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 reduced by a factor of 4.
B) It is reduced by a factor of 2.
C) It is increased by a factor of 4.
D) It is reduced by a factor of 8.
E) It is increased by a factor of 2.

Question

Quizplus · Accepted Answer

The resistance $R$ of a wire is given by $R = \rho \frac{L}{A}$, where $\rho$ is the resistivity, $L$ is the length, and $A$ is the cross-sectional area. Doubling the radius of the wire quadruples its cross-sectional area (since $A = \pi r^2$), which reduces the resistance by a factor of 4.

The Length of a Certain Wire Is Kept Same While