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 new resistance of this wire?
A)It is 2 times as large.
B)It is 4 times as large.
C)It is 6 times as large.
D)It it 8 times as large.
E)It is ½ as large.

Question

Quizplus · Accepted Answer

The resistance of a wire is given by the formula R = ρL/A, where ρ is the resistivity of the material, L is the length of the wire, and A is the cross-sectional area of the wire.

When the length of the wire is doubled, the new length becomes 2L. When the radius of the wire is reduced by a factor of 2, the new radius becomes r/2, where r is the original radius. This means that the new cross-sectional area is (r/2)^2π = r^2π/4.

Substituting these new values into the formula for resistance, we get:
R' = ρ(2L)/(r^2π/4) = 8ρL/(r^2π)

Comparing this to the original resistance, we can see that R' is 8 times as large as R. Therefore, the answer is D.

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