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(C) The resonant frequency $f$ of a series $LCR$ circuit is given by the formula: $f = \frac{1}{2\pi\sqrt{LC}}$.Given the initial frequency $f = \frac

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$f/(3\sqrt{3})$

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(C) The resonant frequency $f$ of a series $LCR$ circuit is given by the formula: $f = \frac{1}{2\pi\sqrt{LC}}$.Given the initial frequency $f = \frac{1}{2\pi\sqrt{LC}}$.The new inductance is $L' = L + 2L = 3L$.The new capacitance is $C' = 9C$.The new resonant frequency $f'$ is given by: $f' = \frac{1}{2\pi\sqrt{L'C'}} = \frac{1}{2\pi\sqrt{(3L)(9C)}} = \frac{1}{2\pi\sqrt{27LC}}$.Simplifying the expression: $f' = \frac{1}{2\pi\sqrt{27}\sqrt{LC}} = \frac{1}{2\pi(3\sqrt{3})\sqrt{LC}}$.Since $f = \frac{1}{2\pi\sqrt{LC}}$, we substitute this into the equation for $f'$:$f' = \frac{f}{3\sqrt{3}}$.Therefore, the new resonant frequency is $f/(3\sqrt{3})$.

$A$ series resonant circuit consists of an inductor $L$ and capacitor $C$ which produces resonant frequency $f$. If $L$ is increased by $2L$ (making the new inductance $L' = L + 2L = 3L$) and $C$ is changed to $9C$, the new resonant frequency will be:

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