Question

The capacitance of a capacitor in an oscillatory LC circuit is increased by $1.0\%$. The change in inductance required to maintain the same frequency of oscillations of charge is -

• A. decrease it by $0.5\%$
• B. increase it by $0.5\%$
• C. decrease it by $1.0\%$
• D. increase it by $1.0\%$

Answer 1

The correct option is C decrease it by $1.0\%$

We know that, frequency of oscillations of charge in the LC circuit is,

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

Given, $f=$ constant.

$\Rightarrow LC=$ constant

After differentiating, we get,

$LdC+CdL=0$

$\Rightarrow \frac{dL}{L}=-\frac{dC}{C}$

$\Rightarrow \frac{dL}{L}\times 100=-\frac{dC}{C}\times 100$

So, percentage change in inductance and that in capacitance are of same magnitude.

Negative sign indicates that, the nature of the change in them will be opposite.

As the capacitance is increased, the inductance should be decreased.

Therefore, the inductance should be decreased by $1.0\%$.

Hence, option $\left(C\right)$ is the correct answer.