Alternating Current | Physics JEE Main questions with Solutions

Q 1 :

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb [2024]

increases
remains same
becomes zero
decreases

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(1)

As dielectric is placed, capacitance will increase.

$X_{C} = \frac{1}{C ω}$

It means the capacitive reactance decreases,so impedance of circuit decreases. Hence current increases. So power increases. So glow of the bulb increases.

Q 2 :

In an a.c. circuit, voltage and current are given by:

$V = 100 \sin (100 t) V$

and $I = 100 \sin (100 t + \frac{π}{3}) m A$ respectively.

The average power dissipated in one cycle is [2024]

10 W
2.5 W
25 W
5 W

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(2)

$P_{avg} = V_{rms}$ $I_{rms} \cos (Δ ϕ)$

$= \frac{100}{\sqrt{2}} \times \frac{100 \times 10^{- 3}}{\sqrt{2}} \times \cos (\frac{π}{3}) = 2.5 W$

Q 3 :

A series L, R circuit connected with an ac source $E = (25$ $\sin$ $1000 t)$ $V$ has a power factor of $\frac{1}{\sqrt{2}}$ . If the source of emf is changed to $E = (20$ $\sin$ $2000 t)$ $V$ , the new power factor of the circuit will be [2024]

$\frac{1}{\sqrt{2}}$
$\frac{1}{\sqrt{3}}$
$\frac{1}{\sqrt{5}}$
$\frac{1}{\sqrt{7}}$

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(3)

For first source power factor

$\cos ϕ = \frac{R}{Z} = \frac{R}{\sqrt{R^{2} + ω^{2} L^{2}}}$

$\Rightarrow \frac{1}{\sqrt{2}} = \frac{R}{\sqrt{R^{2} + ω^{2} L^{2}}} \Rightarrow R^{2} + ω^{2} L^{2} = 2 R^{2}$

$\Rightarrow R = ω L$

for second source, $ω^{'} = 2000 = 2 ω$

Power Factor = $\frac{R}{\sqrt{R^{2} + ω^{' 2} L^{2}}}$

$= \frac{ω L}{\sqrt{ω^{2} L^{2} + 4 ω^{2} L^{2}}} = \frac{ω L}{\sqrt{5 ω^{2} L^{2}}} = \frac{1}{\sqrt{5}}$

Q 4 :

An AC voltage V = 20 sin 200 $π t$ is applied to a series LCR circuit which drives a current $I = 10 \sin (200 π t + \frac{π}{3})$ . The average power dissipated is [2024]

21.6 W
200 W
173.2 W
50 W

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(4)

$< P > = I_{rms}$ $V_{rms} \cos ϕ$

$= \frac{20}{\sqrt{2}} \times \frac{10}{\sqrt{2}} \times \cos 60 ° = 50 W$

Q 5 :

A coil of negligible resistance is connected in series with 90 $Ω$ resistor across 120 V, 60 Hz supply. A voltmeter reads 36 V across resistance. Inductance of the coil is [2024]

0.76 H
0.286 H
2.86 H
0.91 H

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(1)

$36 = I_{r m s} R$

$36 = \frac{120}{\sqrt{X_{L}^{2} + R^{2}}} \times R$

$R = 90 Ω \Rightarrow 36 = \frac{120 \times 90}{\sqrt{X_{L}^{2} + 90^{2}}}$

$\sqrt{X_{L}^{2} + 90^{2}} = 300$

$X_{L}^{2} = 81900 \Rightarrow X_{L} = 286.18 Ω$

$ω L = 286.18$

$\Rightarrow L = \frac{286.18}{376.8} = 0.76 H$

Q 6 :

An alternating emf $E = 110 \sqrt{2} \sin 100 t$ volt is applied to a capacitor of $2 μ F$ , the rms value of current in the circuit is __ mA. [2024]

(22)

$E_{r m s} = \frac{E_{0}}{\sqrt{2}} = \frac{110 \sqrt{2}}{\sqrt{2}} = 110 V$

$I_{r m s} = \frac{E_{r m s}}{X_{c}} = E_{r m s} \cdot ω C$

$= 110 \times 100 \times 2 \times 10^{- 6} = 22 \times 10^{- 3} A$

Q 7 :

