Question

The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated, the frequency is $10\text{kHz}$. When the container is filled with a gas, the frequency changes by $50\text{Hz}$. The dielectric constant of the gas is

• A. $2.01$
• B. $1.01$
• C. $2.001$
• D. $1.001$

Answer 1

The correct option is B $1.01$

We know that

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

$\Rightarrow f\propto \frac{1}{\sqrt{C}}$

$\therefore \frac{f_2}{f_1}=\sqrt{\frac{C_1}{C_2}}$

Given, $f_1=10\times {10}^3\text{Hz};f_2=(10\times {10}^3-50)\text{Hz}$ and also

$K=\frac{C_2}{C_1}$= Dielectric constant

$\Rightarrow \frac{{10}^4-50}{{10}^4}=\sqrt{\frac{1}{K}}$

$\therefore K=1.01$

Hence, $\left(\text{B}\right)$ is the correct answer.