A wire of resistivity ρ must be replaced in a circuit by a wire of the same material but four times as long.If,however,the total resistance is to remain as before,the diameter of the new wire must
A)be the same as the original diameter.
B)be one-half the original diameter.
C)be one-fourth the original diameter.
D)be two times the original diameter.
E)be four times the original diameter.

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. If the length of the wire is quadrupled, to keep the resistance the same, the area must also be quadrupled. Since the area of a circle (the cross-section of the wire) is proportional to the square of the diameter, doubling the diameter quadruples the area.

A Wire of Resistivity ρ Must Be Replaced in a Circuit