Final answer:
The drift speed of the electrons in a wire is primarily affected by the cross-sectional area of the wire and the resistance, which is influenced by material resistivity, length, and area.
Step-by-step explanation:
The drift speed of the electrons in a wire depends on several factors. Among the options provided, the cross-sectional area of the wire and the resistance of the wire strongly affect the drift velocity. According to the relationship I = nqA₊, where I is the current, n is the number of free charges per volume, q is the charge, A is the cross-sectional area, and ₊ is the drift velocity, the drift velocity is inversely proportional to the cross-sectional area. Hence, wires with a smaller cross-sectional area, such as a 14-gauge wire compared to a 12-gauge one, will have a higher drift velocity assuming equal current. As for resistance, it is affected by the material's resistivity, length, and cross-sectional area. Resistance does not directly affect drift velocity; however, the factors determining resistance can influence the conditions under which the electrons move, hence indirectly affecting drift velocity.