Q 12-07-126JEE MainJEE Main 2021 (26 Feb, Shift 1)Medium
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 value type. Enter your answer.
Answer: 282.84
$Q = \dfrac{1}{R}\sqrt{\dfrac{L}{C}}$.
With $L' = 2L$ and $R' = R/2$:
$$Q' = \frac{2}{R}\sqrt{\frac{2L}{C}} = 2\sqrt{2}\,Q = 2\sqrt{2}\times100 \approx 282.84$$
Solution by Sreeraj P, M.Sc Physics