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. $\frac{1}{\sqrt{2}}$
• C. 1
• D. $\frac{\sqrt{3}}{2}$

Answer 1

Answer: (C)

For only $RC:-{\varphi }_{RC}=\frac{\pi }{3}$
$\tan \left(\frac{\pi }{3}\right)=\frac{X_c}{R}$
$\Rightarrow X_c=\sqrt{3}R$
For only $RL:-{\varphi }_{RL}=\frac{\pi }{3}$
$\tan \left(\frac{\pi }{3}\right)=\frac{X_L}{R}$
$\Rightarrow X_L=\sqrt{3}R$
For RL:-
$\tan (\varphi )=\frac{X_L-X_C}{R}=\frac{\sqrt{3}R-\sqrt{3}R}{R}=0$
$\Rightarrow \varphi =0$
$\Rightarrow \cos \varphi =1$