Alternating Current | Physics JEE Main questions with Solutions

Q 1 :

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to

a) pure inductor

b) pure capacitor

c) pure resistor

d) combination of an inductor and capacitor

Choose the correct answer from the options given below [2024]

b, c and d only
a, b and d only
a and b only
a, b and c only

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(2)

This is possible when phase difference is $\frac{π}{2}$ between current and voltage.

Q 2 :

A series LCR circuit is subjected to an ac signal of 200 V, 50 Hz. If the voltage across the inductor (L = 10 mH) is 31.4 V, then the current in this circuit is [2024]

68 A
63 A
10 A
10 mA

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(3)

Voltage across inductor $V_{L} = I X_{L}$

$31.4 = I [L ω]$

$31.4 = I [L (2 π f)]$

$31.4 = I [10 \times 10^{- 3} (2 \times 3.14) \times 50] \Rightarrow I = 10 A$

Q 3 :

Given below are two statements:

Statement I: In an LCR series circuit, current is maximum at resonance.

Statement II: Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source.

In the light of the above statements, choose the correct from the options given below: [2024]

Statement I is true but Statement II is false
Statement I is false but Statement II is true
Both Statement I and Statement II are false
Both Statement I and Statement II are true

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(4)

Statement-I

$I_{m} = \frac{V_{m}}{\sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}}, at resonance X_{L} = X_{C}$

$Thus, I_{m} = \frac{V_{m}}{R}$

$∴$ Impendence is minimum therefore $I$ is maximum at resonance.

Statement-II

$I = (\frac{V}{R}) in purely resistive circuit .$

Q 4 :

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters the same. The current amplitude at resonance will be now [2024]

halved
Zero
same
double

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(4)

At resonance: Z = R

So $I \propto \frac{1}{R}$

$R \to halved \Rightarrow I = 2 I, I becomes doubled .$

Q 5 :

In series LCR circuit, the capacitance is changed from C to 4C. To keep the resonance frequency unchanged, the new inductance should be [2024]

reduced to L/4
increased by 2L
reduced by L/3
increased to 4L

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(1)

$ω^{'} = ω$

$\frac{1}{\sqrt{L^{'} C^{'}}} = \frac{1}{\sqrt{L C}} ∴ L^{'} C^{'} = L C$

$L^{'} (4 C) = L C$

$L^{'} = \frac{L}{4}$

Q 6 :

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5 nF. If resistance of 200 $Ω$ and 100 mH inductor are being used in the given circuit.

The frequency of ac source is _________ $\times 10^{3}$ Hz. (given $π^{2} = 10$ ) [2024]

(10) For maximum current, circuit must be in resonance.

At resonance, $X_{C} = X_{L}$

$ω L = \frac{1}{ω C} \Rightarrow ω^{2} = \frac{1}{100 \times 10^{- 3} \times 2.5 \times 10^{- 9}} = 4 \times 10^{9}$

${(2 π f)}^{2} = 4 \times 10^{9}$

$f^{2} = 10^{8} \Rightarrow f = 10^{4} Hz \Rightarrow f = 10 \times 10^{3} Hz$

Q 7 :

A series LCR circuit with $L = \frac{100}{π} m H$ , $C = \frac{10^{- 3}}{π} F$ and $R = 10 Ω$ , is connected across an ac source of 220V, 50 Hz supply. The power factor of the circuit would be _________ . [2024]

(1) $X_{c} = \frac{1}{ω C} = \frac{π}{2 π \times 50 \times 10^{- 3}} = 10 Ω$

$X_{L} = ω L = 2 π \times 50 \times \frac{100}{π} \times 10^{- 3} = 10 Ω$

$∵ X_{C} = X_{L}, Hence, circuit is in resonance$

$∴ power factor = \frac{R}{Z} = \frac{R}{R} = 1$

Q 8 :

Match List-I with List-II [2024]

Choose the correct answer from the options given below

A-IV, B-I, C-II, D-III
A-I, B-IV, C-III, D-II
A-I, B-IV, C-II, D-III
A-IV, B-I, C-III, D-II

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(3)

A - V lags by 90° from I, hence option (I) is correct.
B - V lead by 90° from I, hence option (IV) is correct.
C - In LCR resonance $X_{L} = X_{C}$ . Hence circuit is purely resistive, so option (II) is correct.
D - In LCR series V is at some angle from I hence (III) is correct.

