The current in a copper wire is increased by increasing the potential difference between its end. Which one of the following statements regarding n, the number of charge carriers per unit volume in the wire and v the drift velocity of the charge carriers is correct -

Options

A. n is unaltered but v is decreased
B. n is unaltered but v is increased
C. n is increased but v is decreased
D. n is increased but v is unaltered

Answer

To solve the question regarding the relationship between the number of charge carriers per unit volume (n) and the drift velocity (v) in a copper wire when the current is increased by increasing the potential difference, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Variables**:
- Let \( n \) be the number of charge carriers per unit volume in the wire.
- Let \( v_d \) be the drift velocity of the charge carriers.
- The current \( I \) in the wire can be expressed by the equation:
\[ I = n \cdot A \cdot e \cdot v_d \]
where \( A \) is the cross-sectional area of the wire and \( e \) is the charge of an electron.

2. **Identify the Effect of Increasing Potential Difference**:
- When the potential difference across the wire is increased, the current \( I \) also increases.
- The charge of the electron \( e \) and the cross-sectional area \( A \) of the wire remain constant.

3. **Analyze the Relationship**:
- Since \( n \) (the number of charge carriers per unit volume) is a property of the material and does not change with the potential difference, we conclude that \( n \) remains constant.
- Therefore, if the current \( I \) increases while \( n \) and \( A \) are constant, the drift velocity \( v_d \) must increase to maintain the equation:
\[ I = n \cdot A \cdot e \cdot v_d \]

4. **Conclusion**:
- From the analysis, we find that:
- \( n \) is unaltered (remains constant).
- \( v_d \) increases as the current increases.
- Thus, the correct statement is that \( n \) is unaltered but \( v_d \) is increased.

### Final Answer:
The correct option is: **b) n is unaltered but v is increased.**