Question

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

Answer 1

Answer: 101

Frequency can be given as
$f=\frac{1}{2\pi \sqrt{LC}}$
Capacitance is directly proportional to dielectric constant $k$
Hence
$f\alpha \frac{1}{\sqrt{c}}\frac{f_1}{f_2}=\sqrt{\frac{c_2}{c_1}}=\sqrt{\frac{kc}{c}}=\sqrt{k}\frac{10000}{9950}=\sqrt{\frac{c_2}{c_1}}=\sqrt{\frac{kc}{c}}=\sqrt{k}k=1.01$