The length of a certain wire is halved while the radius is doubled. What is the change in the resistance of this wire?
A) It stays the same.
B) It is reduced by a factor of 2.
C) It is reduced by a factor of 4.
D) It is reduced by a factor of 8.
E) It is quadrupled.

Question

Quizplus · Accepted Answer

Resistance is inversely proportional to the cross-sectional area and directly proportional to the length. Halving the length reduces resistance by a factor of 2, and doubling the radius increases the area by a factor of 4, reducing resistance by another factor of 4. Overall, resistance is reduced by a factor of 8.

The Length of a Certain Wire Is Halved While the Radius