Question

In an LCR circuit inductance is changed from $L$ to $\frac{L}{2}$. To keep the same resonance frequency, $C$ should be changed to

• A. $2C$
• B. $\frac{C}{2}$
• C. $4C$
• D. $\frac{C}{4}$

Answer 1

The correct option is A $2C$

Resonance frequency, $\left(f\right)=\frac{1}{2\pi \sqrt{LC}}$

For $f$ to be constant the product $LC$ must be constant.

So, if we half the value of inductance then the value of capacitance must be $doubled$.

$C$ should be changed to $2C$.