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