Q142 / 180 · JIPMER 2018 · Physics

In a L-C circuit, angular frequency at resonance is $\omega$. What will be the new angular frequency when inductor's inductance is made two times and capacitor's capacitance is made four times?

  • Correct answer
    A
    $\frac{\omega}{2 \sqrt{2}}$
  • B
    $\frac{\omega}{\sqrt{2}}$
  • C
    $2 \omega$
  • D
    $\frac{2 \omega}{\sqrt{2}}$

Solution

$\because$ Angular frequency at resonance, $\omega=\frac{1}{\sqrt{\mathrm{LC}}}$ ...(i) According to question, when inductor's inductance is made 2 times and capacitance is 4 times, then $\omega^{\prime}=\frac{1}{\sqrt{\mathrm{LC}}}$ or $\quad \omega^{\prime}=\left(\frac{1}{2 \sqrt{2}}\right) \frac{1}{\sqrt{\mathrm{LC}}}$ $=\frac{\omega}{2 \sqrt{2}} \quad$ [From Eq. (i)]

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

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