Current (electricity)

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An electric current is a stream of
charged particle In physics, a charged particle is a particle with an electric charge. It may be an ion, such as a molecule or atom with a surplus or deficit of electrons relative to protons. It can also be an electron or a proton, or another elementary particle, ...
s, such as
electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...
s or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electron ...
through a surface or into a control volume. The moving particles are called charge carriers, which may be one of several types of particles, depending on the conductor. In
electric circuit An electrical network is an interconnection of electronic component, electrical components (e.g., battery (electricity), batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of e ...
s the charge carriers are often
electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...
s moving through a wire. In
semiconductor A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
s they can be electrons or holes. In an
electrolyte An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electr ...
the charge carriers are ions, while in plasma, an ionized gas, they are ions and electrons. The SI unit of electric current is the
ampere The ampere (, ; symbol: A), often Clipping (morphology), shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One amp ...
, or ''amp'', which is the flow of electric charge across a surface at the rate of one
coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In 2019 redefinition of the SI base units, the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant curre ...
per second. The ampere (symbol: A) is an SI base unit. Electric current is measured using a device called an
ammeter An ammeter (abbreviation of ''Ampere meter'') is an measuring instrument, instrument used to measure the electric current, current in a Electrical circuit, circuit. Electric currents are measured in amperes (A), hence the name. For direct measure ...
. Electric currents create magnetic fields, which are used in motors, generators,
inductor An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges ...
s, and
transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple Electrical network, circuits. A varying current in any coil of the transformer produces a varying magnetic flux in ...
s. In ordinary conductors, they cause
Joule heating Joule heating, also known as resistive, resistance, or Ohmic heating, is the process by which the passage of an electric current through a conductor (material), conductor produces heat. Joule's first law (also just Joule's law), also known in c ...
, which creates
light Light or visible light is electromagnetic radiation that can be visual perception, perceived by the human eye. Visible light is usually defined as having wavelengths in the range of 400–700 nanometres (nm), corresponding to frequency, fr ...
in
incandescent light bulbs An incandescent light bulb, incandescent lamp or incandescent light globe is an electric light with a wire #Filament, filament heated until it glows. The filament is enclosed in a glass bulb with a vacuum or inert gas to protect the filament ...
. Time-varying currents emit
electromagnetic waves In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
, which are used in
telecommunications Telecommunication is the transmission of information by various types of technologies over wire, radio Radio is the technology of signaling and telecommunication, communicating using radio waves. Radio waves are electromagnetic waves of ...

# Symbol

The conventional symbol for current is , which originates from the French phrase ''intensité du courant'', (current intensity). Current intensity is often referred to simply as ''current''. The symbol was used by André-Marie Ampère, after whom the unit of electric current is named, in formulating Ampère's force law (1820). The notation travelled from France to Great Britain, where it became standard, although at least one journal did not change from using to until 1896.

# Conventions

The conventional direction of current, also known as electric polarity, is arbitrarily defined as the direction in which charges flow. In a conductive material, the moving charged particles that constitute the electric current are called charge carriers. In metals, which make up the wires and other conductors in most
electrical circuit An electrical network is an interconnection of electronic component, electrical components (e.g., battery (electricity), batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of e ...
s, the positively charged
atomic nuclei The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden experiments, Geiger–Marsden gold foil experiment. After th ...
of the atoms are held in a fixed position, and the negatively charged
electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...
s are the charge carriers, free to move about in the metal. In other materials, notably the
semiconductor A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
s, the charge carriers can be positive ''or'' negative, depending on the
dopant A dopant, also called a doping agent, is a trace of impurity element that is introduced into a chemical material to alter its original electrical or optics, optical properties. The amount of dopant necessary to cause changes is typically very l ...
used. Positive and negative charge carriers may even be present at the same time, as happens in an
electrolyte An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electr ...
in an
electrochemical cell An electrochemical cell is a device capable of either generating electrical energy from chemical reactions or using electrical energy to cause chemical reactions. The electrochemical cells which generate an electric current are called voltaic o ...
. A flow of positive charges gives the same electric current, and has the same effect in a circuit, as an equal flow of negative charges in the opposite direction. Since current can be the flow of either positive or negative charges, or both, a convention is needed for the direction of current that is independent of the type of charge carriers. Negatively charged carriers, such as the electrons (the charge carriers in metal wires and many other electronic circuit components), therefore flow in the opposite direction of conventional current flow in an electrical circuit.

