Question

The capacitor of an oscillatory circuit of negligible resistance is enclosed in a evacuated container. The frequency of the circuit is 150 kHZ and when the container is filled with a gas, the frequency changes by 100 HZ. The dielectric constant of the gas.

• A. 2
• B. 1.53
• C. 1.0012
• D. 3

Answer 1

The correct option is C 1.0012

We know frequency is given by:

$n_1=\frac{1}{2\pi \sqrt{L{C}_1}}$

And

$n_2=\frac{1}{2\pi \sqrt{LK{C}_1}}$

Thus we get the ratio of frequencies as

$\frac{n_1}{n_2}=\frac{150000}{149900}=\sqrt{k}$
Solving the above equation we get, $k\approx 1.0012$