The resonance frequency of LCR series a.c. circuit is f 0 . Now the capacitance is made 4 times, then the new resonance frequency will become

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In LCR series circuit, resonance frequency $f_{0}$ is given by

$L ω = \frac{1}{C ω} \Rightarrow ω^{2} = \frac{1}{L C} ∴ ω = \sqrt{\frac{1}{L C}} = 2 π f_{0}$

$∴ f_{0} = \frac{1}{2 π \sqrt{L C}} or f_{0} \propto \frac{1}{\sqrt{C}}$

When the capacitance of the circuit is made 4 times, its resonant frequency become $f_{0}^{'}$

$∴ \frac{f_{0}^{'}}{f_{0}} = \frac{\sqrt{C}}{\sqrt{4 C}} or f_{0}^{'} = \frac{f_{0}}{2}$

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