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Density and resistivity of materials are called *bulk properties*: their value doesn't depend on the size or shape of a particular sample – only on the material itself.

When we say that copper is a heavier metal than aluminium, we are comparing their*densities*. In a similar way, when we say that copper is a better conductor than aluminium, we are comparing their *resistivities*.

This e-source looks at calculating the density and resistivity of materials, which use similar mathematical methods. Below are different sections, for quick navigation.

When we say that copper is a heavier metal than aluminium, we are comparing their

This e-source looks at calculating the density and resistivity of materials, which use similar mathematical methods. Below are different sections, for quick navigation.

m ∝ V(mass is proportional to volume)

To work out the exact mass from the volume we need to know the density*, ρ* (Greek symbol Rho), and put that in the expression. Density is the mass in kg of 1 m^{3} of the material.

For copper *ρ* = 8940 ( kg m^{-3}). For aluminium *ρ* = 2700 (kg m^{-3}).

Aluminium has less than one third the density of copper (making it good for building aircraft).

Now the proportionality can be changed to an equation.

The densitym = ρ V

Rearranging the equation gives:

ρ = m / V

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To understand this part you need to know Ohm's Law:

R = V / I (resistance = volts per amp).

The next wire with length 2L will have double the resistance of 2R. This is just like adding two pieces of the top wire in series.

Therefore:

R ∝ L(resistance is proportional to length).

The third wire has length L but twice the cross section area, 2A. This is the same as adding two pieces of the top wire in parallel. The resistance will be R/2.

Therefore:

R ∝ 1 / A(resistance is inversely proportional to cross section area).

Combining both proportionalities gives:

The same maths works for aluminium, or any conductor, but if we want to work out the actual resistance we need to know how resistive the material is to an electric current. We need to know theR ∝ L / A

Adding the resistivity term gives:

R =)ρ( L / A

Rearranging gives:

This shows that the units of resistivity are Ω • m (Ohm metres). However, don't panic! You do not need to understand the unit. Provided you use the unit ohm metre as the unit of resistivity, metre as the unit for length and metre)= R ( A / Lρ

Resistivity is a measure of how bad a conductor is. If you look at the table you will see that materials with high resistivity are *insulators*. The opposite of resistivity is conductivity. This is given the letter sigma and is the reciprocal of resistivity:

Electrical conductivity, *σ = 1/ρ*

- If you have two identical saucepans, one made of copper and the other of aluminium, how many times heavier will the copper one be?
- Compare the resistivities of silver and nichrome alloy. How many times better is silver than nichrome at conducting electricity?
- Calculate the resistance of a copper cable 50 mm in diameter and 30 km long.
- If you had to replace the cable in Question 3 with aluminium, what would the diameter need to be to have the same resistance?
- The unit of conductivity is the Siemens m
^{-1}. Find out who Siemens was and where you will find his name today.