In an `AC` circuit, the reactannce is equal to the resistance. The power factor of the circuit will be

Options

A. 1
B. `1/2`
C. `1/(sqrt(2))`
D. zero

Answer

To find the power factor of an AC circuit where the reactance (X) is equal to the resistance (R), we can follow these steps:

### Step-by-Step Solution:

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

2. **Relate Reactance and Resistance**:
In the given circuit, we know that the reactance (X) is equal to the resistance (R). Therefore, we can express this relationship as:
\[ X = R \]

3. **Determine the Phase Angle**:
The phase angle (φ) can be determined using the formula:
\[ \tan(\phi) = \frac{X}{R} \]
Since \(X = R\), we can substitute to get:
\[ \tan(\phi) = \frac{R}{R} = 1 \]

4. **Calculate the Phase Angle**:
The angle whose tangent is 1 is:
\[ \phi = 45^\circ \]

5. **Calculate the Power Factor**:
Now, we can find the power factor using the cosine of the phase angle:
\[ \text{Power Factor} = \cos(45^\circ) \]
The value of \(\cos(45^\circ)\) is:
\[ \cos(45^\circ) = \frac{1}{\sqrt{2}} \]

### Final Answer:
Thus, the power factor of the circuit is:
\[ \text{Power Factor} = \frac{1}{\sqrt{2}} \approx 0.707 \]