In a circuit `L, C` and `R` are connected in series with an alternating voltage source of frequency `f`. The current lead the voltages by `45^(@)`. The value of `C` is :

Options

A. `1/(2pif(2pifL+R))`
B. `1/(pif(2pifL+R))`
C. `1/(2pif(2pifL-R))`
D. `1/(pif(2pifL-R))`

Answer

C

Explanation

`tan varphi=(omegaL-1/(omega C))/R`
`phi` being the angle by which the current leads the voltage.
Given, `phi=45^(@)`
`:. tan 45^(@)=(omegaL-1/(omegaC))/R`
`implies 1=(omegaL-1/(omegaC))/R`
`implies R=omegaL-1/(omegaC)`
`implies omegaC=1/((omegaL-R))`
`implies C=1/(omega(omegaL-R))=1/(2pif(2pifL-R))`