## Reference direction

A current in a wire or circuit element can flow in either of two directions. When defining a variable $I$ to represent the current, the direction representing positive current must be specified, usually by an arrow on the circuit schematic diagram. This is called the ''reference direction'' of the current $I$. When analyzing electrical circuits, the actual direction of current through a specific circuit element is usually unknown until the analysis is completed. Consequently, the reference directions of currents are often assigned arbitrarily. When the circuit is solved, a negative value for the current implies the actual direction of current through that circuit element is opposite that of the chosen reference direction.

# Ohm's law

Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship: $I = \frac,$ where ''I'' is the current through the conductor in units of
ampere The ampere (, ; symbol: A), often Clipping (morphology), shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One amp ...
s, ''V'' is the potential difference measured ''across'' the conductor in units of
volt The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units, International System of Units (SI). It is named after the Italian physicist Alessandro ...
s, and ''R'' is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the ''R'' in this relation is constant, independent of the current.

# Alternating and direct current

In
alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in which ...
(AC) systems, the movement of
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electron ...
periodically reverses direction. AC is the form of
electric power Electric power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of Power (physics), power is the watt, one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions ...
most commonly delivered to businesses and residences. The usual waveform of an AC power circuit is a
sine wave A sine wave, sinusoidal wave, or just sinusoid is a curve, mathematical curve defined in terms of the ''sine'' trigonometric function, of which it is the graph of a function, graph. It is a type of continuous wave and also a Smoothness, smooth p ...
, though certain applications use alternative waveforms, such as triangular or
square wave A square wave is a non-sinusoidal waveform, non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency between fixed minimum and maximum values, with the same duration at minimum and maximum. In an ideal square ...
s. Audio and
radio Radio is the technology of signaling and telecommunication, communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device ...
signals carried on electrical wires are also examples of alternating current. An important goal in these applications is recovery of information encoded (or '' modulated'') onto the AC signal. In contrast,
direct current Direct current (DC) is one-directional electric current, flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor (material), conductor such as a wire, but can also flow throug ...
(DC) refers to a system in which the movement of electric charge in only one direction (sometimes called unidirectional flow). Direct current is produced by sources such as batteries, thermocouples, solar cells, and commutator-type electric machines of the
dynamo "Dynamo Electric Machine" (end view, partly section, ) A dynamo is an electrical generator In electricity generation, a generator is a device that converts motive power (mechanical energy) or fuel-based power (chemical energy) into electri ...
type. Alternating current can also be converted to direct current through use of a rectifier. Direct current may flow in a conductor such as a wire, but can also flow through
semiconductor A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
s, insulators, or even through a
vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Ph ...
as in electron or ion beams. An old name for direct current was ''galvanic current''.

# Occurrences

Natural observable examples of electric current include
lightning Lightning is a naturally occurring electrostatic discharge during which two electric charge, electrically charged regions, both in the atmosphere or with one on the land, ground, temporarily neutralize themselves, causing the instantaneous ...
, static electric discharge, and the solar wind, the source of the polar auroras. Man-made occurrences of electric current include the flow of conduction electrons in metal wires such as the overhead power lines that deliver
electrical energy Electrical energy is energy related to forces on electrically charged particles and the movement of electrically charged particles (often electrons in wires, but not always). This energy is supplied by the combination of electric current and electr ...
across long distances and the smaller wires within electrical and electronic equipment.
Eddy current Eddy currents (also called Foucault's currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magn ...
s are electric currents that occur in conductors exposed to changing magnetic fields. Similarly, electric currents occur, particularly in the surface, of conductors exposed to
electromagnetic wave In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic field, electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, inf ...
s. When oscillating electric currents flow at the correct voltages within radio antennas,
radio wave Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz (GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (short ...
s are generated. In
electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using Electronic component, electronic devices. Electronics uses Passivity (engineering), active devices ...
, other forms of electric current include the flow of electrons through
resistor A resistor is a passivity (engineering), passive terminal (electronics), two-terminal electronic component, electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce c ...
s or through the vacuum in a
vacuum tube A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied. The type kn ...
, the flow of ions inside a battery, and the flow of holes within metals and
semiconductor A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
s. A biological example of current is the flow of ions in
neurons A neuron, neurone, or nerve cell is an membrane potential#Cell excitability, electrically excitable cell (biology), cell that communicates with other cells via specialized connections called synapses. The neuron is the main component of nervous ...
and nerves, responsible for both thought and sensory perception.

