OLA’S EESE

This is actually not a simple question. The first answer appears to be just the difference between a rectangular or triangular cross section and a circular cross section. The conductance is proportional to the cross sectional area.

There are more factors involved in the shape of wire. One big one is cost. Round wire is the cheapest to make. Wire is formed by pulling it through a round die, a small hole. Some of the other reasons are how compact you can wind a bunch of turns of the wire and how the wires are used. Another factor is the voltage on the wire. The last factor is the frequency.

Copper wire from Walmart.

At low frequencies and moderate voltage (less than 1KV) where you want to minimize the resistance and you have limited area you use square or rectangular wire. This is done in many transformers and high current commercial motors.

At high frequencies and high voltages you always use round wires as this results in more uniform electric fields and less chance of breakdown as well as lower loss at the MHz frequencies. All RF components use larger diameter round wire which decreases inductance and resistive loss.

Anything other than circular will result in charge moving to the outermost parts of the wire and increasing the electric field at those points, decreasing breakdown voltage. This is called skin effect and can cause high resistive loss at high frequencies.

As some comments mention, at audio frequencies, and in a few high current low frequency transformers, a flat sheet wire is used. The sheet is not used above audio frequencies because the capacitance between windings is large.

Another comment noted that most applications require bending the wire. Round wires bend easily in all directions.

Thanks for all the comments, I value them all and learn from them along with other readers.