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 :

[c]    when L is removed from the circuit \[\left[ \because \,\,R=\frac{V}{I}=\frac{80}{10}=8 \right]\]   \[{{X}_{C}}=R\,\tan \,\frac{\pi }{3}\]       ??(i) when C is remove from the circuit \[\frac{{{X}_{L}}}{R}=\tan \,\frac{\pi }{3}\] \[{{X}_{C}}=R\,\tan \,\frac{\pi }{3}\]     ??.(ii) net impedence\[Z=\sqrt{{{R}^{2}}+({{X}_{L}}-{{X}_{C}})}=R\] power factor cos \[\phi \,=\frac{R}{Z}=1\]