Question

In an $\text{AC}$ circuit, the reactive impedance is $\sqrt{3}$ times the $R$. Then, the power factor is

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

Answer 1

The correct option is D $\frac{1}{\sqrt{3}}$

Given:-

$Z=\sqrt{3}R$

The power factor is given by

$\cos \varphi =\frac{R}{Z}$

Where, $\varphi \to$ Phase angle
$R\to$ Resistance
$Z\to$ Impedance

$\cos \varphi =\frac{R}{\sqrt{3}R}=\frac{1}{\sqrt{3}}$

Hence, option $\left(\text{D}\right)$ is the correct answer.