Electrical Resistance
Electricity and Magnetism

## Resistance, electrical

Glossary Definition for 16-19 #### Description

The electrical resistance of a component in an electric circuit is a property that describes how the electric current in the component is related to the electrical potential difference (voltage) across it. The greater the resistance, the smaller the current for a given potential difference, and the greater the potential difference, for a given current.

Electrical resistance is usually represented by the symbol R.

Electrical resistance is defined, for some component, by the equation

R = VI

where V is the electrical potential difference across the component and I the corresponding electric current.

#### Discussion

Resistance and Ohm’s law
For a component that obeys Ohm’s law, the electric current, I, in the component is directly proportional to the potential difference, V across it, provided the component’s temperature and other physical conditions remain constant. A graph of V against I, or I against V, is then a straight line passing through the origin. The component has this characteristic behaviour and characteristic graph because its resistance does not change as the current changes.

Ohm’s law is not a law of physics. It is an observation and formalisation of the behaviour of some materials. As such, it is a useful way of distinguishing ‘ohmic conductors’ (those that obey Ohm’s law) from ‘non-ohmic’ ones.

If a component does not obey Ohm’s law, the graph is not a straight line. Its resistance changes as the current changes.

In both cases (ohmic and non-ohmic behaviour), the resistance of the component at any given value of current or potential difference can be calculated from the definition of resistance:

R = VI Figure 1: A current I flows in a sample of material in an electrical circuit. The potential difference across the sample is V.

Resistance and temperature
Resistance is affected by temperature, see electrical resistivity.

The resistance of manufactured resistors is usually quoted for a specific temperature. A maximum operating power is often also specified, above which the resulting temperature rise significantly alters the component’s resistance.

Resistance and conductance
Electrical resistance is the reciprocal of electrical conductance.

ohm, Ω

kg m2 s-3 A-2

#### Mathematical expressions

• R = VI

where V is the electrical potential difference across a component with resistance R and I the corresponding current.
• P = VI = I 2R = V 2R

where P is the power dissipated in a component with resistance R, V is the electrical potential difference across it and I is the current.
• R = ρLA

where R is the resistance of a sample of material with length L, uniform cross-sectional area A and resistivity ρ.

#### Related entries

• Conductance, electrical
• Conductivity, electrical
• Current, electric
• Emf
• Potential difference, electrical
• Power
• Resistivity, electrical
• Voltage

#### In context

Circuit components have a huge range of resistances. Suppliers of components for electronic circuits typically sell resistors ranging from a few ohms to several . The heating element of an electric kettle, designed to have a power of about 1 kW when connected to a 230 V mains supply, has a resistance of about 50 Ω. A torch bulb designed for use with a 3 V battery has a resistance of about 10 Ω when in use.

The connecting wires in a circuit are usually treated as having negligible resistance as their resistance is very small compared to that of other components in the circuit. For example, a 0.1 m length of copper wire of diameter 0.5 mm has a resistance of about 0.01 Ω. Insulators, such as the coverings of electrical leads, are usually treated as having infinite resistance as their resistances are very much larger than those of other items in the circuit. For electrical safety, the resistance between a live circuit (designed to operate from a 230 Ω supply in the UK) and the Earth near the location of the device should be at least 25 MΩ.

###### Electrical Resistance
is used in analyses relating to Superconductor