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 1/9 the resistance of the thinner wire.
C)The thicker wire has 3 times the resistance of the thinner wire.
D)The thicker wire has 9 times 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 of a wire is inversely proportional to its cross-sectional area. Since the diameter of one wire is three times greater than the diameter of the other wire, its cross-sectional area will be $(3/2)^2=2.25$ times greater. Therefore, the resistance of the thicker wire will be $(1/2.25)$ times the resistance of the thinner wire, or 1/9.

Consider Two Copper Wires with Circular Cross-Sections and Equal Lengths 3\sqrt { 3 }3​

Consider Two Copper Wires with Circular Cross-Sections and Equal Lengths $\sqrt { 3 }$