The impedance of a circuit consister of `3Omega`resistance and `4Omega` reactance. The power factor of the circuit is

Options

A. 0.4
B. 0.6
C. 0.8
D. 1

Answer

To find the power factor of the given circuit with a resistance of \(3 \, \Omega\) and a reactance of \(4 \, \Omega\), we can follow these steps:

### Step 1: Identify the values of resistance and reactance
- Given:
- Resistance \( R = 3 \, \Omega \)
- Reactance \( X = 4 \, \Omega \)

### Step 2: Calculate the impedance \( Z \)
- The formula for impedance \( Z \) in an AC circuit is given by:
\[ Z = \sqrt{R^2 + X^2} \]
- Substituting the values:
\[ Z = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \, \Omega \]

### Step 3: Calculate the power factor \( \cos \phi \)
- The power factor is defined as:
\[ \text{Power Factor} = \cos \phi = \frac{R}{Z} \]
- Substituting the values:
\[ \cos \phi = \frac{3}{5} = 0.6 \]

### Conclusion
- The power factor of the circuit is \( 0.6 \).

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