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. 1
D. `sqrt(3) // 2`

Answer

C

Explanation

When L is removed
`(pi)/(3) = tan^(-1) ((X_(C))/(R)) rArr (X_(C))/(R) = sqrt(3) rArr X_(C) = sqrt(3) R `
When C is removed
`tan((pi)/(3)) = (X_(L))/(R) rArr X_(L) = sqrt(3) R `
Since, ` X_(L) = X_(C)` (Resonance condition)
`:. cos phi = (R)/(Z) = 1 rArr cos phi = 1 `