The power factor of an AC circuit having resistance (R) and inductance (L) connected in series and an angular velocity `omega` is

Options

A. zero
B. `(omegaL)/R`
C. `R/(sqrt(R^(2)+omegaL^(2))`
D. `R//omegaL`

Explanation

To find the power factor of an AC circuit with resistance \( R \) and inductance \( L \) connected in series, we can follow these steps:

### Step 1: Understand the Components
In an AC circuit with resistance \( R \) and inductance \( L \), the total impedance \( Z \) can be calculated using the formula:
\[ Z = \sqrt{R^2 + X_L^2} \]
where \( X_L \) is the inductive reactance given by:
\[ X_L = \omega L \]
Thus, we can rewrite the impedance as:
\[ Z = \sqrt{R^2 + (\omega L)^2} \]

### Step 2: Calculate the Power Factor
The power factor \( \text{pf} \) is defined as the cosine of the phase angle \( \phi \) between the voltage and the current in the circuit. It can be expressed as:
\[ \text{pf} = \cos \phi = \frac{R}{Z} \]

### Step 3: Substitute the Impedance
Substituting the expression for \( Z \) into the power factor formula, we get:
\[ \text{pf} = \frac{R}{\sqrt{R^2 + (\omega L)^2}} \]

### Step 4: Final Expression
Thus, the power factor of the AC circuit is:
\[ \text{pf} = \frac{R}{\sqrt{R^2 + \omega^2 L^2}} \]

### Conclusion
The power factor of the AC circuit having resistance \( R \) and inductance \( L \) connected in series is:
\[ \text{pf} = \frac{R}{\sqrt{R^2 + \omega^2 L^2}} \]