Question

A resistor of resistance $2\Omega$ and an inductor of reactance $2\Omega$ are joined in series across an AC supply. The power factor is -

• A. $\frac{1}{\sqrt{2}}$
• B. $\frac{1}{\sqrt{5}}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\frac{1}{\sqrt{7}}$

Answer 1

The correct option is A $\frac{1}{\sqrt{2}}$

Given:

$R=X_L=2\Omega$

Now, impedance,

$Z=\sqrt{R^2+X_L^2}=\sqrt{2^2+2^2}=2\sqrt{2}$

Further, the power factor,

$\cos \varphi =\frac{R}{Z}=\frac{2}{2\sqrt{2}}=\frac{1}{\sqrt{2}}$

Hence, option $\left(A\right)$ is the correct answer.