Question

In an electrical circuit $R, L, C$ and 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 If instead, $C$ is removed from the circuit, the phase difference is again The power factor of the circuit is

• A. $\frac{1}{2}$
• B. $\frac{1}{\sqrt2}$
• C. 1
• D. $\frac{\sqrt3}{2}$

Answer 1

Answer: (C)

For only $RC :-\phi_{ RC }=\frac{\pi}{3}$
$\tan \left(\frac{\pi}{3}\right)=\frac{ X _{c}}{ R }$
$ \Rightarrow X _{ c }=\sqrt{3} R$
For only $RL :-\phi_{ RL }=\frac{\pi}{3}$
$\tan \left(\frac{\pi}{3}\right)=\frac{ X _{ L }}{ R } $
$\Rightarrow X _{ L }=\sqrt{3} R$
For RL:-
$\tan (\phi)=\frac{X_{L}-X_{C}}{R}=\frac{\sqrt{3} R-\sqrt{3} R}{R}=0$
$ \Rightarrow \phi=0 $
$\Rightarrow \cos \phi=1$