In a series LCR circuit, the phase difference between the voltage and the current is `45^(@)`. Then the power factor will be

Options

A. `0.607`
B. `0.707`
C. `0.808`
D. 1

Explanation

To find the power factor in a series LCR circuit where the phase difference between the voltage and the current is \(45^\circ\), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Phase Difference**:
In an LCR circuit, the phase difference (\(\phi\)) between the voltage and the current is given as \(45^\circ\).

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

3. **Substituting the Phase Difference**:
Since we know that \(\phi = 45^\circ\), we can substitute this value into the power factor formula:
\[ \text{Power Factor} = \cos(45^\circ) \]

4. **Calculating \(\cos(45^\circ)\)**:
The cosine of \(45^\circ\) is a well-known trigonometric value:
\[ \cos(45^\circ) = \frac{1}{\sqrt{2}} \]

5. **Converting to Decimal Form**:
To express the power factor in decimal form, we can calculate:
\[ \frac{1}{\sqrt{2}} \approx 0.707 \]

6. **Final Result**:
Therefore, the power factor for the given LCR circuit is:
\[ \text{Power Factor} \approx 0.707 \]

### Summary:
The power factor of the series LCR circuit, where the phase difference between voltage and current is \(45^\circ\), is approximately \(0.707\).