Q 9 :

An AC source is connected in a given series LCR circuit. The RMS potential difference across the capacitor of 20 $μ F$ is ________ V. [2024]

(50)

$X_{L} = ω L = 100 \times 1 = 100 Ω$

$X_{C} = \frac{1}{ω C} = \frac{1}{100 \times 20 \times 10^{- 6}} = 500 Ω$

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

$Z = \sqrt{{(100 - 500)}^{2} + 300^{2}} = 500 Ω$

$i_{r m s} = \frac{V_{r m s}}{Z} = \frac{50}{500} = 0.1 A$

Q 10 :

When a DC voltage of 100 V is applied to an inductor, a DC current of 5 A flows through it. When an AC voltage of 200 V peak value is connected to the inductor, its inductive reactance is found to be $20 \sqrt{3} Ω$ . The power dissipated in the circuit is ______ W. [2024]

(250)

$For DC voltage, R = \frac{V}{i} = \frac{100}{5} = 20 Ω$

$For AC voltage, X_{L} = 20 \sqrt{3} Ω, R = 20 Ω$

$Z = \sqrt{X_{L}^{2} + R^{2}} = \sqrt{3 \times 400 + 400} = 40 Ω$

$Power dissipated, P = i_{r m s} V_{r m s} \cos ϕ$

$P = \frac{V_{r m s}^{2}}{Z} \cdot \cos ϕ = \frac{{(\frac{200}{\sqrt{2}})}^{2}}{40} \times \frac{1}{2} = \frac{2 \times 10000}{40} \times \frac{1}{2} \Rightarrow P = 250 W$

Q 11 :

When a coil is connected across a 20 V DC supply, it draws a current of 5 A. When it is connected across 20 V, 50 Hz AC supply, it draws a current of 4 A. The self-inductance of the coil is (Take $π$ = 3) _____ mH. [2024]

(10)

$In DC circuit:$

$I = \frac{V}{R} (at steady state)$

$R = \frac{20}{5} = 4 Ω$

$In AC circuit:$

$I = \frac{V}{Z} \Rightarrow 4 = \frac{20}{\sqrt{R^{2} + {(L ω)}^{2}}}$

$16 + {(L ω)}^{2} = 25 \Rightarrow L ω = 3$

$L = \frac{3}{2 \times π \times f} = \frac{3}{2 \times 3 \times 50} = \frac{1}{100} = 10 mH$

Q 12 :

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is $I_{0}$ . If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be [2025]

$I_{0}$
$\frac{I_{0}}{2}$
$\frac{I_{0}}{\sqrt{2}}$
$2 I_{0}$

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(2)

At resonance Z = R

Initially, $I_{0} = \frac{E}{R}$

Finally, $I' = \frac{E}{2 R} = \frac{I_{0}}{2}$

Q 13 :

In a series LCR circuit, a resistor of 300 $Ω$ , a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ $\times 10^{4}$ radians $s^{- 1}$ . [2025]

(2)

$ω = \frac{1}{\sqrt{L C}}$ is resonance condition

$= \frac{1}{\sqrt{100 \times 10^{- 3} \times 25 \times 10^{- 9}}} = \frac{10^{6}}{5 \times 10}$

$= 2 \times 10^{4} rad s^{- 1}$

Q 14 :

For the given figure, choose the correct options: [2023]

The rms current in circuit (b) can never be larger than that in (a).
The rms current in figure (a) is always equal to that in figure (b).
The rms current in circuit (b) can be larger than that in (a).
At resonance, current in (b) is less than that in (a).

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(1)

$I_{\max} = \frac{220}{40} = 5.5 A$

$X_{L}$ is not equal to $X_{C}$ . So rms current in (b) can never be larger than (a).

