An image of the device used to measure electrical properties

Physics A level revision resource: Introduction to resistivity

The electrical resistance (R) of a circuit component as given by Ohm’s law is the ratio of voltage (V) to current (I), usually expressed as V = IR. It should not be confused with resistivity (ρ) - an intrinsic property of the material which indicates how strongly it opposes the electric current. 

Resistance or resistivity? 

Circuit components have characteristic resistance behaviours as can be seen from plotting their current against voltage. The resistor has a constant resistance value, the filament lamp has a resistance that increases with temperature, and the diode has a very high resistance in one direction.

An image of the graphs for resistor, lamp and diode

For a wire, resistance (R) is dependent on its: length, cross-sectional area and the material it is made from. It is intuitive to think of current flowing in a wire as water flowing through a pipe - a wire of longer length (l) will have higher resistance than a shorter wire, and a wire with a smaller cross sectional area (A) will have higher resistance than one with a larger cross sectional area. Resistivity (ρ) is the constant that links all these things together, defined by the equation:

R = ρl / A

We can measure the resistivity of a metal in the lab by measuring the voltage and current across a wire of known length and cross-sectional area following the circuit diagram.

An image of a circuit diagram showing the wire, voltmeter,  ammeter and cell.

How do we investigate resistivity in a laboratory?

A woman holding a silver ball
How do we measure resistivity in a wire?

What are the real world applications?

Electricity has now become a part of our everyday lives, so it is useful to at least know the basic circuit symbols. Here are a few common examples:

Basic circuit symbols

Temperature is a variable that does not appear in our equation for resistivity, however resistivity (and hence resistance) is temperature dependent and is usually given at a certain temperature. In general, the higher the temperature the larger the resistivity. One way to picture this is that the hotter the component is, the more the molecules are vibrating making it more difficult for current to flow. Thermistors are a special type of resistor that are particularly temperature sensitive. Negative temperature coefficient (or NTC) thermistors have a decreasing resistance with increasing temperature so are typically used as temperature sensors to prevent overvoltage conditions in most electronic devices.

Laboratory Confessions

In the Laboratory Confessions podcast researchers talk about their laboratory experiences in the context of A Level practical assessments. In this episode we look at instruments to measure small distances and circuit diagrams.

What is the link between resistivity and conductivity?

The inverse of resistivity is conductivity (σ). It’s a measure of how well a material acts as conductor. Superconductors are a special type of material that have close to zero resistance when cooled below a characteristic temperature. As they have no resistance, a persistent electric current flows across the surface of the superconductor, which also excludes its internal magnetic field lines.

A superconductor

The resistance of traditional conductors like copper, will not be zero, even when cooled to near absolute zero, however materials such as bismuth strontium calcium copper oxide (BSCOO) have critical temperatures for superconducting as comparatively high as 77 degrees Kelvin, so are known as high temperature superconductors. These are much easier to cool to their critical temperatures than traditional superconductors which often have critical temperatures around 30K - requiring liquid helium for cooling rather than liquid nitrogen. Superconductors have a wide application from research where conditions require little or no resistance (e.g. particle accelerators) to the development of new technologies (e.g. floating magnetic trains) and MRI scanners.