Resistivity is a property of a material that quantifies its resistance to an electric current flowing through it.
The resistivity (ρ) of a length of material can be calculated using the following equation:
Where R is the resistance measured in ohms (Ω), A is the the cross-sectional area of the material measured in meters squared (m2) and l is the length of the material measured in meters (m).
The SI unit of resistivity is the ohm-meter (Ωm).
If we rearrange the equation for resistance we get the following:
From this we can see that resistance is directly proportional to the length of a wire and the resistivity of the material. Therefore, increasing either of these values will increase the resistance.
We can also see that it is inversely proportional to the cross-sectional area of a wire. By increasing the cross section of a wire the resistance will decrease.
Temperature
As the temperature of a metal increases the internal energy of the atoms increases too. This increase in internal energy is due to an increase in kinetic energy caused by the atoms vibrating.
The more the atoms of a metal vibrate the more difficult it is for conduction electrons to pass through and so the resistance of the material increases.
We can therefore say that the resistance of a material is directly proportional to the temperature.
From the equation above we know that resistance is also directly proportional to resistivity. So if the resistance increases the resistivity must also be increasing.
Therefore, resistivity is dependent on temperature (as temperature increases so does the resistivity). Due to this the value of resistivity for a material is different depending on the temperature.
Important Note: Resistivity also requires the current flowing through the material to be uniform and so is only useful when a direct current is used (not an alternating current).
Worked Examples
Example 1
The resistivity of copper at room temperature is 1.68 x10-8 Ωm. Calculate the resistance of a 2m copper wire that has a cross-sectional area of 2.5 x10-7 m2.
Example 2
The resistivity of aluminium at room temperature is 2.65 x10-8 Ωm. A 1.5m length of aluminium wire has a resistance of 10Ω. Calculate the radius of the wire.
Example 3
Wire 1 has a resistance of 10Ω. Wire 2 has an identical length and cross-sectional area but it is made of a material with a resistivity that is double that of wire 1. Calculate the resistance of wire 2.
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