Q 15 :

In the given circuit, rms value of current $(I_{rms})$ through the resistor $R$ is [2023]

$2 A$
$\frac{1}{2} A$
$20 A$
$2 \sqrt{2} A$

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(1)

$z = \sqrt{100^{2} + {(200 - 100)}^{2}} = 100 \sqrt{2} Ω$

$i_{rms} = \frac{V_{rms}}{Z} = \frac{200 \sqrt{2}}{100 \sqrt{2}} = 2 A$

Q 16 :

Given below are two statements: [2023]

Statement I: Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs.

Statement II: Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage.

In the light of the above statements, choose the correct answer from the options given below:

Statement I is false but Statement II is true
Statement I is true but Statement II is false
Both Statement I and Statement II are true
Both Statement I and Statement II are false

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(3)

$Power will be maximum when impedance is minimum$

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

$At resonance, X_{L} = X_{C}$

$Z_{\min} = R$

Q 17 :

Given below are two statements: [2023]

Statement I: When the frequency of an a.c. source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases.

Statement II: In a series LCR circuit, the value of power factor at resonance is one.

In the light of given statements, choose the most appropriate answer from the options given below:

Statement I is incorrect but Statement II is true
Both Statement I and Statement II are false
Statement I is correct but Statement II is false
Both Statement I and Statement II are true

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(4)

Both statements are correct. Theory based.

Q 18 :

Given below are two statements: [2023]

Statement I: An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.

Statement II: An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.

In the light of above statements, choose the correct answer from the options given below:

Both Statement I and Statement II are false
Statement I is true but Statement II is false
Both Statement I and Statement II are true
Statement I is false but Statement II is true

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(1)

For resonance, $ϕ = 0,$ hence both inductor and capacitor must be present. Also, power factor is zero for pure inductor or pure capacitor, hence both the components consume zero average power.

Q 19 :

In the circuit shown in the figure, the ratio of the quality factor and the band width is ________ s. [2023]

(10)

$Δ ω = \frac{R}{L}$

$Q = \frac{ω_{0}}{Δ ω} = ω_{0} \frac{L}{R}$

$ω_{0} = \frac{1}{\sqrt{3 \times 27 \times 10^{- 6}}} = \frac{1}{9 \times 10^{- 3}}$

$\frac{Q}{Δ ω} = \frac{ω_{0} \frac{L}{R}}{\frac{R}{L}} = ω_{0} \frac{L^{2}}{R^{2}} = \sqrt{\frac{1}{L C}} \frac{L^{2}}{R^{2}}$

$\Rightarrow \frac{Q}{Δ ω} = \frac{1}{9 \times 10^{- 3}} \times \frac{9}{100} = 10 s$

Q 20 :

An LCR series circuit of capacitance 62.5 nF and resistance of $50 Ω$ , is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is ________ mH. (Take $π^{2} = 10$ ) [2023]

(100)

$C = 62.5 nF, R = 50 Ω, f = 2 kHz$

$i_{\max} condition is Z_{\min} (resonance condition)$

$f = \frac{1}{2 π \sqrt{L C}}$

$L = \frac{1}{4 π^{2} f^{2} C} = \frac{1}{4 \times 10 \times 4 \times 10^{6} \times 62.5 \times 10^{- 9}} = 100 mH$

Q 21 :

A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance $R = 8 Ω$ , an inductor of inductive reactance $X_{L} = 70 Ω$ , and a capacitor of capacitive reactance $X_{C} = 130 Ω$ . The power factor of the circuit is $\frac{x}{10}$ . The value of $x$ is _________. [2023]

(8)

$\cos ϕ = \frac{R}{Z} = \frac{R}{\sqrt{R^{2} + {(X_{C} - X_{L})}^{2}}}$

$\cos ϕ = \frac{80}{\sqrt{{(80)}^{2} + {(60)}^{2}}}$

$\cos ϕ = \frac{80}{100} = \frac{8}{10}$

$So, x = 8$

Q 22 :

A series LCR circuit consists of $R = 80 Ω$ , $X_{L} = 100 Ω$ and $X_{C} = 40 Ω$ . The input voltage is $2500 \cos (100 π t) V$ . The amplitude of current in the circuit is ______ A. [2023]

(25)

$ω = 100 π$

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

$= \sqrt{80^{2} + {(100 - 40)}^{2}} = 100 Ω$

$i_{0} = \frac{V_{0}}{Z} = \frac{2500}{100} A = 25 A$

Q 23 :

A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance $R = 100 Ω$ and an inductor of inductive reactance $X_{L} = 79.6 Ω$ . The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be _________ $μF$ . [2023]

(40)

To maximize the average rate at which energy is supplied, i.e. power will be maximum.

