Question

In a series LCR circuit, the inductive reactance (X_L) is $10\Omega$and the capacitive reactance (X_C) is $4\Omega$. The resistance (R) 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

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

Step 1: Given

Inductive reactance, $X_L=10\Omega$

Capacitive reactance, $X_C=4\Omega$

Resistance, $R=6\Omega$

Step 2: Draw the circuit

The circuit is:

Step 3: Determine the impedance

The impedance is given by,

$$\begin{gathered} Z=\sqrt{R^2+{(X_L-X_c)}^2} \\ =\sqrt{6^2+{(10-4)}^2} \\ =6\sqrt{2} \end{gathered}$$

Step 4: Determine the power factor

The power factor is given by,

$$\begin{gathered} \cos \phi =\frac{R}{Z} \\ =\frac{6}{6\sqrt{2}} \\ =\frac{1}{\sqrt{2}} \end{gathered}$$

Therefore, option A is the correct option.