Question

In $L-C-R$ 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. $\frac{L}{2}$
• C. $\frac{L}{4}$
• D. $4L$

Answer 1

Answer: (C)

$\frac{L}{4}$

The resonant frequency in a L-C-R circuit is given by ,

$f=\frac{1}{2\pi \sqrt{LC}}$ ................eq1

Now , if C is changed to 4C ,and L is changed to L' , to keep the $f$ constant , then

$f=\frac{1}{2\pi \sqrt{L^{\prime }\times 4C}}$ .................eq2

From eq1 and eq2 ,

$\frac{1}{2\pi \sqrt{LC}}=\frac{1}{2\pi \sqrt{L^{\prime }\times 4C}}$

or $L^{\prime }=L/4$