Resistance ($R$) is the tendency of a material to oppose the flow of an electric current. It is an extensive property meaning that its value is dependent on the amount of substance present.
For example, the longer a piece of copper wire is, the more resistance it will have. If we get a shorter or thinner piece of copper wire then we will have to measure its resistance as well.
Extensive properties such as resistance are not very useful when being applied to objects of varying shapes and sizes. It is better for us to measure and record intensive properties like resistivity.
What is resistivity?
Resistivity ($\rho$) is the resistance of unit length of a conductor with unit cross-sectional area:
$$R=\frac{\rho L}{A}$$
Challenge
1) The SI unit of resistivity is the
- Ohm-square-metre
- metre per Ohm
- Ohm per metre
- Ohm-metre
Example
A copper wire has a resistance of $0.25\Omega$ and a length of $2 m$. Its cross-sectional area is $5\times 10^{-5} m^2$. Find the resistivity of the copper wire.
Challenge
2) The resistance of a wire is inversely proportional to its
- resistivity
- cross-sectional area
- time
- length
Finding the resistivity of a test wire
In order to determine the resistivity of a piece of a conducting wire, we:
- Measure the cross-sectional area of the wire
- While cutting the wire to shorter lengths, measure and record the resistances at each length
Plotting the graph of the resistance versus the length will produce a best-fit line with gradient $\frac{\rho}{A}$, and y-intercept $0$: $$ \begin{equation}\begin{aligned} y&=\color{royalblue}m\color{normal}x+c\\ R&=\color{royalblue}\frac{\rho}{A}\color{normal}L+0\\ \end{aligned}\end{equation} $$
We can then multiply this gradient by the measured cross-sectional area in order to get resistivity: $$m\times A=\frac{\rho}{A}\times A=\rho$$