First slide

Alternating Current and voltage

Question

The r.m.s. current in an ac circuit is 2 A. If the wattless current be $\sqrt{3} A$ , what is the power factor

Moderate

A

$\frac{1}{\sqrt{3}}$
B

$\frac{1}{\sqrt{2}}$
C

$\frac{1}{2}$
D

$\frac{1}{3}$

Solution

$i_{WL} = i_{rms} sinφ \Rightarrow \sqrt{3} = 2 sinφ \Rightarrow sinφ = \frac{\sqrt{3}}{2}$
$\Rightarrow φ = 60^{o} so p . f . = cosφ = \cos 60^{o} = \frac{1}{2}$

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