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. (a)1.44 V
B. (b)0.144 V
C. (c)1.96 V
D. (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 points.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Potential gradient (K) = 0.8 V/m
- Length of the wire = 10 m
- Position of point A = 65 cm = 0.65 m
- Position of point B = 2.45 m

2. **Calculate the Length of the Segment (AB):**
- Length of segment AB (L) = Position of point B - Position of point A
- L = 2.45 m - 0.65 m
- L = 1.80 m

3. **Use the Formula for Potential Difference:**
- The potential difference (ΔV) between two points in a potentiometer is given by the formula:
\[ \Delta V = K \times L \]
- Where K is the potential gradient and L is the length between the two points.

4. **Substitute the Values into the Formula:**
- ΔV = 0.8 V/m × 1.80 m
- ΔV = 1.44 V

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