Modeling a long single wire in a circuit?
In the lumped circuit approximation, a single wire can't carry signal or power. There must be a return path for any current to flow in the wire, and the loop area between the wire and return path will be important to determining the effective inductance of the wire. You  might also want to model the capacitance between the wire and its surroundings.

Outside the lumped circuit approximation, a single wire carrying a signal without a return path is an antenna. You will need to include radiation effects to model the antenna accurately.