Match List-I with List-II List-i List-II a Phase difference between current and voltage in a purely resistive AC circuit i π 2 ; current leads voltage b Phase difference between current and voltage in a pure inductive AC circuit ii zero c Phase difference between current and voltage in a pure capacitive AC circuit iii π 2 ; current lags voltage d Phase difference between current and voltage in an LCR series circuit iv tan - 1 X C - X L R Choose the most appropriate answer from the options given below :

( a )-( ii ) , ( b ) - ( iii ) , ( c ) - ( i ) , ( d ) - ( iv )

( a ) - ( i ) , ( b ) - ( iii ) , ( c ) - ( iv ) , ( d ) - ( ii )

( a ) - ( ii ) , ( b ) - ( iv ) , ( c ) - ( iii ) , ( d ) - ( i )

( a ) - ( ii ) , ( b ) - ( iii ) , ( c ) - ( iv ) , ( d ) - ( i )

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Phase of current in $L - C - R$ circuits:

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Important Questions on AC Circuits

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Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

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

HARD

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

For a series

R L C

circuit

R = X_{L} = 2 X_{C}

. The impedance of the circuit and phase difference between

V

and

I

, respectively will be

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

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>AC Circuits>Reactance and Impedance

L . C . R .

circuit contains resistance of

110 Ω

and a supply of

220 V

300 rad s^{- 1}

angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by

45 °

. If on the other hand, the only the inductor is removed the current leads by

45 °

with the applied voltage. The

R . M . S .

current flowing in the circuit will be:

HARD

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

750 Hz, 20 V (rms)

source is connected to a resistance of

100 Ω,

an inductance of

0.1803 H

and a capacitance of

10 μ F

all in series. The time in which the resistance (heat capacity

2 J / ° C

) will get heated by

10 ° C .

(assume no loss of heat to the surroundings) is close to :

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

In a series

L C R

circuit with an alternating voltage source of frequency

f

, the current leads the voltage by

45 °

. The value of

c

EASY

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

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>AC Circuits>Reactance and Impedance

In an

L C R

series circuit, an inductor

30 mH

and a resistor

1 Ω

are connected to an

AC

source of angular frequency

300 rad s^{- 1} .

The value of capacitance for which the current leads the voltage by

45 °

\frac{1}{x} \times 10^{- 3} F

. Then the value of

x

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

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:

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

In a series circuit,

R = 300 Ω, L = 0.9 H,

C = 2.0 μF

and

ω = 1000 rad s^{- 1}

. The impedance of the circuit is

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

In a series LCR circuit, the inductive reactance

(X_{L})

10 Ω

and the capacitive reactance

(X_{C})

4 Ω

. The resistance

(R)

in the circuit is

6 Ω

. The power factor of the circuit is :

HARD

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

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>AC Circuits>Reactance and Impedance

Match List-I with List-II

	List-i		List-II
a	Phase difference between current and voltage in a purely resistive AC circuit	i	$\frac{π}{2};$ current leads voltage
b	Phase difference between current and voltage in a pure inductive AC circuit	ii	zero
c	Phase difference between current and voltage in a pure capacitive AC circuit	iii	$\frac{π}{2};$ current lags voltage
d	Phase difference between current and voltage in an LCR series circuit	iv	$\tan^{- 1} (\frac{X_{C} - X_{L}}{R})$

Choose the most appropriate answer from the options given below :

HARD

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

When a $60 mH$ inductor and a resistor are connected in series with an $A C$ voltage source, the voltage leads the current by $60 °$ . If the inductor is replaced by a $0.5 μF$ capacitor, the voltage lags behind the current by $30 °$ . What is the frequency of the $A C$ supply?

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

For a series

LCR

circuit with

R = 100 Ω, L = 0.5 mH

and

C = 0.1 pF

connected across

220 V - 50 Hz

AC

supply, the phase angle between
current and supplied voltage and the nature of the circuit is:

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

A resistance of

5 Ω

is connected in series with a capacitance of

1 mF

. The combination is connected to AC source of angular frequency

200 {rads}^{- 1}

. Then

HARD

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

A $0.07 H$ inductor and a $12 Ω$ resistor are connected in series to a $220 V, 50 Hz$ AC source. The approximate current in the circuit and the phase angle between current and source voltage are respectively.

[Take $π$ as $\frac{22}{7}]$

MEDIUM

Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

A light bulb and an inductor coil are connected to an ac source through a key as shown in the figure below. The key is closed and after sometime an iron rod is inserted into the interior of the inductor. The glow of the light bulb

Question Image

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Physics>Electricity and Magnetism>AC Circuits>Reactance and Impedance

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>AC Circuits>Reactance and Impedance

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:

Phase of current in L-C-R circuits:

Important Questions on AC Circuits

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Phase of current in $L - C - R$ circuits: