Question

In series LCR circuit, the capacitance is changed from C to 4C. To keep the resonance frequency unchanged, the new inductance should be :

• A. reduced by\(\frac{1}{4}L\)
• B. increased by 2L
• C. reduced by\(\frac{3}{4}L\)
• D. increased by 4L

Answer 1

The Correct Option is C

The resonance frequency \(\omega\) remains constant, implying:

\[ \omega' = \omega = \frac{1}{\sqrt{L'C'}} \]

It is provided that:

\[ L'C' = LC \]

Substituting \(C' = 4C\) yields:

\[ L' \cdot (4C) = LC \implies L' = \frac{L}{4} \]

Therefore, the inductance change required is:

\[ L - L' = L - \frac{L}{4} = \frac{3L}{4} \]