Five cylindrical wires are made of the same material. Their lengths and radii are Rank the wires according to their resistances, least to greatest.
A) 1, 2, 3, 4, 5
B) 5, 4, 3, 2, 1
C) 1 and 2 tie, then 5, 3, 4
D) 1, 3, 4, 2, 5
E) 1, 2, 4, 3, 5

Question

Five cylindrical wires are made of the same material. Their lengths and radii are  Rank the wires according to their resistances, least to greatest.
A) 1, 2, 3, 4, 5 
B) 5, 4, 3, 2, 1 
C) 1 and 2 tie, then 5, 3, 4 
D) 1, 3, 4, 2, 5 
E) 1, 2, 4, 3, 5

Quizplus · Accepted Answer

The resistance of a wire is directly proportional to its length and inversely proportional to the square of its radius. Since all wires are made of the same material, their resistivities are equal. 
Thus, we can use the formula R = (ρL)/A = (ρL)/(πr^2) to compare their resistances.

For wires 1 and 2, they have the same length and radius, so they will have the same resistance.

For wires 3, 4, and 5, their radii are decreasing in order, meaning their resistances will be increasing in order.

Therefore, the ranking of the wires from least to greatest resistance is 1,2 (tie), 5, 3, 4, which corresponds to choice C.

Five Cylindrical Wires Are Made of the Same Material