Consider two copper wires. One has twice the length and twice the cross-sectional area of the other. How do the resistances of these two wires compare?
A) Both wires have the same resistance.
B) The shorter wire has twice the resistance of the longer wire.
C) The longer wire has twice the resistance of the shorter wire.
D) The longer wire has four times the resistance of the shorter wire.
E) The shorter wire has four times the resistance of the longer wire.

Question

Quizplus · Accepted Answer

The resistance (R) of a wire is given by R = ρL/A, where ρ is the resistivity of the material, L is the length, and A is the cross-sectional area. For the longer wire, both L and A are doubled. Doubling L would tend to double the resistance, but doubling A would halve it, so these effects cancel out, leaving both wires with the same resistance.

Consider Two Copper Wires