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 $\frac{\pi }{3}$. If instead C is removed from the circuit, the phase difference is again $\frac{\pi }{3}$. 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

The correct option is C 1

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 $RL$:-

$\tan \left(\varphi \right)=\frac{X_L-X_C}{R}=\frac{\sqrt{3}R-\sqrt{3}R}{R}=0\Rightarrow \varphi =0\Rightarrow \cos \varphi =1$