# Measurement

Current can be measured using an
ammeter An ammeter (abbreviation of ''Ampere meter'') is an measuring instrument, instrument used to measure the electric current, current in a Electrical circuit, circuit. Electric currents are measured in amperes (A), hence the name. For direct measure ...
. Electric current can be directly measured with a galvanometer, but this method involves breaking the
electrical circuit An electrical network is an interconnection of electronic component, electrical components (e.g., battery (electricity), batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of e ...
, which is sometimes inconvenient. Current can also be measured without breaking the circuit by detecting the magnetic field associated with the current. Devices, at the circuit level, use various techniques to measure current: * Shunt resistors *
Hall effect The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor that is wikt:transverse, transverse to an electric current in the conductor and to an applied magnetic field perpendicular to the curren ...
current sensor transducers *
Transformers ''Transformers'' is a media franchise produced by American toy company Hasbro and Japanese toy company Tomy, Takara Tomy. It primarily follows the Autobots and the Decepticons, two alien robot factions at war that can transform into other forms ...
(however DC cannot be measured) * Magnetoresistive field sensors * Rogowski coils * Current clamps

# Resistive heating

Joule heating, also known as ''ohmic heating'' and ''resistive heating'', is the process of power dissipation by which the passage of an electric current through a conductor increases the
internal energy The internal energy of a thermodynamic system is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
of the conductor, converting thermodynamic work into
heat In thermodynamics, heat is defined as the form of energy crossing the boundary of a thermodynamic system by virtue of a temperature difference across the boundary. A thermodynamic system does not ''contain'' heat. Nevertheless, the term is al ...
. The phenomenon was first studied by James Prescott Joule in 1841. Joule immersed a length of wire in a fixed
mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to be related to the physical quantity, quantity of matter in a Physical object, physical body, until the discovery of the atom and par ...
of
water Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...
and measured the
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
rise due to a known current through the wire for a 30 minute period. By varying the current and the length of the wire he deduced that the heat produced was proportional to the square of the current multiplied by the
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its Multiplicative inverse, reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares s ...
of the wire. $P \propto I^2 R.$ This relationship is known as Joule's Law. The SI unit of
energy In physics, energy (from Ancient Greek: wikt:ἐνέργεια#Ancient_Greek, ἐνέργεια, ''enérgeia'', “activity”) is the physical quantity, quantitative physical property, property that is #Energy transfer, transferred to a phy ...
was subsequently named the
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units, International System of Units (SI). It is equal to the amount of Work (physics), work done when a force of 1 Newton (unit), newton displaces a mass through ...
and given the symbol ''J''. The commonly known SI unit of power, the
watt The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. It is used to quantify the rate of energy transfer. The watt is named after James W ...
(symbol: W), is equivalent to one joule per second.

# Electromagnetism

## Electromagnet

In an electromagnet a coil of wires behaves like a magnet when an electric current flows through it. When the current is switched off, the coil loses its magnetism immediately. Electric current produces a
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to t ...
. The magnetic field can be visualized as a pattern of circular field lines surrounding the wire that persists as long as there is current.

## Electromagnetic induction

Magnetic fields can also be used to make electric currents. When a changing magnetic field is applied to a conductor, an
electromotive force In electromagnetism and electronics, electromotive force (also electromotance, abbreviated emf, denoted \mathcal or ) is an energy transfer to an electric circuit per unit of electric charge, measured in volts. Devices called electrical ''Transd ...
(EMF) is induced, which starts an electric current, when there is a suitable path.

