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

Answer

D

Explanation

As the current leads the voltage by `45^(@)`, therefore,
`X_(C )gt X_(L), tan phi = (X_(C )-X_(L))/(R )=tan 45^(@)=1`
`rArr X_(C )-X_(L)=R` or `X_(C )=X_(L)+R=omega L+R`
`(1)/(omega C)=omega L+R, C=(1)/(omega(omega L+R))=(1)/(2pi upsilon(2pi upsilon L+R))`