Electrical resistivity

Different materials oppose electric current by different amounts. Electrical resistivity, denoted by $$\rho$$, describes how strongly a material opposes current. A material with higher resistivity produces a greater resistance for conductors of the same dimensions.

For a uniform conductor of length $$L$$, cross-sectional area $$A$$ and resistance $$R$$, resistivity is given by:

The same relationship can be rearranged to show how the resistance depends on the material and dimensions:

For a given resistivity, a longer conductor has greater resistance, while a conductor with a larger cross-sectional area has lower resistance. For example, doubling the length doubles the resistance; doubling the area halves it, provided the other quantities remain unchanged.

Resistivity is a material property; resistance also depends on the conductor’s length and cross-sectional area. The SI unit of resistivity is the ohm metre, $$\Omega,\mathrm{m}$$. Resistivity can depend on temperature, so the value for a material may change as its temperature changes.

Temperature dependence of metal resistance

A metal conductor offers resistance to the flow of electric charge. When the metal’s temperature increases, its resistance increases; when it cools, its resistance decreases.

A metal contains ions arranged in a structure and conduction electrons that can move through it. Heating makes the ions vibrate more strongly. The moving electrons are then scattered more frequently by the vibrating ions, which impedes their flow and increases the resistance.

Cooling has the opposite effect. The ions vibrate less strongly, so the conduction electrons are scattered less frequently and the resistance decreases.

Negative temperature coefficient thermistors

A negative temperature coefficient (NTC) thermistor is a resistor whose resistance changes with temperature. As its temperature increases, its resistance decreases. As it cools, its resistance increases.

The thermistor is made from a semiconductor. Heating it makes more charge carriers available to carry electric current through the material. With more carriers available, current can flow more easily, so the thermistor’s resistance falls.

Resistance–temperature graph

For an NTC thermistor, a graph of resistance against temperature slopes downward: higher temperatures correspond to lower resistances. The graph is generally non-linear, so equal increases in temperature do not necessarily produce equal decreases in resistance.

NTC thermistors as temperature sensors

An NTC thermistor can be used as a temperature sensor because a change in temperature produces a change in its resistance. The resistance can be measured or used by a circuit to indicate the thermistor’s temperature.

Superconductivity

Certain materials can conduct electricity without electrical resistance when cooled sufficiently. This property is called superconductivity.

A material becomes superconducting at and below its critical temperature. The critical temperature depends on the material. In the superconducting state, the material has zero electrical resistivity, so a conductor made from it has no electrical resistance and dissipates no energy through resistive heating.

Uses of superconductors

Superconductors can carry large currents, which can produce strong magnetic fields. They can also reduce energy loss in electric power transmission: while a transmission conductor remains superconducting, it loses no energy through resistive heating.