Question

Resonance frequency of L-C-R series AC circuit is $f_0$ . Now the capacitance is made 4 times, then the new resonance frequency will become

• A. $ \frac{ f_0}{ 4} $
• B. 2$ f_0$
• C. $ f_0$
• D. $ \frac{ f_0}{ 2} $

Answer 1

Answer: (D)

In l-C-R series circuit, resonance occurs when
$ X_L = X_C $
or $ \omega L = \frac{ 1}{ \omega C} $
or $ \omega^2 = \frac{ 1}{ LC} $
or $ \omega = \frac{ 1}{ \sqrt{ LC}} $
$\Rightarrow 2 \pi f_0 = \frac{ 1}{ \sqrt{ LC}} $
$ f_0 = \frac{ 1}{ 2 \pi \sqrt{ LC}} $
$\therefore f_0 \propto \frac{ 1}{ \sqrt C} $
When capacitance of the circuit is made 4 times, Iet its resonant frequency become $ f'_0 $.
$\therefore \frac{ f'_0}{ f_0} = \frac{ \sqrt {C}}{ \sqrt{ 4C}}$ or $f'_0 = \frac{ f_0}{ 2 } $