Electrical resistance is the property of a material or component that opposes the flow of electric current. It is measured in ohms, represented by the Greek capital omega symbol, and is commonly denoted by R. In a simple resistive system, resistance is defined through Ohm's law as R = V divided by I, where V is voltage across the component and I is current through it.
One ohm is the resistance that permits a current of one ampere to flow when a potential difference of one volt is applied, assuming the component behaves according to the relevant linear relationship. Resistance is not a substance that physically blocks every electron like a solid wall; rather, it describes how electrical energy and charge transport respond to an applied electric field. In ordinary conductors, resistance is associated with interactions between charge carriers and the material's atomic structure, imperfections, lattice vibrations and other scattering mechanisms.
The microscopic origin of resistance depends on the material and physical conditions. In metals, electric current is primarily carried by mobile conduction electrons. When an electric field is applied, these electrons acquire a small average drift velocity superimposed on their much faster random thermal motion. Their motion is repeatedly disrupted by interactions with the crystal lattice, impurities, defects, phonons and other scattering processes. These interactions limit the ease with which a net current can develop for a given electric field.
In semiconductors, current can be carried by both electrons and holes, and their concentrations and mobility depend strongly on temperature, impurities and applied electric fields. In ionic solutions, charged ions transport current through the liquid. In plasmas, electrons and ions can contribute to conduction. Resistance therefore has different microscopic origins in different forms of matter, even though the macroscopic quantity is measured in the same unit.
The resistance of a uniform conductor depends on its material, length, cross sectional area and temperature. For a simple uniform conductor under suitable conditions, resistance can be expressed as R = rho L divided by A, where rho is the material's resistivity, L is the conductor length and A is its cross sectional area. Increasing the length generally increases resistance because charge carriers encounter more material through which they must travel.
Increasing cross sectional area generally decreases resistance because a larger conducting region provides more available paths for charge transport. Resistivity is an intrinsic material property expressed in ohm metres, whereas resistance is a property of a particular object or component and depends on its geometry as well as its material. Copper has relatively low resistivity and is therefore widely used for electrical wiring, while materials such as nichrome have much higher resistivity and are useful in heating elements and resistive devices.
Temperature can significantly affect resistance. For many metallic conductors, resistance increases as temperature rises because increased lattice vibrations cause more frequent scattering of conduction electrons. Over a limited temperature range, the resistance of a metal can often be approximated using R = R0[1 + alpha(T - T0)], where alpha is the temperature coefficient of resistance. Semiconductor behaviour is often different, with resistance frequently decreasing as temperature increases because the number of thermally available charge carriers can rise substantially.
Some specialised materials exhibit unusual temperature dependence, including thermistors designed specifically to respond strongly to temperature changes. Superconductors provide an extreme example: below a critical temperature and under appropriate conditions, certain materials enter a superconducting state characterised by zero electrical resistance in the idealised DC sense and additional quantum mechanical phenomena.
Resistance is closely related to current and voltage but should not be confused with either quantity. A resistor with a fixed resistance produces a current determined by the applied voltage, according to Ohm's law when the component is ohmic. Resistance is not necessarily constant in real components. Incandescent lamp filaments, semiconductor diodes, thermistors, varistors and many other devices have nonlinear voltage current characteristics.
In such cases, the ratio V divided by I may vary with operating point, and engineers may distinguish static resistance from differential or dynamic resistance. Static resistance describes the voltage to current ratio at a particular operating point, while differential resistance concerns the local slope of the voltage current characteristic. This distinction becomes important when analysing electronic components whose behaviour changes substantially with current, voltage or temperature.
Resistance also determines how electrical power is converted into other forms of energy. For an ideal resistor, electrical power is dissipated as heat according to P = I squared R, equivalently P = V squared divided by R or P = V I. This phenomenon is called Joule heating or resistive heating. It is useful in electric heaters, kettles, toasters, ovens, soldering equipment and incandescent lamps, although it can be unwanted in electrical cables, motors, transformers and electronic equipment.
The amount of heating depends on resistance, current, duration and thermal conditions. Excessive resistance in a connection can produce local heating, particularly when substantial current passes through a small contact area. Poor electrical connections can therefore become dangerous because oxidation, looseness or mechanical damage may increase contact resistance and produce concentrated heating.
Resistors are deliberately manufactured components used to provide predictable electrical resistance. They can be used to limit current, divide voltage, establish bias conditions, set gains and time constants, terminate transmission lines, discharge capacitors and protect sensitive components. Fixed resistors have approximately fixed nominal resistance, while variable resistors allow resistance to be adjusted. Potentiometers provide an adjustable voltage division arrangement, while rheostats are commonly used when variable resistance is employed directly to control current.
Resistors have ratings for resistance, power dissipation, tolerance, temperature coefficient and sometimes maximum working voltage. A resistor may have the correct resistance value but still be unsuitable if its power rating is too low. Series and parallel combinations produce predictable equivalent resistances: series resistances add directly, while parallel resistances follow the reciprocal relationship 1 divided by Req = 1 divided by R1 plus 1 divided by R2 and so on.
Resistance is important in practical electrical engineering because it influences voltage drops, current levels, power consumption, signal integrity and thermal behaviour. Every real conductor has some resistance, even when it is intended primarily to carry current rather than dissipate energy. Designers therefore select conductor size and material partly according to acceptable resistance and heat generation. Contact resistance, internal resistance of batteries, winding resistance in motors and transformers, and resistance of semiconductor interconnections can all affect system performance.
Resistance measurements can be made with ohmmeters or multimeters, although the circuit generally needs to be de-energised for ordinary resistance measurement. Resistance is also used diagnostically to identify damaged wires, failed components, poor connections and insulation problems. Understanding resistance therefore requires both the macroscopic circuit definition and the microscopic mechanisms that determine how materials respond to electric fields.
