What effect does a smaller surface area have on resistance in a piece of wire?

A smaller surface area in a piece of wire results in higher resistance due to the geometric and physical properties of the material through which electrical current passes. Resistance in a conductor is influenced by its dimensions: the length, cross-sectional area, and the material's intrinsic resistivity.

When the surface area is smaller, it limits the number of pathways available for electrons to flow. Essentially, a narrower wire has less space for the electrons to move, leading to an increase in collisions between the electrons and the atomic lattice of the material. This build-up of collisions hinders the flow of current, thus increasing the resistance.

Additionally, in accordance with Ohm's law (R = ρ(L/A)), where R is resistance, ρ is resistivity, L is the length of the wire, and A is the cross-sectional area, reducing the area (A) while keeping the length (L) and material constant will increase the overall resistance. This relationship underscores the principle that as the cross-sectional area decreases, resistance increases, making the choice that indicates higher resistance the correct one.