A capacitor of reactance $4 \sqrt{3} Ω$ and a resistor of resistance $4 Ω$ are connected in series with an AC source of peak value $8 \sqrt{2} V$ . The power dissipation in the circuit is ______ W. [2024]

(4)

$Z = \sqrt{R^{2} + {(X_{L})}^{2}} = \sqrt{4^{2} + {(4 \sqrt{3})}^{2}} = 8 Ω$

$V_{r m s} = \frac{V}{\sqrt{2}} = \frac{8 \sqrt{2}}{\sqrt{2}} = 8 V$

$I_{r m s} = \frac{V_{r m s}}{Z} = \frac{8}{8} = 1 A$

$Power dissipation P = V_{r m s} I_{r m s} \cos ϕ$

$\cos ϕ = \frac{R}{Z} = \frac{4}{\sqrt{{(4 \sqrt{3})}^{2} + 4^{2}}} = \frac{4}{\sqrt{48 + 16}} = \frac{4}{8} = \frac{1}{2}$

$∴$ $P = 8 \times 1 \times \frac{1}{2} = 4 W$

Q 8 :

Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Choke coil is simply a coil having a large inductance but a small resistance, Choke coils are used with fluorescent mercury-tube fittings. If houehold electric power is directly connected to a mercury tube, the tube will be damaged.

Reason (R) : By using the choke coil, the voltage across the tube is reduced by a factor $(R / \sqrt{R^{2} + ω^{2} L^{2}})$ , where $ω$ is frequency of the supply across resistor R and inductor L. If the choke coil were not used, the voltage across the resistor would be the same as he applied voltage.

In the light of the above statements, choose the most appropriate answer from the options given below: [2025]

Both (A) and (R) are true but (R) is not the correct explanation of (A).
(A) is false but (R) is true.
Both (A) and (R) are true and (R) is the correct explanation of (A).
(A) is true but (R) is false.

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(3)

$I = \frac{V}{\sqrt{R^{2} + ω^{2} L^{2}}}, V_{R} = \frac{R}{\sqrt{R^{2} + ω^{2} L^{2}}} V$

Q 9 :

For ac circuit shown in figure, R = 100 k $Ω$ and C = 100 pF and the phase difference between $V_{in}$ and ( $V_{B} - V_{A}$ ) is 90°. The input signal frequency is $10^{x}$ rad/sec, where 'x' is ________ . [2025]

(5)

Input voltage

$θ + θ = 90 °; θ = 45 °$

$\tan θ = \frac{X_{C}}{R}$

$X_{C} = R \Rightarrow \frac{1}{ω C} = R$

$ω = \frac{1}{R C} = \frac{1}{100 \times 10^{3} \times 100 \times 10^{- 12}} = \frac{10^{12}}{10^{7}} = 10^{5}$

Q 10 :

An inductor of reactance 100 $Ω$ , a capacitor of reactance 50 $Ω$ , and a resistor of resistance 50 $Ω$ are connected in series with an AC source of 10 V, 50 Hz. Average power dissipated by the circuit is ________ W. [2025]

(1)

$P = V_{rms} I_{r m s} \cos ϕ$

$P = V_{rms} \times \frac{V_{rms}}{Z} \times \frac{R}{Z} = V_{rms}^{2} \times \frac{R}{Z^{2}}$

$Z = \sqrt{R^{2} + {(x_{L} - x_{C})}^{2}}$

$Z = 50 \sqrt{2} Ω$

$P = 100 \times \frac{50}{2500 \times 2} = 1 W$

Q 11 :

An inductor of self inductance 1 H connected in series with a resistor of 100 $π Ω$ and an ac supply of 100 $π$ volt, 50 Hz. Maximum current flowing in the circuit is ________ A. [2025]

(1)

Impedance of circuit

$Z = \sqrt{R^{2} + {(X_{L})}^{2}} = \sqrt{R^{2} + {(ω L)}^{2}}$

$= \sqrt{{(100 π)}^{2} + {(2 π \times 50 \times 1)}^{2}}$

$= \sqrt{{(100 π)}^{2} + {(100 π)}^{2}}$

$= \sqrt{2} \times 100 π Ω$

$I_{rms} = \frac{V}{Z} = \frac{100 π}{\sqrt{2} \times 100 π} = \frac{1}{\sqrt{2}}$

