The impedance of a series circuit consists of `3 ohm` resistance and `4 ohm` reactance.The power factor of the circuit is

Options

A. `0.4`
B. `0.6`
C. `0.8`
D. `1.0`

Answer

To find the power factor of the given series circuit with a resistance of 3 ohms and a reactance of 4 ohms, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values:**
- Resistance (R) = 3 ohms
- Reactance (X) = 4 ohms

2. **Calculate the impedance (Z):**
The impedance in a series circuit is calculated using the formula:
\[ Z = \sqrt{R^2 + X^2} \]
Substituting the values:
\[ Z = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5 \text{ ohms} \]

3. **Calculate the power factor (PF):**
The power factor is given by the formula:
\[ \text{Power Factor (PF)} = \cos(\phi) = \frac{R}{Z} \]
Substituting the values:
\[ \text{PF} = \frac{3}{5} = 0.6 \]

4. **Conclusion:**
The power factor of the circuit is 0.6.

### Final Answer:
The power factor of the circuit is **0.6**.

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