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Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in
electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...
between two points. In a static electric field, it corresponds to the work needed per unit of charge to move a
test charge In physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass, charge, or size) are assumed to be negligible except for the property being studied, which is considered to be in ...
between the two points. In the International System of Units, the derived unit for voltage is named '' volt''. The voltage between points can be caused by the build-up 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 electrons res ...
(e.g., a
capacitor A capacitor is a device that stores electrical energy in an electric field by virtue of accumulating electric charges on two close surfaces insulated from each other. It is a passive electronic component with two terminals. The effect of ...
), and from an electromotive force (e.g., electromagnetic induction in generator, inductors, and
transformers ''Transformers'' is a media franchise produced by American toy company Hasbro and Japanese toy company Takara Tomy. It primarily follows the Autobots and the Decepticons, two alien robot factions at war that can transform into other forms, ...
). On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-induced piezoelectric effect, and the thermoelectric effect. A
voltmeter A voltmeter is an instrument used for measuring electric potential difference between two points in an electric circuit. It is connected in parallel. It usually has a high resistance so that it takes negligible current from the circuit. ...
can be used to measure the voltage between two points in a system. Often a common reference potential such as the
ground Ground may refer to: Geology * Land, the surface of the Earth not covered by water * Soil, a mixture of clay, sand and organic matter present on the surface of the Earth Electricity * Ground (electricity), the reference point in an electrical c ...
of the system is used as one of the points. A voltage can represent either a source of energy or the loss, dissipation, or storage of energy.


Definition

In SI units, work per unit charge is expressed as
joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force appli ...
s per coulomb, where 1 volt = 1 joule (of work) per 1 coulomb (of charge). The old SI definition for ''volt'' used power and current; starting in 1990, the quantum Hall and Josephson effect were used, and recently (2019) fundamental physical constants have been introduced for the definition of all SI units and derived units. Voltage difference is denoted symbolically by \Delta V, simplified ''V'', especially in
English English usually refers to: * English language * English people English may also refer to: Peoples, culture, and language * ''English'', an adjective for something of, from, or related to England ** English national ...
-speaking countries, or by ''U'' internationally, for instance in the context of Ohm's or Kirchhoff's circuit laws. There are multiple useful ways to define voltage, including that standard definition. There are also other useful definitions of work per charge (see ). Voltage is defined so that negatively charged objects are pulled towards higher voltages, while positively charged objects are pulled towards lower voltages. Therefore, the conventional current in a wire or resistor always flows from higher voltage to lower voltage. Historically, voltage has been referred to using terms like "tension" and "pressure". Even today, the term "tension" is still used, for example within the phrase " high tension" (HT) which is commonly used in thermionic valve (
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 potential difference has been applied. The type known as ...
) based electronics.


Definition in electrostatics

In electrostatics, the voltage increase from point \mathbf_A to some point \mathbf_B is given by the change in
electrostatic potential Electrostatics is a branch of physics that studies electric charges at rest ( static electricity). Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for a ...
V from \mathbf_A to \mathbf_B. By definition, this is: :\begin \Delta V_ &= V(\mathbf_B) - V(\mathbf_A) \\ &= -\int_^ \mathbf \cdot \mathrm\boldsymbol - \left(-\int_^ \mathbf \cdot \mathrm\boldsymbol \right)\\ &= -\int_^ \mathbf \cdot \mathrm\boldsymbol \end In this case, the voltage increase from point A to point B is equal to the work done per unit charge, against the electric field, to move the charge from A to B without causing any acceleration. Mathematically, this is expressed as the
line integral In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms ''path integral'', ''curve integral'', and ''curvilinear integral'' are also used; '' contour integral'' is used as well, ...
of the electric field along that path. In electrostatics, this line integral is independent of the path taken. Under this definition, any circuit where there are time-varying magnetic fields, such as AC circuits, will not have a well-defined voltage between nodes in the circuit, since the electric force is not a conservative force in those cases.This follows from the
Maxwell-Faraday equation Faraday's law of induction (briefly, Faraday's law) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf)—a phenomenon known as electromagnetic inducti ...
: \nabla\times\mathbf=-\frac If there are changing magnetic fields in some simply connected region, then the curl of the electric field in that region is non-zero, and as a result the electric field is not conservative. For more, see .
However, at lower frequencies when the electric and magnetic fields are not rapidly changing, then this can be neglected (see electrostatic approximation).


