Alternating Current

JEE Main level, single correct, medium

158 of 190

Question 158 of 190

In a LCR circuit capacitance is changed from CC to 2C2 C. For the resonant frequency to remain unchanged, the inductance should be changed from LL to

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Answer: (C) L/2

ωres =1LC\omega_{\text {res }}=\frac{1}{\sqrt{L C}}
if ωres \omega_{\text {res }} is to remain same, the product LC should also not change.
⇒LC=L′C′⇒LC=L′2C⇒L′=L22\begin{aligned} & \Rightarrow \mathrm{LC}=\mathrm{L}^{\prime} \mathrm{C}^{\prime} \\ & \Rightarrow \mathrm{LC}=\mathrm{L}^{\prime} 2 \mathrm{C} \\ & \Rightarrow \mathrm{L}^{\prime}=\mathrm{L}^2 2 \end{aligned}

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