Resistivity
How materials affect resistance
If we take a piece of any material therefore, providing that its dimensions (length and cross sectional area) remain the same, its resistance will remain the same. If two conductors of exactly the same dimensions have a different resistance, they must be made of different materials.
One way in which we can describe a material (any material) is by its RESISTIVITY. This is the amount of resistance present in a piece of the material OF STANDARD DIMENSIONS. Every material can be defined in this way. If we take the resistivity of a material to be the resistance of piece of material whose length is one metre and whose cross sectional area is one square metre (i.e. the standard dimensions are those of a cube of material one metre square) The resistivity of the material being the resistance across opposite faces of the standard cube.
Resistivity is given the symbol; ρ. This is not a letter p but a lower case Greek letter r (called)rho and is measured in a unit called the OHM METER, written ΩM. (Note: this is not the same as ohms/metre or ohms per metre)
. So the resistance of any conductor can be found by relating the three factors;
Length: = L Cross Sectional Area: = A Resistivity: = ρ
We can use the following formula to find the resistance any conductor, providing we know its dimensions and its resistivity.
Remember that, as conductors are often round in section, the cross sectional area may need to be found using the basic formula for the area of a circle. i.e. A = π r2 or A = π(d/2)2 where r and d are the given radius and given diameter, respectively.
Important.
When using this (or any) formula You must convert any sub-unit (mm, cm etc.) into its STANDARD SI UNIT e.g Metres (M). Otherwise your result may be out by a factor of 100 or 1000 or more.
Resistivity problems can be tricky to work out since you have to remember several things at once; using the cross sectional area formula AND the resistivity formula together, converting to standard SI units, using resistivity constants. Maybe you could use a little practice? Try a short Resistivity Quiz and if you need a little help with the maths, download our "Maths Tips" booklet to get you started.
Approximate Resistivity of some common materials. (in Ωm)
CONDUCTORS
- Aluminium 2.7 x 10-8
- Copper 1.7 x 10-8
- Iron 10.5 x 10-8
- Mercury 96 x 10-8
INSULATORS
- P.V.C. 5.4 x 1015
- Glass 104
- Quartz 1012
- P.T.F.E 1012
P.T.F.E.= polytetrafluoroethylene used to insulate high voltage cables.)
It can be seen from the above list that the resistivity of insulators is much higher than that of conductors.