In a series LCR circuit at resonance, the capacitance is made one-fourth. By what factor must the inductance be changed so that the circuit remains at resonance?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4 times
A series LCR circuit is at resonance when \( X_L=X_C \). This happens at the resonant frequency
\( \displaystyle \omega_0=\frac{1}{\sqrt{LC}} \)
For the circuit to stay at resonance at the same frequency, the product \( LC \) must stay the same. With the new capacitance \( C/4 \) and new inductance \( L' \):
\( \displaystyle L'\,\frac{C}{4}=LC \)
\( \Rightarrow\; L'=4L \)
Therefore, the inductance must be made 4 times its original value.