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= (\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 = (RA)/(L)= ((0.25 \Omega)(3.14 \cdot 10^(-6) m^2))/((20 m)) = 3.93 \cdot 10^(-8) \Omega \cdot m`