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 )

EASY

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Assertion : In a series $R, L, C$ circuit if $V_{R}, V_{1},$ and $V_{c}$ denote $r m s$ voltage across $R, L$ and $C$ respectively and $V_{s}$ is the rms voltage across the source, then $V_{s} = V_{R} + V_{L} + V_{c} .$

Reason: Kirchoff voltage law is valid only for $D C$ circuit, but it is not valid for $A C$ circuit.

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Important Questions on Alternating Current

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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?

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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

HARD

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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 :

HARD

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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?

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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 Series LCR Circuit

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 :

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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

HARD

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Series LCR Circuit

The output voltage (taken across the resistance) of a

L C R

series resonant circuit falls to half its peak value at a frequency of

200 Hz

and again reaches the same value at

800 Hz .

The bandwidth of this circuit is:

HARD

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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-

EASY

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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

HARD

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Series LCR Circuit

The angular frequency of alternating current in a L-C-R circuit is $100 rad s^{- 1}$ . The components connected are shown in the figure. Find the value of inductance of the coil and capacity of condenser.

Question Image

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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 :

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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

MEDIUM

Physics>Electricity and Magnetism>Alternating Current>AC Voltage Applied to a Series LCR Circuit

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 Series LCR Circuit

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:

Assertion : In a series R, L, C circuit if VR, V1, and Vc denote r m s voltage across R, L and C respectively and Vs is the rms voltage across the source, then Vs=VR+VL+Vc. Reason: Kirchoff voltage law is valid only for DC circuit, but it is not valid for AC circuit.

Important Questions on Alternating Current

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