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JEE Main 2021 (26 Feb, Shift 1) · Resonance, Bandwidth & Q Factor

Resonance, Bandwidth & Q Factor question from JEE Main 2021 (26 Feb, Shift 1)

Q99JEE Main 2021 · 26 FEB · SHIFT 1Medium

Resonance, Bandwidth & Q Factor

In a series LCR resonant circuit, the quality factor is measured as 100. If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be __________.

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

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Answer: 283

$Q = \frac{1}{R}\sqrt{\frac{L}{C}}$ , so $Q \propto \frac{\sqrt{L}}{R}$ .
$L \to 2L$ , $R \to \frac{R}{2}$ : $Q' = Q\times\frac{\sqrt{2}}{1/2} = 2\sqrt{2}\,Q$
$Q' = 2\sqrt{2}\times100 \approx 283$

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