Physics | VITEEE 2017 | Discussion Page

Resonance frequency of LCR series a.c. circuit is f₀. Now the capacitance is made 4 times, then the new resonance frequency will become

A) $\frac{f_{0}}{4}$

B) $ 2f_{0}$

C) $f_{0}$

D) $\frac{f_{0}}{2}$

Option D

In LCR series circuit, resonance frequency f₀ is given by

$L\omega = \frac{1}{C\omega}\Rightarrow \omega^{2} =\frac{1}{LC}$

$\therefore\omega = \sqrt{\frac{1}{LC}}=2\pi f_{0}$

$\therefore f_{0} = \frac{1}{2\pi\sqrt{LC}}$ or $f_{0} \propto \frac{1}{\sqrt{C}}$

When the capacitance of the circuit is made 4 times, its resonant frequency become f'₀

$\frac{f'_{0}}{f_{0}}=\frac{\sqrt{C}}{\sqrt{4C}}$

OR $f'_{0} = \frac{f_{0}}{2}$

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