Question Detail
Question
A wire that has a resistance of 5.0 Ω is made into a new wire three times as long as the original. Assuming the volume of the wire remains constant, what is the new resistance? (Based on Assignment 13.9)
Correct Answer
Option C is the correct answer.
Detailed Explanation
The resistance of a wire is given by R = ρL/A, where ρ is resistivity, L is length, and A is cross-sectional area. If the length (L) is tripled (L' = 3L) and the volume (V = AL) remains constant, then the new area (A') must be A' = V/L' = AL/(3L) = A/3. The new resistance R' = ρL'/A' = ρ(3L)/(A/3) = 9(ρL/A) = 9R. Given R = 5.0 Ω, the new resistance R' = 9 * 5.0 Ω = 45 Ω.
Hint
When a wire is stretched, its volume remains constant. An increase in length must be accompanied by a proportional decrease in cross-sectional area.