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