Question

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

(1) reduced by \(\frac{1}{4}L\)

(2) increased by 2L

(3) reduced by \(\frac {3}{4}L\)

(4) increased to 4L

Answer 1

(3) reduced by \(\frac {3}{4}L\)

\(\omega '= \omega\)

\(\frac {1}{\sqrt {L'C'}}=\frac {1}{\sqrt {LC}}\)

\(\therefore L'C'=LC\)

\(L'(4C)=LC\)

\(L'= \frac {L}{4}\)

\(\because \) Inductance must be decreased by \(\frac {3L}{4}\)