First slide

Phasors and Phasor Diagrams

Question

A series LCR circuit is connected to an ac voltage source. When L is removed from the circuit, the phase difference between current and voltage is $\frac{π}{3}$ . If instead C is removed from the circuit, the phase difference is again $\frac{π}{3}$ between current and voltage. The power factor of the circuit is :

Moderate

A

0.5
B

1.0
C

-1.0
D

Zero

Solution

$\begin{array}{l} \tan θ = \frac{X_{c}}{R} = \sqrt{3} \\ X_{c} = \sqrt{3} R \\ \tan θ = \frac{X_{L}}{R} = \sqrt{3} \\ X_{c} = \sqrt{3} R \\ X_{L} = X_{c} = Given \end{array}$
Circuit is LCR resonate circuit
$power factor \cos θ = \frac{R}{Z} = \frac{R}{\sqrt{{(X_{2} - X_{c})}^{2} + R^{2}}} = 1$

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