If potential gradient of a wire decreases, then its length

Options

A. remains constant
B. decreases
C. increases
D. none of the above

Answer

To solve the question "If potential gradient of a wire decreases, then its length will be?", we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Potential Gradient**:
- The potential gradient (pg) is defined as the change in potential difference (V) per unit length (L) of the wire. Mathematically, it can be expressed as:
\[ \text{Potential Gradient (pg)} = \frac{V}{L} \]

2. **Analyze the Given Condition**:
- The problem states that the potential gradient of the wire decreases. This means that the value of pg is getting smaller.

3. **Assume Constant Voltage**:
- For this analysis, we will assume that the potential difference (V) across the wire remains constant. This is an important assumption because it allows us to isolate the effect on length (L).

4. **Relate Potential Gradient and Length**:
- From the formula for potential gradient, we can rearrange it to express length in terms of potential gradient:
\[ L = \frac{V}{\text{pg}} \]
- Here, if the potential gradient (pg) decreases while V remains constant, the length (L) must increase to maintain the equality.

5. **Conclusion**:
- Therefore, if the potential gradient of a wire decreases, the length of the wire must increase.

### Final Answer:
If the potential gradient of a wire decreases, then its length will **increase**.

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