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

Answer: (C)

reduced by$\frac{3}{4}L$

Answer 2

To keep the resonance frequency $\omega$ unchanged, we know:

$\omega' = \omega = \frac{1}{\sqrt{L'C'}}$

Given:

$L'C' = LC$

Substituting $C' = 4C$ into the equation:

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

Thus, the inductance must be decreased by:

$L - L' = L - \frac{L}{4} = \frac{3L}{4}$