Length of a potentiometer wire is kept long and uniform to ahcieve:-

Explanation

To complete the statement "Length of a potentiometer wire is kept long and uniform to achieve:", we need to understand the purpose of using a long and uniform potentiometer wire in electrical measurements.

### Step-by-Step Solution:

1. **Understanding Potentiometer Basics**:
- A potentiometer is an instrument used to measure the potential difference (voltage) across two points in a circuit without drawing any current from the circuit.

2. **Length of the Wire**:
- The length of the potentiometer wire is crucial because it affects the potential gradient (voltage per unit length) along the wire. A longer wire allows for a smaller potential gradient.

3. **Potential Gradient**:
- The potential gradient (k) is defined as the voltage drop per unit length of the wire. It is given by the formula:
\[ k = \frac{V}{L} \]
where \( V \) is the total voltage across the wire and \( L \) is the length of the wire.

4. **Effect of Increasing Length**:
- By increasing the length of the potentiometer wire while keeping it uniform, the potential gradient decreases. This means that for a given voltage, the voltage drop per unit length is smaller.

5. **Balancing Point**:
- A longer wire allows for a more precise measurement of the voltage because the balancing point (where the galvanometer shows zero current) can be set at a greater distance. This increases the accuracy of the measurement.

6. **Conclusion**:
- Therefore, the complete statement can be: "Length of a potentiometer wire is kept long and uniform to achieve a smaller potential gradient, which allows for more accurate voltage measurements."