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(D) The resonant frequency of a series $LC$ circuit is given by the formula:$f = \frac{1}{2 \pi \sqrt{LC}}$When the inductance is changed to $L' = 3L$

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$\frac{f}{3 \sqrt{2}}$

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(D) The resonant frequency of a series $LC$ circuit is given by the formula:$f = \frac{1}{2 \pi \sqrt{LC}}$When the inductance is changed to $L' = 3L$ and the capacitance is changed to $C' = 6C$,the new resonant frequency $f'$ is:$f' = \frac{1}{2 \pi \sqrt{L' C'}} = \frac{1}{2 \pi \sqrt{(3L)(6C)}}$$f' = \frac{1}{2 \pi \sqrt{18 LC}} = \frac{1}{2 \pi \sqrt{9 \cdot 2 \cdot LC}}$$f' = \frac{1}{2 \pi \cdot 3 \sqrt{2} \sqrt{LC}}$Since $f = \frac{1}{2 \pi \sqrt{LC}}$,we can substitute this into the equation:$f' = \frac{f}{3 \sqrt{2}}$

$A$ series resonant circuit consists of an inductor '$L$' of negligible resistance and a capacitor '$C$' which produces a resonant frequency '$f$'. If '$L$' is changed to $3L$ and '$C$' is changed to $6C$,the new resonant frequency will become:

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