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In an electrical circuit R,L,C and an AC...

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

A

`(1)/(2)`

B

`(1)/(sqrt(2))`

C

1

D

`(sqrt(3))/(2)`

Text Solution

Verified by Experts

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