Generalization to electrodynamics

The electric potential can be generalized to electrodynamics, so that differences in electric potential between points are well-defined even in the presence of time-varying fields. However, unlike in electrostatics, the electric field can no longer be expressed only in terms of the electric potential. Furthermore, the potential is no longer uniquely determined up to a constant, and can take significantly different forms depending on the choice of
gauge Gauge ( or ) may refer to: Measurement * Gauge (instrument), any of a variety of measuring instruments * Gauge (firearms) * Wire gauge, a measure of the size of a wire ** American wire gauge, a common measure of nonferrous wire diameter, es ...
.For example, in the
Lorenz gauge In electromagnetism, the Lorenz gauge condition or Lorenz gauge, for Ludvig Lorenz, is a partial gauge fixing of the electromagnetic vector potential by requiring \partial_\mu A^\mu = 0. The name is frequently confused with Hendrik Lorentz, who ha ...
, the electric potential is a retarded potential, which propagates 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 theory of relativity, is the upper limit fo ...
; whereas in the Coulomb gauge, the potential changes instantaneously when the source charge distribution changes.
In this general case, some authors use the word "voltage" to refer to the line integral of the electric field, rather than to differences in electric potential. In this case, the voltage rise along some path \mathcal from \mathbf_A to \mathbf_B is given by: :\Delta V_ = -\int_\mathcal \mathbf \cdot \mathrm\boldsymbol However, in this case the "voltage" between two points depends on the path taken.


Treatment in circuit theory

In
circuit analysis A network, in the context of electrical engineering and electronics, is a collection of interconnected components. Network analysis is the process of finding the voltages across, and the currents through, all network components. There are many ...
and
electrical engineering Electrical engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an identifiable occupation in the l ...
, lumped element models are used to represent and analyze circuits. These elements are idealized and self-contained circuit elements used to model physical components. When using a lumped element model, it is assumed that the effects of changing magnetic fields produced by the circuit are suitably contained to each element. Under these assumptions, the electric field in the region exterior to each component is conservative, and voltages between nodes in the circuit are well-defined, where :\Delta V_ = -\int_^ \mathbf \cdot \mathrm\boldsymbol as long as the path of integration does not pass through the inside of any component. The above is the same formula used in electrostatics. This integral, with the path of integration being along the test leads, is what a voltmeter will actually measure.This statement makes a few assumptions about the nature of the voltmeter (these are discussed in the cited paper). One of these assumptions is that the current drawn by the voltmeter is negligible. If uncontained magnetic fields throughout the circuit are not negligible, then their effects can be modelled by adding mutual inductance elements. In the case of a physical inductor though, the ideal lumped representation is often accurate. This is because the external fields of inductors are generally negligible, especially if the inductor has a closed magnetic path. If external fields are negligible, we find that :\Delta V_ = -\int_\mathrm\mathbf\cdot \mathrm\boldsymbol=L\frac is path-independent, and there is a well-defined voltage across the inductor's terminals. This is the reason that measurements with a voltmeter across an inductor are often reasonably independent of the placement of the test leads.


Volt

The volt (symbol: ) is the derived unit for
electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...
, voltage, and electromotive force. The volt is named in honour of the Italian physicist
Alessandro Volta Alessandro Giuseppe Antonio Anastasio Volta (, ; 18 February 1745 – 5 March 1827) was an Italian physicist, chemist and lay Catholic who was a pioneer of electricity and power who is credited as the inventor of the electric battery and th ...
(1745–1827), who invented the voltaic pile, possibly the first chemical
battery Battery most often refers to: * Electric battery, a device that provides electrical power * Battery (crime), a crime involving unlawful physical contact Battery may also refer to: Energy source *Automotive battery, a device to provide power t ...
.