When an electric current flows in a suitably shaped conductor at radio frequencies,
radio waves Radio waves are a type of electromagnetic radiation with the longest wavelengths in the electromagnetic spectrum, typically with frequencies of 300 gigahertz (GHz) and below. At 300 GHz, the corresponding wavelength is 1 mm (short ...
can be generated. These travel at the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special relativity, special theory of relativity, is ...
and can cause electric currents in distant conductors.

# Conduction mechanisms in various media

In metallic solids, electric charge flows by means of
electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...
s, from lower to higher
electrical potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work (physics), work energy needed to move a unit of electric charge from a reference point to the sp ...
. In other media, any stream of charged objects (ions, for example) may constitute an electric current. To provide a definition of current independent of the type of charge carriers, ''conventional current'' is defined as moving in the same direction as the positive charge flow. So, in metals where the charge carriers (electrons) are negative, conventional current is in the opposite direction to the overall electron movement. In conductors where the charge carriers are positive, conventional current is in the same direction as the charge carriers. In a
vacuum A vacuum is a space devoid of matter. The word is derived from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Ph ...
, a beam of ions or electrons may be formed. In other conductive materials, the electric current is due to the flow of both positively and negatively charged particles at the same time. In still others, the current is entirely due to positive charge flow. For example, the electric currents in
electrolyte An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electr ...
s are flows of positively and negatively charged ions. In a common lead-acid
electrochemical Electrochemistry is the branch of physical chemistry concerned with the relationship between Electric potential, electrical potential difference, as a measurable and quantitative phenomenon, and identifiable chemical change, with the potential dif ...
cell, electric currents are composed of positive hydronium ions flowing in one direction, and negative sulfate ions flowing in the other. Electric currents in sparks or plasma are flows of electrons as well as positive and negative ions. In ice and in certain solid electrolytes, the electric current is entirely composed of flowing ions.

## Metals

In a
metal A metal (from ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, e ...
, some of the outer electrons in each atom are not bound to the individual molecules as they are in molecular solids, or in full bands as they are in insulating materials, but are free to move within the metal lattice. These conduction electrons can serve as charge carriers, carrying a current. Metals are particularly conductive because there are many of these free electrons. With no external
electric field An electric field (sometimes E-field) is the field (physics), physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the ...
applied, these electrons move about randomly due to thermal energy but, on average, there is zero net current within the metal. At room temperature, the average speed of these random motions is 106 metres per second. Given a surface through which a metal wire passes, electrons move in both directions across the surface at an equal rate. As George Gamow wrote in his
popular science ''Popular Science'' (also known as ''PopSci'') is an American digital magazine carrying popular science content, which refers to articles for the general reader on science and technology subjects. ''Popular Science'' has won over 58 awards, inclu ...
book, '' One, Two, Three...Infinity'' (1947), "The metallic substances differ from all other materials by the fact that the outer shells of their atoms are bound rather loosely, and often let one of their electrons go free. Thus the interior of a metal is filled up with a large number of unattached electrons that travel aimlessly around like a crowd of displaced persons. When a metal wire is subjected to electric force applied on its opposite ends, these free electrons rush in the direction of the force, thus forming what we call an electric current." When a metal wire is connected across the two terminals of a DC
voltage source A voltage source is a two-terminal (electronics), terminal device which can maintain a fixed voltage. An ideal voltage source can maintain the fixed voltage independent of the load resistance or the output Electric current, current. However, a re ...
such as a battery, the source places an electric field across the conductor. The moment contact is made, the free electrons of the conductor are forced to drift toward the positive terminal under the influence of this field. The free electrons are therefore the charge carrier in a typical solid conductor. For a steady flow of charge through a surface, the current ''I'' (in amperes) can be calculated with the following equation: $I = \, ,$ where ''Q'' is the electric charge transferred through the surface over a
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
''t''. If ''Q'' and ''t'' are measured in
coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In 2019 redefinition of the SI base units, the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant curre ...
s and seconds respectively, ''I'' is in amperes. More generally, electric current can be represented as the rate at which charge flows through a given surface as: $I = \frac \, .$

