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 1: Understand the Power Factor Definition
The power factor (PF) is defined as the cosine of the phase angle (φ) between the voltage and current in an AC circuit. Mathematically, it is given by:
\[ \text{Power Factor} = \cos \phi = \frac{R}{Z} \]
where \( R \) is the resistance and \( Z \) is the impedance of the circuit.

### Step 2: Determine the Impedance in a Series LR Circuit
In a series LR circuit, the total impedance \( Z \) is given by:
\[ Z = \sqrt{R^2 + X_L^2} \]
where \( X_L \) is the inductive reactance, which can be calculated as:
\[ X_L = \omega L \]
with \( \omega \) being the angular frequency and \( L \) being the inductance.

### Step 3: Substitute Impedance into Power Factor Formula
Now, substituting the expression for \( Z \) into the power factor formula:
\[ \cos \phi = \frac{R}{Z} = \frac{R}{\sqrt{R^2 + X_L^2}} \]

### Step 4: Final Expression for Power Factor
Thus, the power factor for a series LR circuit can be expressed as:
\[ \text{Power Factor} = \frac{R}{\sqrt{R^2 + (\omega L)^2}} \]

### Conclusion
The value of the power factor for a series LR circuit is given by the formula:
\[ \text{Power Factor} = \frac{R}{\sqrt{R^2 + (\omega L)^2}} \]

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