A wire of resistivity @ must be replaced in a circuit by a wire of the same material but four times as long. If, however, the total resistance is to remain as before, the diameter of the new wire must
A) be the same as the original diameter.
B) be one-fourth the original diameter.
C) be four times the original diameter.
D) be two times the original diameter.
E) be one-half the original diameter.

Question

Quizplus · Accepted Answer

The resistance of a wire is given by R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area. If the length is quadrupled (4L) and resistance is to remain the same, the area must also be quadrupled to compensate. Since area A = π(d/2)^2, the diameter must be doubled to make the area four times larger.

A Wire of Resistivity @ Must Be Replaced in a Circuit