A series LCR circuit is connected across a source of alternating emf of changing frequency and resonates at frequency $f_{0}$ keeping capacitance constant, if the inductance(L) is increased by $\sqrt{3}$ times and resistance (R) is increased by 1.4times, the new resonant frequency will be

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${(\frac{1}{3})}^{1 / 4} f_{0}$

${(\sqrt{3} - 1)}^{1 / 4} f_{0}$

$\sqrt{3} f_{0}$

$3^{1 / 4} f_{0}$

answer is C.

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Detailed Solution

Resonant frequency series LCR circuit is

$f = \frac{1}{2 π} \frac{1}{\sqrt{L C}}$

$f \propto \frac{1}{\sqrt{L}}$ as C is same

$\frac{f_{0}}{f_{1}} = \sqrt{\frac{\sqrt{3} L}{L}} = 3^{1 / 4}$

$f_{1} = f_{0} {(\frac{1}{3})}^{1 / 4}$

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