## Electrolytes

Electric currents in
electrolyte An electrolyte is a medium containing ions that is electrically conducting through the movement of those ions, but not conducting electron The electron ( or ) is a subatomic particle with a negative one elementary charge, elementary electr ...
s are flows of electrically charged particles ( ions). For example, if an electric field is placed across a solution of Na+ and Cl (and conditions are right) the sodium ions move towards the negative electrode (cathode), while the chloride ions move towards the positive electrode (anode). Reactions take place at both electrode surfaces, neutralizing each ion. Water-ice and certain solid electrolytes called proton conductors contain positive hydrogen ions ("
proton A proton is a stable subatomic particle, symbol , H+, or 1H+ with a positive electric charge of +1 ''e'' elementary charge. Its mass is slightly less than that of a neutron and 1,836 times the mass of an electron (the proton–electron mass ...
s") that are mobile. In these materials, electric currents are composed of moving protons, as opposed to the moving electrons in metals. In certain electrolyte mixtures, brightly coloured ions are the moving electric charges. The slow progress of the colour makes the current visible.

## Gases and plasmas

In air and other ordinary gases below the breakdown field, the dominant source of electrical conduction is via relatively few mobile ions produced by radioactive gases, ultraviolet light, or cosmic rays. Since the electrical conductivity is low, gases are
dielectric In electromagnetism, a dielectric (or dielectric medium) is an Insulator (electricity), electrical insulator that can be Polarisability, polarised by an applied electric field. When a dielectric material is placed in an electric field, electr ...
s or insulators. However, once the applied
electric field An electric field (sometimes E-field) is the field (physics), physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the ...
approaches the breakdown value, free electrons become sufficiently accelerated by the electric field to create additional free electrons by colliding, and ionizing, neutral gas atoms or molecules in a process called avalanche breakdown. The breakdown process forms a plasma that contains enough mobile electrons and positive ions to make it an electrical conductor. In the process, it forms a light emitting conductive path, such as a spark, arc or
lightning Lightning is a naturally occurring electrostatic discharge during which two electric charge, electrically charged regions, both in the atmosphere or with one on the land, ground, temporarily neutralize themselves, causing the instantaneous ...
. Plasma is the state of matter where some of the electrons in a gas are stripped or "ionized" from their
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...
s or atoms. A plasma can be formed by high
temperature Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temp ...
, or by application of a high electric or alternating magnetic field as noted above. Due to their lower mass, the electrons in a plasma accelerate more quickly in response to an electric field than the heavier positive ions, and hence carry the bulk of the current. The free ions recombine to create new chemical compounds (for example, breaking atmospheric oxygen into single oxygen 2 → 2O which then recombine creating
ozone Ozone (), or trioxygen, is an inorganic molecule with the chemical formula . It is a pale blue gas with a distinctively pungent smell. It is an allotrope of oxygen that is much less stable than the diatomic Allotropy, allotrope , breaking down i ...
3.

## Vacuum

Since a " perfect vacuum" contains no charged particles, it normally behaves as a perfect insulator. However, metal electrode surfaces can cause a region of the vacuum to become conductive by injecting free electrons or ions through either field electron emission or thermionic emission. Thermionic emission occurs when the thermal energy exceeds the metal's work function, while field electron emission occurs when the electric field at the surface of the metal is high enough to cause tunneling, which results in the ejection of free electrons from the metal into the vacuum. Externally heated electrodes are often used to generate an electron cloud as in the filament or indirectly heated cathode of
vacuum tube A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied. The type kn ...
s. Cold electrodes can also spontaneously produce electron clouds via thermionic emission when small incandescent regions (called ''cathode spots'' or ''anode spots'') are formed. These are incandescent regions of the electrode surface that are created by a localized high current. These regions may be initiated by field electron emission, but are then sustained by localized thermionic emission once a vacuum arc forms. These small electron-emitting regions can form quite rapidly, even explosively, on a metal surface subjected to a high electrical field.
Vacuum tube A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied. The type kn ...
s and sprytrons are some of the electronic switching and amplifying devices based on vacuum conductivity.

