Question

What is the change in resistance of a wire which is stretched triple its length?

Answer 1

Step 1: The expression for resistance

$\mathrm{R}=\frac{\mathrm{\rho L}}{\mathrm{A}}$

Here,

$\rho$ is the resistivity of the wire.

$\mathrm{L}$ is the length of wire.

$\mathrm{A}$ is a cross-section of the wire.

Step 2: The new resistance

1. The wire is stretched 3 times the original length, and the cross-section of the wire is cut to $\frac{1}{3}\mathrm{rd}$ it’s original cross-section.

Hence, the new resistance can be written as:

$$\begin{gathered} {\mathrm{R}}^{\text{'}}=\frac{\mathrm{\rho }\left(3\mathrm{L}\right)}{\left({\displaystyle \frac{\mathrm{A}}{3}}\right)} \\ =\frac{9\mathrm{\rho L}}{\mathrm{A}} \\ =9\mathrm{R} \end{gathered}$$

Therefore, The length while cutting the cross-section by $3\mathrm{x}$, the new resistance will be $9$ times the original resistance.