Resonance frequency of L-C-R series AC circui | vedclass

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(B) The resonance frequency of a series $L-C-R$ circuit is given by the formula:$f_0 = \frac{1}{2 \pi \sqrt{L C}} \quad \dots (i)$When the inductance

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$\frac{f_0}{2}$

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(B) The resonance frequency of a series $L-C-R$ circuit is given by the formula:$f_0 = \frac{1}{2 \pi \sqrt{L C}} \quad \dots (i)$When the inductance is reduced to $L^{\prime} = \frac{L}{4}$ and the capacitance is increased to $C^{\prime} = 16 C$,the new resonance frequency $f_0^{\prime}$ is:$f_0^{\prime} = \frac{1}{2 \pi \sqrt{L^{\prime} C^{\prime}}}$Substituting the new values:$f_0^{\prime} = \frac{1}{2 \pi \sqrt{(\frac{L}{4}) 	imes (16 C)}}$$f_0^{\prime} = \frac{1}{2 \pi \sqrt{4 L C}}$$f_0^{\prime} = \frac{1}{2} 	imes \frac{1}{2 \pi \sqrt{L C}}$Using equation $(i)$,we get:$f_0^{\prime} = \frac{f_0}{2}$

Resonance frequency of $L-C-R$ series $AC$ circuit is $f_0$. Now,if the inductance is reduced to $\frac{1}{4}$ times and the capacitance is increased to $16$ times,then the new resonance frequency becomes:

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