Q 12-07-046JEE MainJEE Main 2024 (1 Feb, Shift 1)Easy
In a series LCR circuit, the capacitance is changed from $C$ to $4C$. To keep the resonance frequency unchanged, the new inductance should be
Answer: (C) reduced by $\dfrac{3}{4}L$
$\omega_0 = \dfrac{1}{\sqrt{LC}}$, so $LC$ must stay constant: $L'(4C) = LC \Rightarrow L' = \dfrac{L}{4}$.
The inductance is reduced by $L - \dfrac{L}{4} = \dfrac{3}{4}L$.
Solution by Sreeraj P, M.Sc Physics