## Superconductivity

Superconductivity is a phenomenon of exactly zero
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its Multiplicative inverse, reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares s ...
and expulsion of
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to t ...
s occurring in certain materials when cooled below a characteristic critical temperature. It was discovered by Heike Kamerlingh Onnes on April 8, 1911 in
Leiden Leiden (; in English language, English and Archaism, archaic Dutch language, Dutch also Leyden) is a List of cities in the Netherlands by province, city and List of municipalities of the Netherlands, municipality in the Provinces of the Nethe ...
. Like ferromagnetism and atomic spectral lines, superconductivity is a quantum mechanical phenomenon. It is characterized by the Meissner effect, the complete ejection of magnetic field lines from the interior of the superconductor as it transitions into the superconducting state. The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of '' perfect conductivity'' in
classical physics Classical physics is a group of physics theories that predate modern, more complete, or more widely applicable theories. If a currently accepted theory is considered to be modern, and its introduction represented a major paradigm shift, then the ...
.

## Semiconductor

In a
semiconductor A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
it is sometimes useful to think of the current as due to the flow of positive " holes" (the mobile positive charge carriers that are places where the semiconductor crystal is missing a valence electron). This is the case in a p-type semiconductor. A semiconductor has
electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 10−2 to 104
siemens Siemens AG ( ) is a German Multinational corporation, multinational Conglomerate (company), conglomerate corporation and the largest industrial manufacturing company in Europe headquartered in Munich with branch offices abroad. The principal ...
per centimeter (S⋅cm−1). In the classic crystalline semiconductors, electrons can have energies only within certain bands (i.e. ranges of levels of energy). Energetically, these bands are located between the energy of the ground state, the state in which electrons are tightly bound to the atomic nuclei of the material, and the free electron energy, the latter describing the energy required for an electron to escape entirely from the material. The energy bands each correspond to many discrete
quantum state In quantum physics, a quantum state is a mathematical entity that provides a probability distribution for the outcomes of each possible measurement in quantum mechanics, measurement on a system. Knowledge of the quantum state together with the rul ...
s of the electrons, and most of the states with low energy (closer to the nucleus) are occupied, up to a particular band called the ''
valence band In solid-state physics, the valence band and conduction band are the electronic band structure, bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence electron, valence band is t ...
''. Semiconductors and insulators are distinguished from
metals A metal (from ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, e ...
because the valence band in any given metal is nearly filled with electrons under usual operating conditions, while very few (semiconductor) or virtually none (insulator) of them are available in the ''conduction band'', the band immediately above the valence band. The ease of exciting electrons in the semiconductor from the valence band to the conduction band depends on the band gap between the bands. The size of this energy band gap serves as an arbitrary dividing line (roughly 4 eV) between semiconductors and insulators. With covalent bonds, an electron moves by hopping to a neighboring bond. The
Pauli exclusion principle In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spin (physics), spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle ...
requires that the electron be lifted into the higher anti-bonding state of that bond. For delocalized states, for example in one dimensionthat is in a nanowire, for every energy there is a state with electrons flowing in one direction and another state with the electrons flowing in the other. For a net current to flow, more states for one direction than for the other direction must be occupied. For this to occur, energy is required, as in the semiconductor the next higher states lie above the band gap. Often this is stated as: full bands do not contribute to the
electrical conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
. However, as a semiconductor's temperature rises above absolute zero, there is more energy in the semiconductor to spend on lattice vibration and on exciting electrons into the conduction band. The current-carrying electrons in the conduction band are known as ''free electrons'', though they are often simply called ''electrons'' if that is clear in context.

