If the length and diameter of a wire of circular cross section are both tripled,the resistance will be
A)unchanged.
B)tripled.
C)increased by a factor of 9.
D)1/3 of what it originally was.
E)1/9 of what it originally was.

Question

Quizplus · Accepted Answer

The resistance of a wire is given by the formula R = ρL/A, where ρ is the resistivity, L is the length, and A is the cross-sectional area. If the length is tripled, L becomes 3L. The diameter being tripled means the radius is also tripled, so the area A, which is πr², becomes 9A. Therefore, the new resistance is (3L)/(9A) = (1/3)(L/A), which is 1/3 of the original resistance.

If the Length and Diameter of a Wire of Circular