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 times the resistance of the thinner wire.

Question

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 times the resistance of the thinner wire.

Quizplus · Accepted Answer

The resistance of a wire is inversely proportional to the cross-sectional area of the wire. The cross-sectional area of a wire is proportional to the square of its diameter. Therefore, if one wire has 3 times the diameter of the other wire, it has 9 times the cross-sectional area. The resistance of the thicker wire is therefore 1/9 the resistance of the thinner wire. So, the thicker wire has 1/9 the resistance of the thinner wire (option B).

Consider Two Copper Wires with Circular Cross-Sections and Equal Lengths