# Current density and Ohm's law

Current density is the rate at which charge passes through a chosen unit area. It is defined as a vector whose magnitude is the current per unit cross-sectional area. As discussed in Reference direction, the direction is arbitrary. Conventionally, if the moving charges are positive, then the current density has the same sign as the velocity of the charges. For negative charges, the sign of the current density is opposite to the velocity of the charges. In
SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. ...
, current density (symbol: j) is expressed in the SI base units of amperes per square metre. In linear materials such as metals, and under low frequencies, the current density across the conductor surface is uniform. In such conditions,
Ohm's law Ohm's law states that the electric current, current through a Electrical conductor, conductor between two points is directly Proportionality (mathematics), proportional to the voltage across the two points. Introducing the constant of proporti ...
states that the current is directly proportional to the potential difference between two ends (across) of that metal (ideal)
resistor A resistor is a passivity (engineering), passive terminal (electronics), two-terminal electronic component, electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce c ...
(or other ohmic device): $I = \, ,$ where $I$ is the current, measured in amperes; $V$ is the potential difference, measured in
volt The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units, International System of Units (SI). It is named after the Italian physicist Alessandro ...
s; and $R$ is the resistance, measured in ohms. For
alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in which ...
s, especially at higher frequencies,
skin effect Skin effect is the tendency of an alternating current, alternating electric current (AC) to become distributed within a Conductor (material), conductor such that the current density is largest near the surface of the conductor and decreases exp ...
causes the current to spread unevenly across the conductor cross-section, with higher density near the surface, thus increasing the apparent resistance.

# Drift speed

The mobile charged particles within a conductor move constantly in random directions, like the particles of a gas. (More accurately, a
Fermi gas An ideal Fermi gas is a state of matter which is an ensemble of many non-interacting fermions. Fermions are subatomic particle, particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with ...
.) To create a net flow of charge, the particles must also move together with an average drift rate. Electrons are the charge carriers in most
metal A metal (from ancient Greek, Greek μέταλλον ''métallon'', "mine, quarry, metal") is a material that, when freshly prepared, polished, or fractured, shows a lustrous appearance, and conducts electrical resistivity and conductivity, e ...
s and they follow an erratic path, bouncing from atom to atom, but generally drifting in the opposite direction of the electric field. The speed they drift at can be calculated from the equation: $I=nAvQ \, ,$ where *$I$ is the electric current *$n$ is number of charged particles per unit volume (or charge carrier density) *$A$ is the cross-sectional area of the conductor *$v$ is the drift velocity, and *$Q$ is the charge on each particle. Typically, electric charges in solids flow slowly. For example, in a
copper Copper is a chemical element with the Symbol (chemistry), symbol Cu (from la, cuprum) and atomic number 29. It is a soft, malleable, and ductility, ductile metal with very high thermal conductivity, thermal and electrical conductivity. A fre ...
wire of cross-section 0.5 mm2, carrying a current of 5 A, the drift velocity of the electrons is on the order of a millimetre per second. To take a different example, in the near-vacuum inside a
cathode-ray tube A cathode-ray tube (CRT) is a vacuum tube containing one or more electron guns, which emit electron beams that are manipulated to display images on a Phosphorescence, phosphorescent screen. The images may represent electrical waveforms (osci ...
, the electrons travel in near-straight lines at about a tenth of the
speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special relativity, special theory of relativity, is ...
. Any accelerating electric charge, and therefore any changing electric current, gives rise to an electromagnetic wave that propagates at very high speed outside the surface of the conductor. This speed is usually a significant fraction of the speed of light, as can be deduced from
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. Th ...
, and is therefore many times faster than the drift velocity of the electrons. For example, in AC power lines, the waves of electromagnetic energy propagate through the space between the wires, moving from a source to a distant load, even though the electrons in the wires only move back and forth over a tiny distance. The ratio of the speed of the electromagnetic wave to the speed of light in free space is called the velocity factor, and depends on the electromagnetic properties of the conductor and the insulating materials surrounding it, and on their shape and size. The magnitudes (not the natures) of these three velocities can be illustrated by an analogy with the three similar velocities associated with gases. (See also hydraulic analogy.) * The low drift velocity of charge carriers is analogous to air motion; in other words, winds. * The high speed of electromagnetic waves is roughly analogous to the speed of sound in a gas (sound waves move through air much faster than large-scale motions such as
convection Convection is single or Multiphase flow, multiphase fluid flow that occurs Spontaneous process, spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoya ...
) * The random motion of charges is analogous to heatthe thermal velocity of randomly vibrating gas particles.