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)

$\frac{ f_0}{ 2}$

Answer 2

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 $f'_0 = \frac{ f_0}{ 2 }$