1. The problem statement, all variables and given/known data There are two wires: Wire one looks like --=========-- Wire two looks like --------------- Do they have the same resistance? So this isn't actually one of my homework problems, but I'm just debating this with a friend and neither of us can come to an agreement. So here are the arguments. 1: The wires have the same resistance 2: The top wire has less resistance than the bottom wire 2. Relevant equations The middle portion of the top wire has less resistance due to larger cross sectional area The resistance of wires doubles as the length doubles 3. The attempt at a solution For position 1: Because the wire on the top has thinner ends, the flow of electrons is limited to however many can flow through the thin end, making the thicker middle section of the wire useless, like a pipe with water flowing through it. So therefore, the resistances of the wires are equal. For position 2: The middle section of the top wire has less resistance than a thin piece of wire of equal length. If you add up the resistance of the short wires on either side plus the middle like resisters in series, it would be less than adding up the whole length of the bottom wire.