Q212 / 225 · JEE Main 2004 · Physics

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

  • A
    $4 \mathrm{~L}$
  • B
    $2 \mathrm{~L}$
  • Correct answer
    C
    L/2
  • D
    L/4

Solution

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

Hence, the correct answer is option: 'C'.

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