$I_{\max} = \sqrt{2} I_{rms} = \sqrt{2} \times \frac{1}{\sqrt{2}} = 1 Ampere$

Q 12 :

An alternating voltage source $V = 260 \sin (628 t)$ is connected across a pure inductor of 5 mH. The inductive reactance in the circuit is [2023]

$3.14 Ω$
$6.28 Ω$
$0.5 Ω$
$0.318 Ω$

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(1)

$X_{L} = L ω = 5 mH \times 628 = 3.14 Ω$

Q 13 :

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is __________. $(π = 3.14)$ [2026]

(314)

$\frac{1}{2} L i_{rms}^{2} = 16 \Rightarrow L = 8$

$i^{2} R = 32 \Rightarrow R = 8$

$X_{L} = ω L = 2 \times 3.14 \times 50 \times 8$

$= 800 \times 3.14$

$R = 8$

$\frac{X_{L}}{R} = 314$

Q 14 :

The figure given below shows an LCR series circuit with two switches $S_{1}$ and $S_{2}$ . When switch $S_{1}$ is closed keeping $S_{2}$ open, the phase difference $(ϕ)$ between the current and source voltage is $30 °$ and phase difference is $60 °$ when $S_{2}$ is closed keeping $S_{1}$ open. The value of $(3 L_{1} - L_{2})$ is ______ H. [2026]

$\frac{9}{2}$
$\frac{2}{9}$
$\frac{1}{3}$
$3$

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(2)

Case - I

$ω = 300 rad/sec$

$X_{C} = \frac{1}{ω C} = \frac{1}{300 \times 100 \times 10^{- 6}} = \frac{1}{0.03} = \frac{100}{3} Ω$

$\tan 30 ° = \frac{| X_{L_{1}} - X_{C} |}{R}$

$\frac{1}{\sqrt{3}} = \frac{| X_{L_{1}} - \frac{100}{3} |}{R}$ $. . . (i)$

Case - II

$\tan 60 ° = \frac{| X_{L_{2}} - X_{C} |}{R}$

$\sqrt{3} = \frac{| X_{L_{2}} - \frac{100}{3} |}{R}$ $. . . (i i)$

$\frac{1}{\sqrt{3} \times \sqrt{3}} = \frac{X_{L_{1}} - \frac{100}{3}}{X_{L_{2}} - \frac{100}{3}}$

$3 X_{L_{1}} - 100 = X_{L_{2}} - \frac{100}{3}$

$3 X_{L_{1}} - X_{L_{2}} = 100 - \frac{100}{3} = \frac{200}{3}$

$3 L_{1} - L_{2} = \frac{200}{3 ω} = \frac{200}{3 \times 300} = \frac{2}{9}$

Q 15 :

An a.c. source of angular frequency $ω$ is connected across a resistor R and a capacitor C in series. The current is observed as $I$ . Now the frequency of the source is changed to $ω / 4$ , (keeping the voltage unchanged) the current is found to be $I / 3$ . The ratio of resistance to reactance at frequency $ω$ is [2026]

$\sqrt{\frac{6}{7}}$
$\sqrt{\frac{3}{5}}$
$\sqrt{\frac{7}{8}}$
$\sqrt{\frac{3}{4}}$

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(3)

$As we know that current in RLC circuit is given by$

$I = \frac{V}{Z} = \frac{V}{{[R^{2} + {(X_{L} - X_{C})}^{2}]}^{1 / 2}}$

$I = \frac{V_{0}}{\sqrt{R^{2} + {(ω L - \frac{1}{ω C})}^{2}}}$

$As circuit is RC$

$I_{0} = \frac{V_{0}}{{(R^{2} + X_{C}^{2})}^{1 / 2}}$

$\frac{I_{0}}{3} = \frac{V_{0}}{{[R^{2} + {(4 X_{C})}^{2}]}^{1 / 2}}$

$R^{2} + {(X_{C})}^{2} = \frac{R^{2} + 16 X_{C}^{2}}{9}$

$\frac{8 R^{2}}{9} = \frac{7 X_{C}^{2}}{9}$

$\frac{R}{X_{C}} = \sqrt{\frac{7}{8}}$

Q 16 :