Hydraulic analogy

A simple analogy for an electric circuit is water flowing in a closed circuit of pipework, driven by a mechanical
pump A pump is a device that moves fluids (liquids or gases), or sometimes slurries, by mechanical action, typically converted from electrical energy into hydraulic energy. Pumps can be classified into three major groups according to the method they ...
. This can be called a "water circuit". The potential difference between two points corresponds to the pressure difference between two points. If the pump creates a pressure difference between two points, then water flowing from one point to the other will be able to do work, such as driving a
turbine A turbine ( or ) (from the Greek , ''tyrbē'', or Latin ''turbo'', meaning vortex) is a rotary mechanical device that extracts energy from a fluid flow and converts it into useful work. The work produced by a turbine can be used for generating ...
. Similarly, work can be done by an
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The movi ...
driven by the potential difference provided by a
battery Battery most often refers to: * Electric battery, a device that provides electrical power * Battery (crime), a crime involving unlawful physical contact Battery may also refer to: Energy source *Automotive battery, a device to provide power t ...
. For example, the voltage provided by a sufficiently-charged automobile battery can "push" a large current through the windings of an automobile's starter motor. If the pump isn't working, it produces no pressure difference, and the turbine will not rotate. Likewise, if the automobile's battery is very weak or "dead" (or "flat"), then it will not turn the starter motor. The hydraulic analogy is a useful way of understanding many electrical concepts. In such a system, the work done to move water is equal to the "
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...
drop" (compare p.d.) multiplied by the
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). ...
of water moved. Similarly, in an electrical circuit, the work done to move electrons or other charge-carriers is equal to "electrical pressure difference" multiplied by the quantity of electrical charges moved. In relation to "flow", the larger the "pressure difference" between two points (potential difference or water pressure difference), the greater the flow between them (electric current or water flow). (See "
electric power Electric power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions and billions ...
".)


Applications

Specifying a voltage measurement requires explicit or implicit specification of the points across which the voltage is measured. When using a voltmeter to measure voltage, one electrical lead of the voltmeter must be connected to the first point, one to the second point. A common use of the term "voltage" is in describing the voltage dropped across an electrical device (such as a resistor). The voltage drop across the device can be understood as the difference between measurements at each terminal of the device with respect to a common reference point (or
ground Ground may refer to: Geology * Land, the surface of the Earth not covered by water * Soil, a mixture of clay, sand and organic matter present on the surface of the Earth Electricity * Ground (electricity), the reference point in an electrical c ...
). The voltage drop is the difference between the two readings. Two points in an electric circuit that are connected by an ideal conductor without resistance and not within a changing
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 ...
have a voltage of zero. Any two points with the same potential may be connected by a conductor and no current will flow between them.


Addition of voltages

The voltage between ''A'' and ''C'' is the sum of the voltage between ''A'' and ''B'' and the voltage between ''B'' and ''C''. The various voltages in a circuit can be computed using Kirchhoff's circuit laws. When talking about
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 whic ...
(AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added for
direct current Direct current (DC) is one-directional flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or ev ...
(DC) and AC, but average voltages can be meaningfully added only when they apply to signals that all have the same frequency and phase.


Measuring instruments

Instruments for measuring voltages include the
voltmeter A voltmeter is an instrument used for measuring electric potential difference between two points in an electric circuit. It is connected in parallel. It usually has a high resistance so that it takes negligible current from the circuit. ...
, the potentiometer, and the oscilloscope. Analog voltmeters, such as moving-coil instruments, work by measuring the current through a fixed resistor, which, according to
Ohm's Law Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equa ...
, is proportional to the voltage across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in a
bridge circuit A bridge circuit is a topology of electrical circuitry in which two circuit branches (usually in parallel with each other) are "bridged" by a third branch connected between the first two branches at some intermediate point along them. The bridge ...
. The cathode-ray oscilloscope works by amplifying the voltage and using it to deflect an
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...
beam from a straight path, so that the deflection of the beam is proportional to the voltage.


