Alternating Current | Physics JEE Main questions with Solutions

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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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(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

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

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

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