In the circuit shown in the figure, a.c. source gives voltage V =… | MHT CET 2021 (24 Sep, Shift 1)

Q51MHT CET 2021 · 24 SEP · SHIFT 1Medium

Series LCR Circuit

In the circuit shown in the figure, a.c. source gives voltage $V = 20\cos(2000t)$ . Impedance and r.m.s. current respectively will be

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Answer: (c)

$\omega = 2000\text{ rad/s}$ , $V_0 = 20\text{ V}$ .
$X_L = \omega L = 2000 \times 5\times10^{-3} = 10\ \Omega$
$X_C = \dfrac{1}{\omega C} = \dfrac{1}{2000 \times 50\times10^{-6}} = 10\ \Omega$
$X_L = X_C$ (resonance), so $Z = R = 10\ \Omega$ .
$I_{rms} = \dfrac{V_0/\sqrt{2}}{Z} = \dfrac{20}{10\sqrt{2}} = \sqrt{2}\text{ A}$
So the answer is (c) $10\ \Omega,\ \sqrt{2}\text{ A}$ .

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