Frequency of L-C circuit is `f_(1)`. If a resistance R is also added to it the frequency becomes `f_(2)`. The ratio of `(f_(1))/(f_(1))` will be.

Options

A. `sqrt(1+(R^2C)/(4L))`
B. `sqrt(1-(R^(2)C)/(4L))`
C. `sqrt(1+(R^(2)C)/(L))`
D. `sqrt(1-(R^(2)C)/(L))`

Answer

B

Explanation

`omega^(2)=(1)/(sqrt(LC))`
`omega_(2)=sqrt(((1)/(sqrt(LC)))^(2)-((R)/(2L))^(2))`
`(omega_(2))/(omega_(1))=(sqrt((1)/(LC)-(R^(2))/(4L^(2))))/((1)/(sqrt(LC)))=sqrt(1-(R^(2)C)/(4L))`