Question

In an $\text{AC}$ circuit, the impedance is $\sqrt{3}$ times the $R$. Then, the phase angle is

• A. ${\cos }^{-1}\left(\frac{1}{\sqrt{2}}\right)$
• B. ${\cos }^{-1}\left(\frac{1}{3}\right)$
• C. ${\cos }^{-1}\left(\frac{1}{2}\right)$
• D. ${\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)$

Answer 1

The correct option is D ${\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)$

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

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

$\therefore \varphi ={\cos }^{-1}\left(\frac{1}{\sqrt{3}}\right)$

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