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

Answer: (C)

1

Answer 2

: When L is removed from the circuit, it becomes RC circuit.

$\tan\varphi = \tan\frac{\pi}{3} = \frac{X_{C}}{R}\therefore X_{C} = R\tan\frac{\pi}{3} = \sqrt{3}R$

When C is removed from the circuit, it becomes RL circuit.

$\therefore\tan\varphi = \tan\frac{\pi}{3} = \frac{X_{L}}{R}$

$X_{L} = R\tan\frac{\pi}{3} = \sqrt{3}R$

Impedance of the circuit,

$Z = \sqrt{R^{2} + (X_{L} - X_{C})^{2}} = R$

Power factor, ,$\cos\varphi = \frac{R}{Z} = \frac{R}{R} = 1.$