Typical voltages

A common voltage for flashlight batteries is 1.5 volts (DC). A common voltage for automobile batteries is 12 volts (DC). Common voltages supplied by power companies to consumers are 110 to 120 volts (AC) and 220 to 240 volts (AC). The voltage in
electric power transmission Electric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant, to an electrical substation. The interconnected lines that facilitate this movement form a ''transmission network''. This is d ...
lines used to distribute electricity from power stations can be several hundred times greater than consumer voltages, typically 110 to 1200 kV (AC). The voltage used in
overhead line An overhead line or overhead wire is an electrical cable that is used to transmit electrical energy to electric locomotives, trolleybuses or trams. It is known variously as: * Overhead catenary * Overhead contact system (OCS) * Overhead equipm ...
s to power railway locomotives is between 12 kV and 50 kV (AC) or between 0.75 kV and 3 kV (DC).


Galvani potential vs. electrochemical potential

Inside a conductive material, the energy of an electron is affected not only by the average electric potential but also by the specific thermal and atomic environment that it is in. When a
voltmeter A voltmeter is an instrument used for measuring electric potential difference between two points in an electric circuit. It is connected in parallel. It usually has a high resistance so that it takes negligible current from the circuit. ...
is connected between two different types of metal, it measures not the electrostatic potential difference, but instead something else that is affected by thermodynamics. The quantity measured by a voltmeter is the negative of the difference of the electrochemical potential of electrons (
Fermi level The Fermi level of a solid-state body is the thermodynamic work required to add one electron to the body. It is a thermodynamic quantity usually denoted by ''µ'' or ''E''F for brevity. The Fermi level does not include the work required to remove ...
) divided by the electron charge and commonly referred to as the voltage difference, while the pure unadjusted
electrostatic potential Electrostatics is a branch of physics that studies electric charges at rest ( static electricity). Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for a ...
(not measurable with a voltmeter) is sometimes called Galvani potential. The terms "voltage" and "electric potential" are ambiguous in that, in practice, they can refer to ''either'' of these in different contexts.


History

The term ''electromotive force'' was first used by Volta in a letter to Giovanni Aldini in 1798, and first appeared in a published paper in 1801 in ''
Annales de chimie et de physique __NOTOC__ ''Annales de chimie et de physique'' ( French for ''Annals of Chemistry and Physics'') is a scientific journal founded in Paris, France, in 1789 under the title ''Annales de chimie''. One of the early editors was the French chemist Ant ...
''. Volta meant by this a force that was not an
electrostatic Electrostatics is a branch of physics that studies electric charges at rest ( static electricity). Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for ...
force, specifically, an electrochemical force.Robert N. Varney, Leon H. Fisher
"Electromotive force: Volta's forgotten concept"
''American Journal of Physics'', vol. 48, iss. 5, pp. 405–408, May 1980.
The term was taken up by
Michael Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic inducti ...
in connection with electromagnetic induction in the 1820s. However, a clear definition of voltage and method of measuring it had not been developed at this time.C. J. Brockman
"The origin of voltaic electricity: The contact vs. chemical theory before the concept of E. M. F. was developed"
''Journal of Chemical Education'', vol. 5, no. 5, pp. 549–555, May 1928
Volta distinguished electromotive force (emf) from ''tension'' (potential difference): the observed potential difference at the terminals of an electrochemical cell when it was open circuit must exactly balance the emf of the cell so that no current flowed.


See also

*
Electric shock Electrical injury is a physiological reaction caused by electric current passing through the body. The injury depends on the density of the current, tissue resistance and duration of contact. Very small currents may be imperceptible or produce a ...
* Mains electricity by country (list of countries with mains voltage and frequency) * Open-circuit voltage * Phantom voltage


References


Footnotes


External links


Electrical voltage ''V'', current ''I'', resistivity ''R'', impedance ''Z'', wattage ''P''
{{Authority control Electromagnetism Electrical systems Physical quantities