Alternating Current Question 2
Question 2 - 2024 (01 Feb Shift 1)
In series LCR circuit, the capacitance is changed from $C$ to $4 C$. To keep the resonance frequency unchanged, the new inductance should be :
(1) reduced by $\frac{1}{4} L$
(2) increased by $2 L$
(3) reduced by $\frac{3}{4} L$
(4) increased to $4 L$
Show Answer
Answer: (3)
Solution:
$\omega^{\prime}=\omega$
$\frac{1}{\sqrt{L^{\prime} C^{\prime}}}=\frac{1}{\sqrt{LC}}$
$\therefore L^{\prime} C^{\prime}=LC$
$L^{\prime}(4 C)=LC$
$L^{\prime}=\frac{L}{4}$
$\because \quad$ Inductance must be decreased by $\frac{3 L}{4}$