So in LCR circuit power will be maximum at the condition of resonance and in resonance condition

$X_{L} = X_{C}$

$79.6 = \frac{1}{ω C}$

$∴$ $C = \frac{1}{2 π \times 50 \times 79.6} = 40 μ F$

Q 24 :

An inductor of inductance $2 μ H$ is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x} F$ , where the value of $x$ is _______. (Take $π = \frac{22}{7}$ ) [2023]

(3872)

$\frac{1}{2 π f C} = 2 π f L$

$C = \frac{1}{4 π^{2} f^{2} L} = \frac{1}{4 \times π^{2} \times 49 \times 10^{6} \times 2 \times 10^{- 6}}$

$C = \frac{1}{3872} F$

$\Rightarrow x = 3872$

Q 25 :

An inductor of 0.5 mH, a capacitor of $20 μ F$ and a resistance of $20 Ω$ are connected in series with a 220 V AC source. If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt{x} A$ . The value of $x$ is _______. [2023]

(242)

$X_{L} = X_{C}$

$So, Z = R = 20 Ω$

$i_{rms} = \frac{220}{20} = 11$

$i_{\max} = 11 \sqrt{2} = \sqrt{242}$

Q 26 :

A series combination of a resistor of resistance $100 Ω$ , an inductor of inductance 1 H and a capacitor of capacitance $6.25 μ F$ is connected to an AC source. The quality factor of the circuit will be ________. [2023]

(4)

$Quality factor = \frac{X_{L}}{R} = \frac{ω L}{R}$

$ω = \frac{1}{\sqrt{L C}} = \frac{1}{\sqrt{1 \times 6.25 \times 10^{- 6}}} = \frac{10^{3}}{2.5} = 400 / sec$

$Q -factor = \frac{400 \times 1}{100} = 4$

Q 27 :

Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for V = 5sin(100t). The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ______ $µ F$ . [2026]

(50)

Current is maximum, so resonance

and $ω = \frac{1}{\sqrt{L C}}$

$C = \frac{1}{ω^{2} L} = \frac{1}{2 \times 10^{4}}$

$= 50 \times 10^{- 6} = 50 μ F$

Q 28 :

For the series LCR circuit connected with 220 V, 50 Hz a.c. source as shown in the figure, the power factor is $\frac{α}{10}$ . The value of $α$ is ________. [2026]

10
4
8
6

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(4)

$Power factor = \frac{R}{Z}$

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

$= \sqrt{60^{2} + {(150 - 70)}^{2}} = 100 Ω$

$∴$ $Power factor = \frac{60}{100} = \frac{6}{10}$

$Then a = 6$

Q 29 :

Suppose a long solenoid of 100 cm length, radius 2 cm having 500 turns per unit length, carries a $I = 10 \sin (ω t) A, where ω = 1000 rad/s .$ A circular conducting loop (B) of radius 1 cm coaxially slides through the solenoid at speed v = 1 cm/s. The r.m.s. current through the loop when the coil B is inserted 10 cm inside the solenoid is $\frac{α}{\sqrt{2}} μ A$ . The value of $α$ is ______.

