At a constant temperature, the resistance of a piece of wire is dependant on both the length of the wireand the cross-sectional area of the wire:

• as the length of the wire increases, the resistance increases
• as the cross-sectional area increases, the resistance decreases

The resistance (R), length (L) and cross-sectional area (A) is taken into account by resistivity (?). Resistivity is measured in ohm metres (?m):

? = RA / L

In which:

• ? = resistivity of the material in ohm metres (?m)
• R = resistance of the material in ohms (?)
• A = cross-sectional area of the material in metres squared (m²)
• L = length of the material in metres (m)

Resistivity and temperature

If you increase the temperature of a metal, the atoms within the structure of the metal vibrate more and more. This increases the difficulty with which electrons are able to travel through the material. In other words, the resistance of the material increases. One example is a filament bulb.

In the graph below you will see a curve because the resistance of the filament increases as it heats up.

In a semi-conducting material the resistance of the material decreases as the temperature increases. This is because more charge carriers are released. One example would be a negative temperature coefficient thermistor.

Superconductivity

When certain metals and alloys are cooled to a critical temperature their resistance drops to zero. This critical temperature is dependant upon the material but tends to be around -196