Question

The capacitor of an oscillatory circuit is enclosed in $a$ container. When the container is evacuated, the resonance frequency of the circuit is $10\,kHz$ . When the container is filled with $a$ gas, the resonance frequency changes by $50\,Hz$ . The dielectric constant of the gas is $\frac{x}{100}$ . What is the value of $x$ ?

Answer 1

Frequency can be given as
$f=\frac{1}{2 \pi \sqrt{LC}}$
Capacitance is directly proportional to dielectric constant $k$
Hence
$f\alpha \frac{1}{\sqrt{c}}\frac{f_{1}}{f_{2}}=\sqrt{\frac{c_{2}}{c_{1}}}=\sqrt{\frac{k c}{c}}=\sqrt{k}\frac{10000}{9950}=\sqrt{\frac{c_{2}}{c_{1}}}=\sqrt{\frac{k c}{c}}=\sqrt{k}k=1.01$