The capacitor of an oscillatory circuit ina container. when the container is evacuated, the resonance frequency of the circuit is $10 k H z$ . when the container is filled with a gas, the resonance frequency changes by $50 H z$ . The dielectric constant of the gas is :

Question

The capacitor of an oscillatory circuit of frequency 10-000 Hz is enclosed in a container-When the container is evacuated - the frequency changes by 50 Hz- the dielectric constant of the gas is

Toppr Admin · Accepted Answer

Correct option is B- 1-01-f-dfrac-1-2 -pi -sqrt-LC- -f-50-dfrac-1-2 -pi -sqrt-LC - k-Rightarrow K-dfrac-f-50-f-2-1-dfrac-50-f-2-Rightarrow K-1-dfrac-100-f-1-dfrac-100-10000-1-01-

The capacitor of an oscillatory circuit of frequency 10,000 Hz is enclosed in a container.When the container is evacuated , the frequency changes by 50 Hz, the dielectric constant of the gas is

Correct option is B. 1.01
$$f=\dfrac{1}{2 \pi \sqrt{LC}} $$

$$,f+50=\dfrac{1}{2 \pi \sqrt{LC / k}}$$
$$\Rightarrow K=(\dfrac{f+50}{f})^2=(1+\dfrac{50}{f})^2$$
$$\Rightarrow K=1+\dfrac{100}{f}$$

$$=1+\dfrac{100}{10000}=1:01$$

The capacitor of an oscillatory circuit of frequency 10,000 Hz is enclosed in a container.When the container is evacuated , the frequency changes by 50 Hz, the dielectric constant of the gas is

Correct option is B. 1.01$$f=\dfrac{1}{2 \pi \sqrt{LC}} $$$$,f+50=\dfrac{1}{2 \pi \sqrt{LC / k}}$$$$\Rightarrow K=(\dfrac{f+50}{f})^2=(1+\dfrac{50}{f})^2$$$$\Rightarrow K=1+\dfrac{100}{f}$$$$=1+\dfrac{100}{10000}=1:01$$

Correct option is B. 1.01
$$f=\dfrac{1}{2 \pi \sqrt{LC}} $$

$$,f+50=\dfrac{1}{2 \pi \sqrt{LC / k}}$$
$$\Rightarrow K=(\dfrac{f+50}{f})^2=(1+\dfrac{50}{f})^2$$
$$\Rightarrow K=1+\dfrac{100}{f}$$

$$=1+\dfrac{100}{10000}=1:01$$