### Defining resistivity

**Electrical resistivity is a property of a material**. It does not depend upon the size or shape of the sample being tested. That could be a short thick bar or a long thin wire, it makes no difference as long as they are made from the same material. The resistivity is a measure of the amount that a material will resist the flow of an electric current.

**The formal definition is that it the resistance of a one metre cube between opposite faces.** However it is entirely impractical to test a shape like that so we use the formula that:

**Resistivity =cross sectional area x resistance/length**

### Measuring resistivity

In order to **calculate the resistivity** we need to measure the length, diameter and resistance of our sample of wire. The length is measured with a long tape and the diameter measured (in at least three places with accurate callipers or micrometer.

**To measure the resistance** of a sample wire it is best to measure a range of values of potential difference (volts) and current (amps).

The variable resistor is adjusted to give as wide a range as possible with values evenly spaced. From the range the graph plotted will provide a reliable value of resistance.

The graph is plotted with PD, the controlling factor, on the x axis and current on the y axis. The line of best fit helps to even out small errors and would highlight any major mistakes in taking a result. The line does not have to pass through the origin. The value of resistance V/I is the inverse of the gradient. Select any two convenient values, providing they employ most of the graph line, to make the calculation.

### Resistivity calculation

**Calculating resistivity**

From the measurements taken for the sample of steel wire:

Length 2.78m

Diameter 0.38mm

Resistance 4.29 ohms

### PDF notes

**You can download a copy of two A4 sheets of notes in PDF here:Resistivity notes**

**Other pages on resistance you might find useful:**

**Electrical resistance and Ohm's Law notes and video Resistance and temperature graphs Resistance of a filament bulb The characteristics of a diode Electrical resistivity Internal resistance and EMF**