The capacitor of an oscillatory circuit of frequency `10000 Hz` is enclosed in a container. When the container is evacuated, the frequency changes by`50 Hz`, the delectric constant of the gas is

Options

A. `1.1`
B. `1.01`
C. `1.001`
D. `1.0001`

Answer

B

Explanation

`f = (1)/(2pi sqrt(LC)), f + 50 = (1)/(2pi sqrt(LC//K))`
`rArr K = ((f + 50)/(f))^(2) = (1 + (50)/(f))^(2)`
`rArr K = 1 + (100)/(f) = 1 + (100)/(10,000) = 1.01`