Question

In an LCR series circuit, the capacitor is changed from C to 4C. For the same resonant frequency, the inductance should be changed from L to

• A. 2L
• B. L/2
• C. L/4
• D. 4L

Answer 1

The correct option is C L/4

For resonance:

$X_L=X_C$

$\omega L=\frac{1}{\omega C}$

$\omega =\frac{1}{\sqrt{2C}}$

$2\pi f=\frac{1}{\sqrt{2C}}$

For same resonant frequency:
LC should be constant.

So, LC = $4C{L}_1$

$\Rightarrow L_1=\frac{LC}{4C}$$=\frac{L}{4}$