[Resistance of the loop = $10 Ω$ ] [2026]

280
80
197
100

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(3)

$EMF induced ε = A \frac{d B}{d t} = A μ_{0} n \frac{d i}{d t}$

$ε = A μ_{0} n i_{0} ω \cos ω t$

$current induced i = \frac{ε}{R} = \frac{π r^{2} μ_{0} n i_{0} ω}{R} \cos ω t$

$So i = \frac{π r^{2} μ_{0} n i_{0} ω}{\sqrt{2} R}$

$= \frac{π \times 10^{- 4} \times 4 π \times 10^{- 7} \times 500 \times 10 \times 10^{3}}{\sqrt{2} \times 10}$

$= \frac{20 π^{2}}{\sqrt{2}} \times 10^{- 6}$

$= \frac{197}{\sqrt{2}} μ A$

Q 30 :

A capacitor C is first charged fully with potential difference of $V_{0}$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In ts, 25% of the initial energy in the capacitor is transferred to the inductor. The value of t is ________ s. [2026]

$\frac{π \sqrt{L C}}{2}$
$π \sqrt{\frac{L C}{2}}$
$\frac{π \sqrt{L C}}{3}$
$\frac{π \sqrt{L C}}{6}$

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(4)

$U_{e_{r}} = 75 % U_{e_{i}}$

$Q_{F}^{2} = \frac{3}{4} Q_{i}^{2}$

$Q_{i} \cos ω t = \frac{\sqrt{3}}{2} Q_{i} \Rightarrow t = \frac{T}{12}$

$t = \frac{π}{6} \sqrt{L C}$

Topic Question Set

Q 2 :

A series LCR circuit is subjected to an ac signal of 200 V, 50 Hz. If the voltage across the inductor (L = 10 mH) is 31.4 V, then the current in this circuit is [2024]

Q 4 :

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters the same. The current amplitude at resonance will be now [2024]

Q 5 :

In series LCR circuit, the capacitance is changed from C to 4C. To keep the resonance frequency unchanged, the new inductance should be [2024]

Q 6 :

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5 nF. If resistance of 200 $Ω$ and 100 mH inductor are being used in the given circuit.

The frequency of ac source is _________ $\times 10^{3}$ Hz. (given $π^{2} = 10$ ) [2024]

Q 7 :

A series LCR circuit with $L = \frac{100}{π} m H$ , $C = \frac{10^{- 3}}{π} F$ and $R = 10 Ω$ , is connected across an ac source of 220V, 50 Hz supply. The power factor of the circuit would be _________ . [2024]

Q 8 :

Match List-I with List-II [2024]

Choose the correct answer from the options given below

Q 9 :

An AC source is connected in a given series LCR circuit. The RMS potential difference across the capacitor of 20 $μ F$ is ________ V. [2024]

Q 10 :

When a DC voltage of 100 V is applied to an inductor, a DC current of 5 A flows through it. When an AC voltage of 200 V peak value is connected to the inductor, its inductive reactance is found to be $20 \sqrt{3} Ω$ . The power dissipated in the circuit is ______ W. [2024]

Q 11 :

When a coil is connected across a 20 V DC supply, it draws a current of 5 A. When it is connected across 20 V, 50 Hz AC supply, it draws a current of 4 A. The self-inductance of the coil is (Take $π$ = 3) _____ mH. [2024]

Q 12 :

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is $I_{0}$ . If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be [2025]

Q 13 :

In a series LCR circuit, a resistor of 300 $Ω$ , a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ $\times 10^{4}$ radians $s^{- 1}$ . [2025]

Q 14 :

For the given figure, choose the correct options: [2023]

Q 15 :

In the given circuit, rms value of current $(I_{rms})$ through the resistor $R$ is [2023]

Q 19 :

In the circuit shown in the figure, the ratio of the quality factor and the band width is ________ s. [2023]

Q 20 :

An LCR series circuit of capacitance 62.5 nF and resistance of $50 Ω$ , is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is ________ mH. (Take $π^{2} = 10$ ) [2023]

Q 22 :

A series LCR circuit consists of $R = 80 Ω$ , $X_{L} = 100 Ω$ and $X_{C} = 40 Ω$ . The input voltage is $2500 \cos (100 π t) V$ . The amplitude of current in the circuit is ______ A. [2023]

Q 25 :

An inductor of 0.5 mH, a capacitor of $20 μ F$ and a resistance of $20 Ω$ are connected in series with a 220 V AC source. If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt{x} A$ . The value of $x$ is _______. [2023]

