The length of a certain wire is doubled and at the same time its radius is reduced by a factor of 2. What is the change in the resistance of this wire?
A) It is doubled.
B) It is quadrupled.
C) It increases by a factor of 6.
D) It increases by a factor of 8.
E) It is reduced by a factor of 2.

Question

Quizplus · Accepted Answer

The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area (which is proportional to the square of its radius).

When the length of the wire is doubled, its resistance also doubles.

When the radius is reduced by a factor of 2 (meaning it is divided by 2), the cross-sectional area becomes 1/4 of the original area. Therefore, the resistance becomes 4 times the original resistance.

Overall, the resistance becomes (2 x 4) = 8 times the original resistance when the length is doubled and the radius is reduced by half.

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