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In an LC oscillator, if values of inductance and capacitance becomes twice and eighteen times respectively then the resonant frequency of oscillator becomes ${}^{'}x^{'}$ times its initial resonant frequency $ω_{o}$ the value of ${}^{'}x^{'}$ is

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$6$

$\frac{1}{6}$

$\frac{1}{16}$

$16$

answer is B.

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Detailed Solution

$W_{o} = \frac{1}{\sqrt{L} C}$

$L = 2 L, C = 18 C$

$W_{0}^{1} = \frac{1}{\sqrt{2 L \times 18 C}} = \frac{1}{\sqrt{36 L C}} = \frac{1}{6 \sqrt{L C}}$

$ω_{0}^{1} = \frac{1}{6} ω$

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