The length of a certain wire is doubled and at the same time its radius is increased by a factor of 4. What is the change in the resistance of this wire?
A) It is reduced by a factor of 8.
B) It increases by a factor of 8.
C) It is reduced by a factor of 4.
D) It increases by a factor of 4.
E) It stays the same.

Question

Quizplus · Accepted Answer

Resistance is given by R = ρL/A, where L is the length and A is the cross-sectional area (πr²). Doubling the length doubles the resistance, but increasing the radius by a factor of 4 increases the area by a factor of 16 (since area is proportional to the square of the radius). Thus, the resistance is reduced by a factor of 2/16 = 1/8.

The Length of a Certain Wire Is Doubled and at the Same