Question

A wire is stretched to n times it's length. What happens to its resistance?

Answer 1

First of all, the resistance is proportional to the quantity $\frac{l}{S}$, where $S$ is a cross-section area and $l$ is wire's length. Secondly, let us remark that the wire's total volume, $V=S\cdot l$, in conserved during the stretching. Therefore, if we have stretch its length by $n$ times, we have reduced its cross-section area by $n$ times. From this we conclude that the resistance is increased by $\frac{n}{1/n}=n^2$ times.