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 1/2 as large.

Question

Quizplus · Accepted Answer

The resistance of a wire is directly proportional to its length (R ∝ L) and inversely proportional to the square of its radius (R ∝ 1/r^2). Therefore, if the length is doubled and the radius is halved, the new resistance (R') can be calculated as follows:

R' = 2R × (1/2)^2
R' = (2/4)R
R' = 0.5R

Therefore, the new resistance is half of the original resistance, which means it is eight times as large. The correct answer is D.

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