Q 26 :

A series combination of a resistor of resistance $100 Ω$ , an inductor of inductance 1 H and a capacitor of capacitance $6.25 μ F$ is connected to an AC source. The quality factor of the circuit will be ________. [2023]

Q 27 :

Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for V = 5sin(100t). The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ______ $µ F$ . [2026]

Q 28 :

For the series LCR circuit connected with 220 V, 50 Hz a.c. source as shown in the figure, the power factor is $\frac{α}{10}$ . The value of $α$ is ________. [2026]

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Topic Question Set

Q 2 : A series LCR circuit is subjected to an ac signal of 200 V, 50 Hz. If the voltage across the inductor (L = 10 mH) is 31.4 V, then the current in this circuit is [2024]

Q 4 : A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters the same. The current amplitude at resonance will be now [2024]

Q 5 : In series LCR circuit, the capacitance is changed from C to 4C. To keep the resonance frequency unchanged, the new inductance should be [2024]

Q 6 : For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5 nF. If resistance of 200 Ω and 100 mH inductor are being used in the given circuit. The frequency of ac source is _________ ×103 Hz. (given π2=10) [2024]

Q 7 : A series LCR circuit with L=100πmH, C=10-3πF and R=10Ω, is connected across an ac source of 220V, 50 Hz supply. The power factor of the circuit would be _________ . [2024]

Q 8 : Match List-I with List-II [2024] Choose the correct answer from the options given below

Q 9 : An AC source is connected in a given series LCR circuit. The RMS potential difference across the capacitor of 20 μF is ________ V. [2024]

Q 10 : When a DC voltage of 100 V is applied to an inductor, a DC current of 5 A flows through it. When an AC voltage of 200 V peak value is connected to the inductor, its inductive reactance is found to be 203Ω. The power dissipated in the circuit is ______ W. [2024]

Q 11 : When a coil is connected across a 20 V DC supply, it draws a current of 5 A. When it is connected across 20 V, 50 Hz AC supply, it draws a current of 4 A. The self-inductance of the coil is (Take π = 3) _____ mH. [2024]

Q 12 : A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is I0. If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be [2025]

Q 13 : In a series LCR circuit, a resistor of 300Ω, a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ ×104 radians s–1. [2025]

Q 14 : For the given figure, choose the correct options: [2023]

Q 15 : In the given circuit, rms value of current (Irms) through the resistor R is [2023]

Q 19 : In the circuit shown in the figure, the ratio of the quality factor and the band width is ________ s. [2023]

Q 20 : An LCR series circuit of capacitance 62.5 nF and resistance of 50 Ω, is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is ________ mH. (Take π2=10) [2023]

Q 21 : A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance R=8 Ω, an inductor of inductive reactance XL=70 Ω, and a capacitor of capacitive reactance XC=130 Ω. The power factor of the circuit is x10. The value of x is _________. [2023]

Q 22 : A series LCR circuit consists of R=80 Ω, XL=100 Ω and XC=40 Ω. The input voltage is 2500cos(100πt) V. The amplitude of current in the circuit is ______ A. [2023]

Q 23 : A series LCR circuit is connected to an AC source of 220 V, 50 Hz. The circuit contains a resistance R=100 Ω and an inductor of inductive reactance XL=79.6 Ω. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be _________ μF. [2023]

Q 24 : An inductor of inductance 2 μH is connected in series with a resistance, a variable capacitor and an AC source of frequency 7 kHz. The value of capacitance for which maximum current is drawn into the circuit is 1xF, where the value of x is _______. (Take π=227) [2023]

Q 25 : An inductor of 0.5 mH, a capacitor of 20 μF and a resistance of 20 Ω are connected in series with a 220 V AC source. If the current is in phase with the emf, the amplitude of current of the circuit is xA. The value of x is _______. [2023]

Q 26 : A series combination of a resistor of resistance 100 Ω, an inductor of inductance 1 H and a capacitor of capacitance 6.25 μF is connected to an AC source. The quality factor of the circuit will be ________. [2023]

