Question

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

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

Answer 1

The correct option is C $\frac{L}{2}$

$W_{res}=\frac{1}{\sqrt{LC}}$. If ${}^{\prime }{W}_{res}^{\prime }$ is to remain same, the product LC should also not change.
$\Rightarrow$ LC = L'C' $\Rightarrow$ LC = L'(2C) $\Rightarrow L^{\prime }=\frac{L}{2}$