The length of a certain wire is kept same while its radius is doubled.What is the new resistance of this wire?
A)It is increased by a factor of 2.
B)It is increased by a factor of 4.
C)It is reduced by a factor of 2.
D)It is reduced by a factor of 4.
E)It is reduced by a factor of 8.

Question

Quizplus · Accepted Answer

The resistance of a wire is directly proportional to its length and inversely proportional to the cross-sectional area of the wire.

Let the original radius be r and the new radius be 2r. The cross-sectional area of the wire is proportional to the square of its radius.

So, the new cross-sectional area is (2r)^2=4r^2 times the original cross-sectional area.

Therefore, the resistance of the wire becomes (1/4) times the original resistance because the cross-sectional area has increased fourfold.

Hence, the new resistance is reduced by a factor of 4.

The Length of a Certain Wire Is Kept Same While