The power factor of L-R circuit is-

Options

A. `(omegaL)/( R)`
B. `(R)/(sqrt((omegaL)^(2)+R^(2)))`
C. `omega`LR
D. `sqrt(omegaLR)`

Answer

To find the power factor of an L-R (inductor-resistor) circuit, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Components of the Circuit**:
- In an L-R circuit, we have a resistor (R) and an inductor (L) connected to an AC source.

2. **Define Power Factor**:
- The power factor (PF) is defined as the cosine of the phase angle (φ) between the voltage and the current in the circuit. Mathematically, it is expressed as:
\[ \text{Power Factor} (PF) = \cos \phi \]

3. **Relate Power Factor to Resistance and Impedance**:
- The power factor can also be expressed in terms of resistance (R) and impedance (Z):
\[ \cos \phi = \frac{R}{Z} \]

4. **Calculate Impedance (Z)**:
- The impedance in an L-R circuit is given by:
\[ Z = \sqrt{R^2 + X_L^2} \]
- Where \(X_L\) is the inductive reactance, defined as:
\[ X_L = \omega L \]
- Here, \(\omega\) is the angular frequency of the AC source.

5. **Substitute Inductive Reactance into Impedance**:
- Substitute \(X_L\) into the impedance formula:
\[ Z = \sqrt{R^2 + (\omega L)^2} \]

6. **Substitute Impedance into Power Factor Formula**:
- Now, substitute the expression for Z back into the power factor equation:
\[ \cos \phi = \frac{R}{\sqrt{R^2 + (\omega L)^2}} \]

7. **Conclusion**:
- The power factor of an L-R circuit is given by:
\[ \text{Power Factor} = \frac{R}{\sqrt{R^2 + (\omega L)^2}} \]