Consider two copper wires with circular cross-sections and equal lengths. One wire has 3 times the diameter of the other. How do the resistances of these two wires compare?
A) The thicker wire has $1 / 3$ the resistance of the thinner wire.
B) The thicker wire has 9 times the resistance of the thinner wire.
C) The thicker wire has 3 times the resistance of the thinner wire.
D) The thicker wire has $1 / 9$ the resistance of the thinner wire.
E) The thicker wire has $\sqrt { 3 }$ times the resistance of the thinner wire.

Question

Quizplus · Accepted Answer

The resistance $R$ of a wire is inversely proportional to its cross-sectional area $A$, given by $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity and $L$ is the length. If the diameter of one wire is 3 times that of the other, its radius is also 3 times larger, making its area $9$ times larger ($A = \pi r^2$). Therefore, its resistance is $1/9$ the resistance of the thinner wire.

Consider Two Copper Wires with Circular Cross-Sections and Equal Lengths 1/31 / 31/3

Consider Two Copper Wires with Circular Cross-Sections and Equal Lengths $1 / 3$