Question

For the same resonant frequency, if \( L \) is changed from \( L \) to \( \frac{L}{3} \), then capacitance should change from \( C \) to

• A. \( \frac{C}{3} \)
• B. \( 3C \)
• C. \( \frac{2}{3}C \)
• D. \( 2C \)

Hint:

In LC resonance, product \( LC \) must remain constant. Use this when one parameter changes.

Answer 1

The Correct Option is B

Resonant frequency is: \[ f = \frac{1}{2\pi \sqrt{LC}} \Rightarrow f \propto \frac{1}{\sqrt{LC}} \Rightarrow LC = \text{constant} \] If \( L \to \frac{L}{3} \), to maintain same \( LC \): \[ \left( \frac{L}{3} \right) \cdot C' = L \cdot C \Rightarrow C' = 3C \] So, the capacitance should be increased three times.