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

Options

A. `(1)/(2pi(2pifL+R))`
B. `(1)/(2pi(2piR+L))`
C. `(2)/(2pi(R+L))`
D. `(2)/(2pi(R+(1)/(L)))`

Explanation

Current leads the voltage by `45^(@)`
`therefrore " " phi = 45^(@)`
Since, `tanphi = (X_( c) - X_(L))/( R)`
`rArr " " 1 = (x_( c) - X_(L))/( R)`
`rArr (1)/(omegaC) - omegaL = R`
`rArr " " (1)/(omegaC) = R + omegaL`
`C = (1)/(omega[R + omegaL])`
`rArr " " C = (1)/(2pir[p2pirL + R])`