The resistance, in ohms, of a 25 foot piece of wire is given by the function $R(d)=\frac{0.025}{d^{2}}$, where $d$ is the diameter of the wire in inches. What happens to the resistance of the wire as the diameter of the wire decreases?
A) The resistance remains constant.
B) The answer cannot be determined without additional information.
C) The resistance increases.
D) The resistance decreases.

Question

Quizplus · Accepted Answer

The resistance $R(d)$ is inversely proportional to the square of the diameter $d$. Therefore, as the diameter decreases, the value of $d^2$ in the denominator decreases, making the overall value of $R(d)$ increase.

The Resistance, in Ohms, of a 25 Foot Piece of Wire