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)/(2 pi f ( 2 pi f L + R))`
B. `(1)/(pi f (2 pi f L + R))`
C. `(1)/(2 pi f ( 2 pi f L - R))`
D. `(1)/( pi f (2 pi f L - R))`

Answer

A

Explanation

`tan phi = (X_(C) - X_(L))/(R) rArr 1 = (X_(C) - X_(L))/( R)`
`rArr (1)/(omega C) = R + omega L rArr (1)/( 2 pi f C) = R + 2 pi f L`
`rArr C = (1)/( 2 pi f (R + 2 pi f L))`