For the same potential difference, a potentiometer wire is replaced by another one of a high specific resistance. The potential gradient then (`r=R_h=0`)

Options

A. decreases
B. remains same
C. increases
D. data is incomplete

Explanation

To solve the problem, we need to analyze the effect of replacing a potentiometer wire with another wire of higher specific resistance on the potential gradient.

### Step-by-Step Solution:

1. **Understanding Potential Gradient**:
The potential gradient (E) is defined as the potential difference (V) across a length (L) of the wire. Mathematically, it can be expressed as:
\[ E = \frac{V}{L} \]
where \(E\) is the potential gradient, \(V\) is the potential difference, and \(L\) is the length of the wire.

2. **Given Conditions**:
- The potential difference (V) remains the same for both wires.
- The length (L) of the potentiometer wire is assumed to be the same for both cases.
- The specific resistance (ρ) of the new wire is higher than that of the original wire.

3. **Effect of Specific Resistance**:
The specific resistance (ρ) of the wire does not appear in the formula for potential gradient. The potential gradient depends only on the potential difference and the length of the wire. Therefore, even if the specific resistance increases, the potential gradient remains unchanged as long as the potential difference and length are constant.

4. **Conclusion**:
Since both the potential difference (V) and the length (L) remain the same, the potential gradient (E) will also remain the same. Thus, we conclude:
\[ E = \frac{V}{L} \quad \text{(remains constant)} \]

### Final Answer:
The potential gradient remains the same when the potentiometer wire is replaced by another one of higher specific resistance, given that the potential difference and length are unchanged.

---