question_answer

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

A) \[1/2\]                           

B) \[1/\sqrt{2}\]  

C) 1         

D) \[\sqrt{3}/2\]

Correct Answer: C

Solution :

when L is removed from the circuit
\[\frac{{{X}_{C}}}{R}=\tan \frac{\pi }{3}\]
\[{{X}_{C}}=R\tan \frac{\pi }{3}\]	?(1)
when C is remove from the circuit
\[\frac{{{X}_{L}}}{R}=\tan \frac{\pi }{3}\]
\[{{X}_{C}}=R\,\tan \frac{\pi }{3}\]	?(2)
net impedence \[Z=\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{X}_{C}})}^{2}}}=R\]
power factor \[\cos \phi =\frac{R}{Z}=1\]