An electrical conductor is a material through which electric charge can move relatively easily, allowing an electric current to flow under an applied electric field. Metals are familiar examples, but conduction also occurs in solutions containing mobile ions. A conductor is distinguished from an electrical insulator by its comparatively high electrical conductivity, although this classification depends on the material’s condition and the application. The term also denotes a component, such as a wire, whose function is to carry current. (openstax.org)
Charge carriers and microscopic conduction
In metals, the mobile charge carriers are electrons that are not confined to individual atoms. Without an applied field, their motion produces no net current. An applied field adds a small average drift to their motion. Because electrons have negative charge, their drift direction is opposite to conventional current, which is defined as the direction in which positive charge would move. (openstax.org)
For a simple conductor with one carrier species, the magnitude of current is
[ I=n|q|Av_d, ]
where (n) is the number of mobile carriers per unit volume, (q) their charge, (A) the cross-sectional area, and (v_d) their average drift speed. Drift is distinct from the much faster propagation of an electrical disturbance through a circuit: electrons need not travel from the source to a device before that device responds. (openstax.org)
The electronic properties of crystalline solids are explained more fully through quantum mechanics and electronic band structure. Metallic conductors possess partially occupied electronic bands, providing nearby unoccupied states into which electrons can move when a field is applied. In an insulator, occupied and unoccupied bands are separated by a substantial band gap. A semiconductor has a smaller gap, and its carrier population can change strongly with temperature or impurities. These distinctions concern available electronic states, not simply the total number of electrons present. (openstax.org)
Conductivity, resistivity, and resistance
Electrical conductivity, denoted by (\sigma), measures a material’s response to an applied field. For an isotropic material in its linear-response regime,
[ \mathbf{J}=\sigma\mathbf{E}, ]
where (\mathbf{J}) is current density. This is the local form of Ohm’s law. Electrical resistivity, (\rho), is the reciprocal of conductivity:
[ \rho=\frac{1}{\sigma}. ]
In the International System of Units, conductivity is measured in siemens per metre and resistivity in ohm-metres. (openstax.org)
Resistivity describes a material, whereas resistance describes a particular object. For a uniform wire of length (L) and cross-sectional area (A),
[ R=\rho\frac{L}{A}. ]
Consequently, a longer wire has greater resistance, while a thicker wire of the same material has less. At 20 °C, representative resistivities are approximately (1.68\times10^{-8}\ \Omega\cdot\mathrm{m}) for copper and (1.59\times10^{-8}\ \Omega\cdot\mathrm{m}) for silver; purity affects measured values. (openstax.org)
A resistive conductor converts electrical energy into heat, a process called Joule heating. For an ohmic component carrying current (I), the dissipated power is (P=I^2R). This dissipation is useful in electric heaters but represents an energy loss in transmission wiring. (openstax.org)
Materials and temperature dependence
Copper is widely used in electrical wiring because it combines low room-temperature resistivity with greater economic practicality than silver. Silver conducts somewhat better, but its cost limits its use as a general-purpose wiring material. Ordinary metallic conductors retain finite resistance, unlike materials in a superconducting state. (openstax.org)
Metallic resistivity generally increases with temperature. Over a limited interval, its change can often be approximated by a linear temperature coefficient. This relationship is not universal: semiconductor resistivity may decrease as temperature raises the population of mobile carriers. Accordingly, conductivity values require specified measurement conditions rather than serving as immutable material constants. (openstax.org)
Conduction need not involve electrons moving through a metal. In an electrolyte solution, mobile ions carry charge. Positive and negative ions move in opposite directions under an applied field, both contributing to conventional current. Pure water is a very poor conductor because it contains few ions; dissolving substances that produce ions can greatly increase its conductivity. Merely dissolving a substance is insufficient: dissolved neutral molecules do not themselves provide ionic charge carriers. (openstax.org)
Electrostatic behavior
A conductor in electrostatic equilibrium has no macroscopic electric field within its conducting bulk. Otherwise, its mobile charges would continue to redistribute. Any excess charge resides on its surfaces, and the electric field immediately outside a smooth conducting surface is perpendicular to that surface. Charges tend to concentrate more strongly near sharply curved regions. (openstax.org)
An equilibrium conductor also has the same electric potential throughout. These properties underlie electrostatic shielding: a closed conducting enclosure shields an empty internal cavity from external static electric fields. They do not imply that every conductor always has zero internal field. A resistive wire carrying steady current requires an internal field to sustain charge drift and is not in electrostatic equilibrium. (openstax.org)
Alternating currents and superconductors
With alternating current, current distribution can become nonuniform. The skin effect concentrates current near a conductor’s surface, reducing the effective area carrying current and increasing resistance. For a good conductor, the characteristic penetration depth depends on frequency, conductivity, and magnetic permeability; it generally decreases as frequency rises. (live.ocw.mit.edu)
Superconductivity is a distinct state characterized by zero electrical resistance and, in the Meissner state, magnetic-field expulsion. It occurs within material-dependent limits of temperature, current, and magnetic field. A superconductor is therefore not merely an ordinary conductor with unusually low resistivity; its magnetic behavior distinguishes it from the idealized model of a perfectly conducting material. (openstax.org)