Q 27 : Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for V = 5sin(100t). The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ______ µF. [2026]

Q 28 : For the series LCR circuit connected with 220 V, 50 Hz a.c. source as shown in the figure, the power factor is α10. The value of α is ________. [2026]

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Q 2 :

A series LCR circuit is subjected to an ac signal of 200 V, 50 Hz. If the voltage across the inductor (L = 10 mH) is 31.4 V, then the current in this circuit is [2024]

Q 4 :

A LCR circuit is at resonance for a capacitor C, inductance L and resistance R. Now the value of resistance is halved keeping all other parameters the same. The current amplitude at resonance will be now [2024]

Q 5 :

In series LCR circuit, the capacitance is changed from C to 4C. To keep the resonance frequency unchanged, the new inductance should be [2024]

Q 6 :

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 2.5 nF. If resistance of 200 $Ω$ and 100 mH inductor are being used in the given circuit.

The frequency of ac source is _________ $\times 10^{3}$ Hz. (given $π^{2} = 10$ ) [2024]

Q 7 :

A series LCR circuit with $L = \frac{100}{π} m H$ , $C = \frac{10^{- 3}}{π} F$ and $R = 10 Ω$ , is connected across an ac source of 220V, 50 Hz supply. The power factor of the circuit would be _________ . [2024]

Q 8 :

Match List-I with List-II [2024]

Choose the correct answer from the options given below

Q 9 :

An AC source is connected in a given series LCR circuit. The RMS potential difference across the capacitor of 20 $μ F$ is ________ V. [2024]

Q 10 :

When a DC voltage of 100 V is applied to an inductor, a DC current of 5 A flows through it. When an AC voltage of 200 V peak value is connected to the inductor, its inductive reactance is found to be $20 \sqrt{3} Ω$ . The power dissipated in the circuit is ______ W. [2024]

Q 11 :

When a coil is connected across a 20 V DC supply, it draws a current of 5 A. When it is connected across 20 V, 50 Hz AC supply, it draws a current of 4 A. The self-inductance of the coil is (Take $π$ = 3) _____ mH. [2024]

Q 12 :

A series LCR circuit is connected to an alternating source of emf E. The current amplitude at resonant frequency is $I_{0}$ . If the value of resistance R becomes twice of its initial value then amplitude of current at resonance will be [2025]

Q 13 :

In a series LCR circuit, a resistor of 300 $Ω$ , a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ $\times 10^{4}$ radians $s^{- 1}$ . [2025]

Q 14 :

For the given figure, choose the correct options: [2023]

Q 15 :

In the given circuit, rms value of current $(I_{rms})$ through the resistor $R$ is [2023]

Q 19 :

In the circuit shown in the figure, the ratio of the quality factor and the band width is ________ s. [2023]

Q 20 :

An LCR series circuit of capacitance 62.5 nF and resistance of $50 Ω$ , is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is ________ mH. (Take $π^{2} = 10$ ) [2023]

Q 22 :

A series LCR circuit consists of $R = 80 Ω$ , $X_{L} = 100 Ω$ and $X_{C} = 40 Ω$ . The input voltage is $2500 \cos (100 π t) V$ . The amplitude of current in the circuit is ______ A. [2023]

Q 25 :

An inductor of 0.5 mH, a capacitor of $20 μ F$ and a resistance of $20 Ω$ are connected in series with a 220 V AC source. If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt{x} A$ . The value of $x$ is _______. [2023]

Q 26 :

A series combination of a resistor of resistance $100 Ω$ , an inductor of inductance 1 H and a capacitor of capacitance $6.25 μ F$ is connected to an AC source. The quality factor of the circuit will be ________. [2023]

Q 27 :

Using a variable frequency a.c. voltage source the maximum current measured in the given LCR circuit is 50 mA for V = 5sin(100t). The values of L and R are shown in the figure. The capacitance of the capacitor (C) used is ______ $µ F$ . [2026]

Q 28 :

For the series LCR circuit connected with 220 V, 50 Hz a.c. source as shown in the figure, the power factor is $\frac{α}{10}$ . The value of $α$ is ________. [2026]