Question

In a $LCR$ circuit capacitance is changed from $C$ to $2$. For the resonant frequency to remain unchanged, the inductance should be changed from $L$ to

• A. $4L$
• B. $2L$
• C. $L/2$
• D. $L/4$

Answer 1

Answer: (C)

$L/2$

Resonant frequency $f=\frac{1}{2\pi \sqrt{LC}}$

Now, $f^{\prime }=\frac{1}{2\pi \sqrt{L^{\prime }2C}}$

for $f^{\prime }=f$ $\frac{1}{2\pi \sqrt{L^{\prime }2C}}=\frac{1}{2\pi \sqrt{LC}}$

$\Rightarrow L^{\prime }2C=LC$

$\Rightarrow L^{\prime }=L/2$ .