What is the value of power factor for series LR circuit ?

Answer

To find the value of the power factor for a series LR circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Definition of Power Factor**:
The power factor (PF) is defined as the ratio of the resistance (R) to the impedance (Z) in an AC circuit. It can be mathematically expressed as:
\[ \text{Power Factor (PF)} = \cos \phi = \frac{R}{Z} \]

2. **Identify the Components of the LR Circuit**:
In a series LR circuit, we have:
- Resistance (R)
- Inductive reactance (X_L), which is the opposition to the change of current by the inductor.

3. **Calculate the Impedance (Z)**:
The total impedance (Z) in a series LR circuit is given by:
\[ Z = \sqrt{R^2 + X_L^2} \]
where \(X_L\) is the inductive reactance.

4. **Substitute Impedance into the Power Factor Formula**:
Now, substituting the expression for impedance into the power factor formula, we get:
\[ \text{Power Factor (PF)} = \frac{R}{\sqrt{R^2 + X_L^2}} \]

5. **Conclusion**:
Thus, the value of the power factor for a series LR circuit is:
\[ \text{Power Factor (PF)} = \frac{R}{\sqrt{R^2 + X_L^2}} \]