A series L-C-R circuit is connected to an alternating voltage source of frequecy f. If the current leads the e.m.f. By `45^(@)`, then the value of C is

Options

A. `1/(2 pi f(2 pi fL+R))`
B. `1/(2 pi fC(2 pi fL-R))`
C. `1/(pi f(2 pi fL-R))`
D. `1/(pi f(2 pi fL+R))`

Answer

B

Explanation

In a series L-C-R circuit, `tan phi = (X_(C)-X_(L))/R`
As the current leads the e.m.f. `X_(C) gt X_(L)`.
`:. tan 45^(@) = (X_(C)-X_(L))/R =1`
`:. X_(C) = X_(L)+R`
`:. 1/(omega C) = omega L + R :. Omega C = 1/(omegaL+R)`
`:. C = 1/(omega(omegaL+R)) = 1/(2pi f(2 pi f L+R))`.