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

1

2

3

4

(A) 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

1

2

3

4

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

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

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]

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

1

2

3

4

(C) 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

1

2

3

4

(D) $< P > = I_{rms}$ $V_{rms} \cos ϕ$

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

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

1

2

3

4

(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]

0%

(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]

0%

(4)

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

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

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

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

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

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

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]

0%

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]

0%

Want Us to Email you About Special Offers & Updates?

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]

0%

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]

0%

Want Us to Email you About Special Offers & Updates?

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]