The length of a certain wire is doubled while the radius is reduced by a factor of 4. What is the change in the resistance of this wire?
A) It stays the same.
B) It is quadrupled.
C) It is increased by a factor of 32.
D) It is increased by a factor of 16.
E) It is increased by a factor of 8.

Question

Quizplus · Accepted Answer

Resistance is proportional to the length and inversely proportional to the cross-sectional area (which is proportional to the square of the radius). Doubling the length doubles the resistance, and reducing the radius by a factor of 4 increases the resistance by a factor of 16 (since area decreases by 16). Therefore, the resistance increases by a factor of 32 (2 * 16).

The Length of a Certain Wire Is Doubled While the Radius