MHT CET · Physics · Alternating Current
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
- A \(2 L\)
- B \(4 L\)
- C \(\frac{L}{2}\)
- D \(L\)
Answer & Solution
Correct Answer
(C) \(\frac{L}{2}\)
Step-by-step Solution
Detailed explanation
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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