Question

A 2.0 mm diameter wire of length 20 m has a resistance of 0.25 ȍ. what is the resistivity of the wire?

Answer 1

The relationship between resistance R and resistivity $\rho$ is
$R= \frac{\rho L}{A}$ (1)
where L is the length of the wire and A is the cross-sectional area.

In our problem, the radius of the wire is half the diameter: r=1 mm=0.001 m, so the cross-sectional area is
$A=\pi r^2 = \pi (0.001 m)^2=3.14 \cdot 10^{-6} m^2$
The length of the wire is L=20 m and the resistance is $R=0.25 \Omega$.

By re-arranging equation (1), we can find the resistivity of the wire:
$\rho = \frac{RA}{L}= \frac{(0.25 \Omega)(3.14 \cdot 10^{-6} m^2)}{(20 m)} = 3.93 \cdot 10^{-8} \Omega \cdot m$