Question

In series L-C-R circuit, the capacitance is changed from C to 2C. The inductance should be changed from L to ... to obtain same resonance frequency.

• A. 4L
• B. L/2
• C. L/4
• D. 2L

Answer 1

Answer: (B)

L/2

Answer 2

At resonance,
$X_L = X_C$
ie, $\omega_r \, L = \frac{ 1}{ \omega_r \, C}$
or $\omega_r = \frac{ 1}{ \sqrt{ LC}}$
or $2 \pi v_r = \frac{ 1}{ \sqrt{ LC}}$

or $v_r = \frac{ 1}{ 2 \pi \sqrt{ LC}}$
or LC = constant ( as v remains same)
$\therefore \frac{ L_2 }{ L_1 } = \frac{ C_1 }{ C_2 }$
or $\frac{ L_2 }{ L} = \frac{ C}{ 2 C}$ or $L_2 = \frac{ L }{ 2}$