A

The potential gradient of a potentiometer wire is defined as the fall of potential per unit length.
Explanation:
1. A potentiometer is an instrument used to measure the potential difference (voltage) by balancing it against a known reference voltage.
2. As the current flows through a potentiometer wire, there is a voltage drop along its length due to its resistance.
3. The potential gradient is calculated by taking the potential difference across a length of the wire and dividing it by that length. This can be expressed mathematically as:
$$ ext{Potential Gradient} = -\frac{V}{L} $$
where $V$ is the potential difference, and $L$ is the length of the wire.
4. Therefore, Option A accurately describes the potential gradient.