Why does potential vary along nichrome wires in series?

[jdstokes]

Homework Statement

One end of a nichrome wire of length 2L and cross-sectional area A is attached to an end of another nichrome wire of length L and cross-sectional area 2A. If the free end of the longer wire is at an electric potential of 8.0 V, and the free end of the shorter wire is at an electric potential of 1.0 V, the potential at the junction of the two wires is equal to

The Attempt at a Solution

I have conceptual problems with this question. In an ordinary piece of `circuit wire' it is impossible to maintain a nonzero potential difference between each end. Does this mean that a wire with variable width behaves as a kind of resistor? Would the potential difference not be everywhere the same because of equipoential on a conductor?

 

[jdstokes]

I was missing the point, the idea is to compute the potential drop across one component, as a fraction of the total potential drop. Knowing the absolute potentials at the ends allows the junction potential to be calculated.