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/sqrt(2)`
C. `sqrt(3)`
D. `(sqrt(3))/(2)`

Answer

C

Explanation

Here, phase difference
`tanphi=(X_(L)-X_(C))/(R)`
`"tan"(pi)/(3)=(X_(L)-X_(C))/(R)`
When L is removed
`sqrt(3)=(X_(C))/(R)`
`X_(C)=sqrt(3)R`