Question

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

Answer 1

Correct Answer - B
As current lead the voltage by `45^(@)`, therefore
`tan phi = (X_(C ) - X_(L))/(R ) = tan 45^(@) = 1`
`:. X_(C ) - X_(L) = R` or `X_(C ) = X_(L) + R`
or `1//omega C = omega L + R`
`C = (1)/(omega (omega L + R))`
`C = (1)/(2 pi f (2 pi f L + R))`