Question

In a series $LCR$ circuit, the inductive reactance $\left(X_L\right)$ is $10\Omega$ and the capacitive reactance $\left(X_C\right)$ is $4\Omega$. The resistance $\left(R\right)$ in the circuit is $6\Omega$. Find the power factor of the circuit.

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

Answer 1

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

Given:
$X_L=10\Omega$
$X_C=4\Omega$
$R=6\Omega$

We know that power factor,
$=\cos \varphi =\frac{R}{Z}$

$=\frac{R}{\sqrt{R^2+(X_L-X_C{)}^2}}$

$=\frac{6}{\sqrt{6^2+(10-4{)}^2}}$

$=\frac{6}{6\sqrt{2}}$

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

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