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//sqrt2`
C. 1
D. `sqrt3 // 2`

Answer

C

Explanation

When `L` is removed from the circuit, it becomces `RC` circuit.
`tan phi = "tan" (pi)/(3) = (X_(C ))/(R )`
`:. X_(C ) = R tan phi//3 = sqrt3 R`
When `C` is removed from the circuit,it becomes. `RL` circuit.
`:.tan phi = tan` `(pi)/(3) = (X_(L))/(R )`
`X_(L) = R tan pi//3 = sqrt3 R`
Impedance of the circuit,
`Z = sqrt(R^(2) + (X_(L) - X_(C ))^(2)) = R`
Power factor, `cos phi = (R )/(Z) = (R )/(R ) = 1`