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JEE Main 2022 (25 Jun, Shift 2) · Resonance, Bandwidth & Q Factor

Resonance, Bandwidth & Q Factor question from JEE Main 2022 (25 Jun, Shift 2)

Q78JEE Main 2022 · 25 JUN · SHIFT 2Medium

Resonance, Bandwidth & Q Factor

In a series LCR circuit, the inductance, capacitance and resistance are L = 100 mH, C = 100 $\mu$ F and R = 10 $\Omega$ respectively. They are connected to an AC source of voltage 220 V and frequency of 50 Hz. The approximate value of current in the circuit will be ___________ A.

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

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Answer: 22

$\omega = 2\pi(50) = 314\text{ rad/s}$
$X_L = 314 \times 0.1 = 31.4\ \Omega$ , $X_C = \frac{1}{314\times10^{-4}} = 31.8\ \Omega$
$Z = \sqrt{10^2 + (0.4)^2} \approx 10\ \Omega$ (almost at resonance)
$I = \frac{220}{10} = 22\text{ A}$

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