In an electrical circuit `R,L,C` and an `AC` voltage source are all connected in series. When `L` is removed from the circuit, the phase difference between the voltage and the current in the circuit is `pi//3`. If instead, `C` is removed from the circuit, difference the phase difference is again `pi//3`. The power factor of the circuit is

Options

A. `1/2`
B. 1
C. zero
D. `1/(sqrt2)`

Answer

B

Explanation

When L is removed from the circuit it becomes a C-R circuit for which `tan phi = (X_C)/R`
When C is removed from the circuit it becomes a L-R circuit for which `tan phi' = (X_L)/R` but `phi = phi' = (pi)/3`
`:. X_(C) = X_(L) or 1/(omega C) = omega L`
`:.` This is a series resonant circuit, For which,
Net impedance `Z = sqrt(R^(2)+(X_(L)-X_(C))^(2)) = R`
`:.` Power factor = `R/Z =1`.