Question:
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 __________.
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 __________.
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Quality factor \(Q = \frac{1}{R}\sqrt{\frac{L}{C}}\); it varies as \(\sqrt{L}/R\) at fixed C.
Updated On: Nov 4, 2026
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Correct Answer: 283
Solution and Explanation
\(Q = \frac{1}{R}\sqrt{\frac{L}{C}}\) and C is unchanged.
New values: \(L' = 2L\), \(R' = \frac{R}{2}\).
\(Q' = \frac{1}{R/2}\sqrt{\frac{2L}{C}} = 2\sqrt{2}\,Q = 2\sqrt{2}\times 100 \approx 282.8\).
To the nearest integer, \(Q' \approx 283\).
Answer: 283
New values: \(L' = 2L\), \(R' = \frac{R}{2}\).
\(Q' = \frac{1}{R/2}\sqrt{\frac{2L}{C}} = 2\sqrt{2}\,Q = 2\sqrt{2}\times 100 \approx 282.8\).
To the nearest integer, \(Q' \approx 283\).
Answer: 283
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