A LCR series circuit driven with $E_{rms} = 90 V$ at frequency $f_{d} = 30 Hz$ has resistance $R = 80 Ω$ , an inductance with inductive reactance $X_{L} = 20.0 Ω$ and capacitance with capacitive reactance $X_{C} = 80.0 Ω$ . The power factor of the circuit is ______. [2026]

0.8
0.64
0.9
0.5

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(1)

$Power factor is \cos ϕ = \frac{R}{Z}$

$Z = \sqrt{R^{2} + {(X_{L} - X_{C})}^{2}} = 100 Ω$

$\cos ϕ = \frac{80}{100} = 0.8$

Topic Question Set

Q 1 :

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb [2024]

Q 2 :

In an a.c. circuit, voltage and current are given by:

$V = 100 \sin (100 t) V$

and $I = 100 \sin (100 t + \frac{π}{3}) m A$ respectively.

The average power dissipated in one cycle is [2024]

Q 3 :

A series L, R circuit connected with an ac source $E = (25$ $\sin$ $1000 t)$ $V$ has a power factor of $\frac{1}{\sqrt{2}}$ . If the source of emf is changed to $E = (20$ $\sin$ $2000 t)$ $V$ , the new power factor of the circuit will be [2024]

Q 4 :

An AC voltage V = 20 sin 200 $π t$ is applied to a series LCR circuit which drives a current $I = 10 \sin (200 π t + \frac{π}{3})$ . The average power dissipated is [2024]

Q 5 :

A coil of negligible resistance is connected in series with 90 $Ω$ resistor across 120 V, 60 Hz supply. A voltmeter reads 36 V across resistance. Inductance of the coil is [2024]

Q 6 :

An alternating emf $E = 110 \sqrt{2} \sin 100 t$ volt is applied to a capacitor of $2 μ F$ , the rms value of current in the circuit is __ mA. [2024]

Q 7 :

A capacitor of reactance $4 \sqrt{3} Ω$ and a resistor of resistance $4 Ω$ are connected in series with an AC source of peak value $8 \sqrt{2} V$ . The power dissipation in the circuit is ______ W. [2024]

Q 9 :

For ac circuit shown in figure, R = 100 k $Ω$ and C = 100 pF and the phase difference between $V_{in}$ and ( $V_{B} - V_{A}$ ) is 90°. The input signal frequency is $10^{x}$ rad/sec, where 'x' is ________ . [2025]

Q 10 :

An inductor of reactance 100 $Ω$ , a capacitor of reactance 50 $Ω$ , and a resistor of resistance 50 $Ω$ are connected in series with an AC source of 10 V, 50 Hz. Average power dissipated by the circuit is ________ W. [2025]

Q 11 :

An inductor of self inductance 1 H connected in series with a resistor of 100 $π Ω$ and an ac supply of 100 $π$ volt, 50 Hz. Maximum current flowing in the circuit is ________ A. [2025]

Q 12 :

An alternating voltage source $V = 260 \sin (628 t)$ is connected across a pure inductor of 5 mH. The inductive reactance in the circuit is [2023]

Q 13 :

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is __________. $(π = 3.14)$ [2026]

Q 16 :

A LCR series circuit driven with $E_{rms} = 90 V$ at frequency $f_{d} = 30 Hz$ has resistance $R = 80 Ω$ , an inductance with inductive reactance $X_{L} = 20.0 Ω$ and capacitance with capacitive reactance $X_{C} = 80.0 Ω$ . The power factor of the circuit is ______. [2026]

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Topic Question Set

Q 1 : A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb [2024]

Q 2 : In an a.c. circuit, voltage and current are given by: V=100sin(100t) V and I=100sin(100t+π3)mA respectively. The average power dissipated in one cycle is [2024]

Q 3 : A series L, R circuit connected with an ac source E=(25 sin 1000t)V has a power factor of 12. If the source of emf is changed to E=(20 sin 2000t)V, the new power factor of the circuit will be [2024]

Q 4 : An AC voltage V = 20 sin 200πt is applied to a series LCR circuit which drives a current I=10sin(200πt+π3). The average power dissipated is [2024]

Q 5 : A coil of negligible resistance is connected in series with 90 Ω resistor across 120 V, 60 Hz supply. A voltmeter reads 36 V across resistance. Inductance of the coil is [2024]

