voltage

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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 (physics), work energy needed to move a unit of electric charge from a reference point to the sp ...
between two points. In a static
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 ...
, it corresponds to the work needed per unit of charge to move a test charge between the two points. In the
International System of Units The International System of Units, known by the international abbreviation SI in all languages and sometimes Pleonasm#Acronyms and initialisms, pleonastically as the SI system, is the modern form of the metric system and the world's most wid ...
, the derived unit for voltage is named ''
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 ...
''. 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 electron ...
(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 passivity (engineering), passive electronic component with two termi ...
), and from 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 ...
(e.g.,
electromagnetic induction Electromagnetic or magnetic induction is the production of an electromotive force, electromotive force (emf) across an electrical conductor in a changing magnetic field. Michael Faraday is generally credited with the discovery of induction in 1 ...
in generator, inductors, and
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 ...
). On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-induced
piezoelectric effect Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied Stress (mechanics), mechanical s ...
, and the
thermoelectric effect The thermoelectric effect is the direct conversion of temperature differences to electric voltage and vice versa via a thermocouple. A thermoelectric device creates a voltage when there is a different temperature on each side. Conversely, when ...
. A voltmeter can be used to measure the voltage between two points in a system. Often a common reference potential such as the ground 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, 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 ...
s per
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 ...
, 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-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 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 moving par ...
in a wire or
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 ...
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 voltage, potential difference has been applied. The type kn ...
) based electronics.

## Definition in electrostatics

In
electrostatics Electrostatics is a branch of physics that studies electric charges at Rest (physics), rest (static electricity). Since classical antiquity, classical times, it has been known that some materials, such as amber, attract lightweight particles af ...
, the voltage increase from point $\mathbf_A$ to some point $\mathbf_B$ is given by the change in electrostatic potential $V$ from $\mathbf_A$ to $\mathbf_B$. By definition, this is: :$\begin \Delta V_ &= V\left(\mathbf_B\right) - V\left(\mathbf_A\right) \\ &= -\int_^ \mathbf \cdot \mathrm\boldsymbol - \left\left(-\int_^ \mathbf \cdot \mathrm\boldsymbol \right\right)\\ &= -\int_^ \mathbf \cdot \mathrm\boldsymbol \end$ 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 (mathematics), function to be integrated is evaluated along a curve. The terms ''path integral'', ''curve integral'', and ''curvilinear integral'' are also used; ''contour integra ...
of the
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 ...
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 physics, a conservative force is a force with the property that the total Work (physics), work done in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the total work ...
in those cases.This follows from the Maxwell-Faraday equation: $\nabla\times\mathbf=-\frac$ 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.For example, in the Lorenz gauge, 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 relativity, special theory of relativity, is ...
; 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 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 (physics), work energy needed to move a unit of electric charge from a reference point to the sp ...
, voltage, and
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 ...
. 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 List of lay Catholic scientists, Catholic who was a pioneer of electricity and Power (physics), power who is credite ...
(1745–1827), who invented the
voltaic pile file:Voltaic pile.svg, upright=1.2, Schematic diagram of a copper–zinc voltaic pile. The copper and zinc discs were separated by cardboard or felt spacers soaked in salt water (the electrolyte). Volta's original piles contained an additional zin ...
, possibly the first chemical battery.

# Hydraulic analogy

A simple analogy for an
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 ...
is water flowing in a closed circuit of
pipework Within industry, piping is a system of Pipe (fluid conveyance), pipes used to convey fluids (liquids and gases) from one location to another. The engineering discipline of piping design studies the efficient transport of fluid. Industrial pro ...
, driven by a mechanical
pump A pump is a device that moves fluids (liquids or gases), or sometimes Slurry, slurries, by mechanical action, typically converted from electrical energy into hydraulic energy. Pumps can be classified into three major groups according to the metho ...
. 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 Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area ...
. 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 moving par ...
driven by the potential difference provided by a battery. 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 A starter (also self-starter, cranking motor, or starter motor) is a device used to rotate (crank) an internal-combustion engine so as to initiate the engine's operation under its own power. Starters can be electric motor, electric, pneumatic ...
. 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 and e ...
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 (physics), power is the watt, one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions ...
".)

# 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). 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 t ...
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.

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 which ...
(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 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) 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, the
potentiometer A potentiometer is a three-terminal (electronics), terminal resistor with a sliding or rotating contact that forms an adjustable voltage divider. If only two terminals are used, one end and the wiper, it acts as a variable resistor or rheostat. ...
, and the
oscilloscope An oscilloscope (informally a scope) is a type of electronic test instrument that graphically displays varying electrical voltages as a two-dimensional plot of one or more signals as a function of time. The main purposes are to display repetitiv ...
. 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 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 ...
, 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 (electrical circuits), topology of electrical network, 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 ...
. 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 charge, elementary electric charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are generally thought t ...
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 power generation, generating site, such as a power plant, to an electrical substation. The interconnected lines that facilitate this movement form a ''transmission net ...
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 equipment ...
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 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 In electrochemistry, the electrochemical potential (ECP), ', is a thermodynamic measure of chemical potential that does not omit the energy contribution of electrostatics. Electrochemical potential is expressed in the unit of Joule, J/Mole (unit), ...
of electrons ( Fermi level) divided by the electron charge and commonly referred to as the voltage difference, while the pure unadjusted electrostatic potential (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 Giovanni Aldini (10 April 1762 – 17 January 1834) was an Italian physician A physician (American English), medical practitioner (English in the Commonwealth of Nations, Commonwealth English), medical doctor, or simply doctor, is a he ...
in 1798, and first appeared in a published paper in 1801 in '' Annales de chimie et de physique''. 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 f ...
force, specifically, an
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 ...
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 induction, ...
in connection with
electromagnetic induction Electromagnetic or magnetic induction is the production of an electromotive force, electromotive force (emf) across an electrical conductor in a changing magnetic field. Michael Faraday is generally credited with the discovery of induction in 1 ...
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.