Alternating Current | Physics JEE Main questions with Solutions

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]

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(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]

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(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]

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(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]

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(100)

$C = 62.5 nF, R = 50 Ω, f = 2 kHz$

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

$f = \frac{1}{2 π \sqrt{L C}}$

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

Topic Question Set

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]

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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]

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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]

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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]

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