In a potentiometer, a uniform potential gradient of `0.8 V m^(-1)` is maintained across its 10 m wire . The potential difference across two points on the wire located at 65 cm and 2.45 m is

Options

A. 1.44 V
B. 0.144 V
C. 1.96 V
D. 0.196 V

Answer

To solve the problem, we need to find the potential difference across two points on a potentiometer wire. Given the potential gradient and the positions of the two points, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Potential gradient (k) = 0.8 V/m
- Length of the wire = 10 m
- Position of the first point (P1) = 65 cm = 0.65 m
- Position of the second point (P2) = 2.45 m

2. **Calculate the Length Between the Two Points:**
- The length (L) between the two points is calculated as:
\[ L = P2 - P1 = 2.45 \, \text{m} - 0.65 \, \text{m} = 1.80 \, \text{m} \]

3. **Use the Formula for Potential Difference:**
- The potential difference (ΔV) across the two points can be calculated using the formula:
\[ \Delta V = k \times L \]
- Substituting the values:
\[ \Delta V = 0.8 \, \text{V/m} \times 1.80 \, \text{m} \]

4. **Calculate the Potential Difference:**
- Performing the multiplication:
\[ \Delta V = 1.44 \, \text{V} \]

5. **Conclusion:**
- The potential difference across the two points located at 65 cm and 2.45 m is **1.44 V**.