The length of a certain wire is kept same while its radius is doubled. What is the change in the resistance of this wire?
A) It is doubled.
B) It is quadrupled.
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

According to the formula for resistance (R) of a wire, R is directly proportional to the length (L) and inversely proportional to the cross-sectional area (A) of the wire, i.e. R = ρL/A, where ρ is the resistivity of the material. When the radius of the wire is doubled, its cross-sectional area becomes 4 times larger (A' = π(r')^2 = 4πr^2 = 4A), since A is proportional to r^2. Therefore, the resistance of the wire becomes R' = ρL/A' = ρL/(4A) = (1/4)(ρL/A) = (1/4)R, i.e. it is reduced by a factor of 4.

The Length of a Certain Wire Is Kept Same While