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. Therefore, combining these proportionalities, we have R ∝ l/r^2. We can calculate the resistances of each wire using this formula, and we find that wires 1 and 2 have the same resistance, wire 5 has the next highest resistance, followed by wires 3 and 4. Therefore, the correct ranking is that 1 and 2 tie, then 5, 3, 4.

Five Cylindrical Wires Are Made of the Same Material