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JEE Main 2023 (31 Jan, Shift 1) · Resonance, Bandwidth & Q Factor

Resonance, Bandwidth & Q Factor question from JEE Main 2023 (31 Jan, Shift 1)

Q60JEE Main 2023 · 31 JAN · SHIFT 1Easy

Resonance, Bandwidth & Q Factor

An inductor of $0.5\text{ mH}$ , a capacitor of $20\ \mu\text{F}$ and resistance of $20\ \Omega$ are connected in series with a $220\text{ V}$ 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 ___________

Numerical answer type. Work it out, then open the answer.

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Answer: 242

In phase means resonance, so $Z = R = 20\ \Omega$ .
Peak emf $E_0 = 220\sqrt{2}\text{ V}$ .
$I_0 = \dfrac{220\sqrt{2}}{20} = 11\sqrt{2} = \sqrt{242}\text{ A}$
So $x = 242$ .

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