Potential along a uniform current-carrying wire

From the equation for resistance below, you can see that the resistance of an object is dependent on its length.

Consider a uniform current-carrying wire, which has constant resistivity and cross-sectional area. Therefore, as the length of a wire increases, its resistance will increase uniformly. Using Ohm’s law (V = IR), you can see that as resistance increases, potential will also increase.

This means that the potential along a uniform current-carrying wire increases uniformly with the distance along it.