Resistivity, Conductivity, Resistance and Conductance

Resistivity

Resistivity is an attribute of a material, such as copper for example, which is proportional to how strongly it resists an electric current flowing through it.

Hence a material with a high resistivity strongly opposes electric current flowing through it and conversely a material with a low resistivity permits electric current and makes a better conductor.

Resistivity is given the symbol ρ (pronounced rho) and has units of Ohm metre [Ωm].

Conductivity

Conductivity is a related property of a material which is the reciprocal of resistivity and reflects how strongly a material conducts an electric current.

Copper is a material which has high conductivity and low resistivity.

Conductivity is given the symbol σ (pronounced sigma) and has units of Siemens per metre [S/m].

Resistance and Conductance

Electrical resistance is a measure of an objects opposition to an electric current.

It has units of ohms (Ω) and depends on three factors: resistivity (ρ), length (L) and cross sectional area (A) and is qualitatively described with the equation below:

And shown diagrammatically as:

Intuitively from this we can see that longer objects will have an increased resistance which is understandable as the charges have more resistance to get through and a smaller cross section area also increases resistance as less charges will be able to pass through it per second and there are also less charges in the material itself to help conduction.

A related measurement to resistance is conductance which has the units of Siemens (S). Similar to resitivity and conductivity, conductance is the reciprocal of resistance.

Objects with a larger conductance allow higher currents to flow.

Example:

Q. What is the resistance of a 15cm long wire with an area of 100mm² and resisitivity of 1.68*10^-8Ωm?

For this it is best to first determine each parameter in its base units of m and then apply the formula for a final result in Ω. An excellent tool for confirming that all the units are in their required metric unit is dimensional analysis where we check the units on both sides of the equation. In our case we want to confirm that if all units are in m, then the final result will be in Ω's:

Which proves that we will achieve the desired result by converting the length and area into base units of m. Now to calculate each of the parameters in units of m and then substitute them into the formula for resistance:

When possible it is best practice to express the final answer in the units which will simplify the result. Unless the question specifically asks for an answer in specific units, for example: "Provide the answer in Ω's", be careful of this especially in exams and assignments!

Questions:

1. An object has a resistance of 5Ω, a length of 40cm and an area of 10mm². What is its resistivity?

2. An object has a resistance of 2mΩ, a length of 40cm and a resistivity of 1.79*10^-5Ωm. What is its area?

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