The resonant frequency of a circuit is f. If | vedclass

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(A) The resonant frequency of an $LC$ circuit is given by the formula: $f = \frac{1}{2\pi \sqrt{LC}}$.From this expression,we can see that the resonan

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$f / 2$

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(A) The resonant frequency of an $LC$ circuit is given by the formula: $f = \frac{1}{2\pi \sqrt{LC}}$.From this expression,we can see that the resonant frequency is inversely proportional to the square root of the capacitance: $f \propto \frac{1}{\sqrt{C}}$.Let the initial frequency be $f_1 = f$ and the initial capacitance be $C_1 = C$.If the new capacitance is $C_2 = 4C$,the new resonant frequency $f_2$ is given by:$f_2 = \frac{1}{2\pi \sqrt{L(4C)}} = \frac{1}{2\pi \sqrt{4} \sqrt{LC}} = \frac{1}{2} 	imes \frac{1}{2\pi \sqrt{LC}}$.Substituting the initial frequency $f$ into the equation,we get:$f_2 = \frac{f}{2}$.

The resonant frequency of a circuit is $f$. If the capacitance is made $4$ times the initial value,then the resonant frequency will become

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