular frequency

320 s^{- 1}

is applied to a series

L C R

circuit. Given that

R = 5 Ω, L = 25 mH

and

C = 1000 μF

. The total impedance and phase difference between the voltage across the source and the current will respectively be-

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

An arc lamp requires a direct current of 10 A at 80 V to function. If it is connected to a 220 V (rms), 50 Hz AC supply, the series inductor needed for it to work is close to:

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

Three identical emf sources are attached to a single circuit element: a resistor, a capacitor, or an inductor. The current amplitude is then measured as a function of frequency. Which one of the following curve corresponds to inductive circuit?

Question Image

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

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

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

A series

L C R

circuit with

R = 43 Ω

and

L = 0.5 H

has a leading phase angle of

45 °

at a frequency of

50 Hz

. The capacitance used in the circuit is

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

A series

L C R

circuit is connected to an ac voltage source. When

L

is removed from the circuit, the phase difference between current and voltage is

\frac{π}{3}

. If instead

C

is removed from the circuit, the phase difference is again

\frac{π}{3}

between current and voltage. The power factor of the circuit is:

HARD

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

An ideal choke draws a current of

8 A

when connected to a source of

100 V, 50 Hz

When a resistor is connected to the same source, it draws a current of

10 A

. Now the choke and the resistor are connected in series and then connected to a source of

100 V, 40 Hz

. The current in the circuit is

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

600 Hz

, an inductor and capacitor have equal reactances, the ratio of the capacitive reactance to the inductive reactance at

60 Hz

will be

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

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

HARD

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

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

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

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:

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Capacitor

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:
Question Image

Explain the term: Capacitive reactance.

Important Questions on Alternating Current

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