The length of a potentiometer wire is 10m and a potential difference of 2 volt is applied to its ends. If the length of its wire is increased by 1m, the value of potential gradient in volt/m will be (potential difference across potentiometer wire remain same)

Options

A. 0.18
B. 0.22
C. 1.3
D. 0.9

Explanation

To solve the problem, we need to find the potential gradient of the potentiometer wire after its length is increased from 10 meters to 11 meters, while keeping the potential difference constant at 2 volts.

### Step-by-Step Solution:

1. **Identify the initial conditions:**
- Initial length of the potentiometer wire, \( L = 10 \, \text{m} \)
- Potential difference applied, \( V = 2 \, \text{V} \)

2. **Determine the new length of the wire:**
- The length of the wire is increased by 1 meter.
- New length, \( L' = L + 1 = 10 \, \text{m} + 1 \, \text{m} = 11 \, \text{m} \)

3. **Calculate the potential gradient:**
- The potential gradient (PG) is defined as the potential difference per unit length of the wire.
- The formula for potential gradient is:
\[ \text{Potential Gradient} = \frac{V}{L'} \]
- Substituting the values:
\[ \text{Potential Gradient} = \frac{2 \, \text{V}}{11 \, \text{m}} \approx 0.1818 \, \text{V/m} \]

4. **Final answer:**
- The potential gradient after increasing the length of the wire to 11 meters is approximately \( 0.1818 \, \text{V/m} \).