Q 6 : An alternating emf E=1102sin100t volt is applied to a capacitor of 2μF, the rms value of current in the circuit is __ mA. [2024]

Q 7 : A capacitor of reactance 43Ω and a resistor of resistance 4Ω are connected in series with an AC source of peak value 82V. The power dissipation in the circuit is ______ W. [2024]

Q 9 : For ac circuit shown in figure, R = 100 kΩ and C = 100 pF and the phase difference between Vin and (VB–VA) is 90°. The input signal frequency is 10x rad/sec, where 'x' is ________ . [2025]

Q 10 : An inductor of reactance 100Ω, a capacitor of reactance 50Ω, and a resistor of resistance 50Ω are connected in series with an AC source of 10 V, 50 Hz. Average power dissipated by the circuit is ________ W. [2025]

Q 11 : An inductor of self inductance 1 H connected in series with a resistor of 100πΩ and an ac supply of 100π volt, 50 Hz. Maximum current flowing in the circuit is ________ A. [2025]

Q 12 : An alternating voltage source V=260sin(628 t) is connected across a pure inductor of 5 mH. The inductive reactance in the circuit is [2023]

Q 13 : An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is __________. (π=3.14) [2026]

Q 16 : A LCR series circuit driven with Erms=90 V at frequency fd=30 Hz has resistance R=80 Ω, an inductance with inductive reactance XL=20.0 Ω and capacitance with capacitive reactance XC=80.0 Ω. The power factor of the circuit is ______. [2026]

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Q 1 :

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb [2024]

Q 2 :

In an a.c. circuit, voltage and current are given by:

$V = 100 \sin (100 t) V$

and $I = 100 \sin (100 t + \frac{π}{3}) m A$ respectively.

The average power dissipated in one cycle is [2024]

Q 3 :

A series L, R circuit connected with an ac source $E = (25$ $\sin$ $1000 t)$ $V$ has a power factor of $\frac{1}{\sqrt{2}}$ . If the source of emf is changed to $E = (20$ $\sin$ $2000 t)$ $V$ , the new power factor of the circuit will be [2024]

Q 4 :

An AC voltage V = 20 sin 200 $π t$ is applied to a series LCR circuit which drives a current $I = 10 \sin (200 π t + \frac{π}{3})$ . The average power dissipated is [2024]

Q 5 :

A coil of negligible resistance is connected in series with 90 $Ω$ resistor across 120 V, 60 Hz supply. A voltmeter reads 36 V across resistance. Inductance of the coil is [2024]

Q 6 :

An alternating emf $E = 110 \sqrt{2} \sin 100 t$ volt is applied to a capacitor of $2 μ F$ , the rms value of current in the circuit is __ mA. [2024]

Q 7 :

A capacitor of reactance $4 \sqrt{3} Ω$ and a resistor of resistance $4 Ω$ are connected in series with an AC source of peak value $8 \sqrt{2} V$ . The power dissipation in the circuit is ______ W. [2024]

Q 9 :

For ac circuit shown in figure, R = 100 k $Ω$ and C = 100 pF and the phase difference between $V_{in}$ and ( $V_{B} - V_{A}$ ) is 90°. The input signal frequency is $10^{x}$ rad/sec, where 'x' is ________ . [2025]

Q 10 :

An inductor of reactance 100 $Ω$ , a capacitor of reactance 50 $Ω$ , and a resistor of resistance 50 $Ω$ are connected in series with an AC source of 10 V, 50 Hz. Average power dissipated by the circuit is ________ W. [2025]

Q 11 :

An inductor of self inductance 1 H connected in series with a resistor of 100 $π Ω$ and an ac supply of 100 $π$ volt, 50 Hz. Maximum current flowing in the circuit is ________ A. [2025]

Q 12 :

An alternating voltage source $V = 260 \sin (628 t)$ is connected across a pure inductor of 5 mH. The inductive reactance in the circuit is [2023]

Q 13 :

An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is __________. $(π = 3.14)$ [2026]

Q 16 :

A LCR series circuit driven with $E_{rms} = 90 V$ at frequency $f_{d} = 30 Hz$ has resistance $R = 80 Ω$ , an inductance with inductive reactance $X_{L} = 20.0 Ω$ and capacitance with capacitive reactance $X_{C} = 80.0 Ω$ . The power factor of the circuit is ______. [2026]