In series $L-C-R$ circuit, the capacitance is changed from $C$ to $2 C$. To obtain the same resonance…

In series $L-C-R$ circuit, the capacitance is changed from $C$ to $2 C$. To obtain the same resonance frequency the inductance should be changed from $L$ to
  1. $2 L$
  2. $4 L$
  3. $\frac{L}{2}$
  4. $L$

Solution

Resonant frequency, $f=\frac{1}{2 \pi \sqrt{L C}}$ As the frequency is unchanged so $f=f^{\prime}$ $\begin{aligned} & \therefore L C=L^{\prime} C^{\prime}=L^{\prime}(2 C) \\ & \therefore L^{\prime}=\frac{L}{2} \end{aligned}$

Asked in: MHT CET 2022 (08 Aug Shift 1)

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