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 proportional to its length and inversely proportional to the cross-sectional area. Since the length and material of the wires are the same, we only need to compare their cross-sectional areas. The area of a circular cross-section is proportional to the square of its diameter, so the larger wire has 9 times the cross-sectional area of the smaller wire. Therefore, the smaller wire has 9 times the resistance of the larger wire. So, the thicker wire has 1/9 the resistance of the thinner wire.

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 $\sqrt { 3 }$