TheInfoList

Voltage, electric potential difference, electric pressure or electric tension 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 spe ...

between two points, which (in a static
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically-charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' ' ...

) is defined as the
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking * Work (physics), the product of ...
needed per unit of charge to move a
test chargeIn physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass Mass is the physical quantity, quantity of ''matter'' in a physical body. It is also a measure (mathematics), mea ...
between the two points. In the
International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael album), ''International'' (Kevin Michael album), 2011 * International (New Order album), '' ...
, the derived unit for voltage (potential difference) is named ''
volt The volt is the derived unit for electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is the amount of work energy needed to move a unit of electric charge ...

''. In SI units, work per unit charge is expressed as
joule The joule ( ; symbol: J) is a SI derived unit, derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work (physics), work done on) an object when a force of one Newton (unit), newton acts on th ...

s per
coulomb The coulomb (symbol: C) is the International System of Units International is an adjective (also used as a noun) meaning "between nations". International may also refer to: Music Albums * International (Kevin Michael album), ''International'' ( ...

, where 1 volt = 1 joule (of work) per 1 coulomb (of charge). The old SI definition for ''volt'' used
power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In the International System of Units, the unit of power is the watt, equal to one joule per second. In older works, p ...
and
current Currents or The Current may refer to: Science and technology * Current (fluid) A current in a fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an applied shear stress, or external force. ...
; starting in 1990, the and
Josephson effect The Josephson effect is the phenomenon of supercurrent, a current that flows continuously without any voltage applied, across a device known as a Josephson junction (JJ), which consists of two or more superconductors coupled by a weak link. The ...
were used, and recently (2019) fundamental physical constants have been introduced for the definition of all SI units and derived units. Voltage or electric potential difference is denoted symbolically by $\Delta V$, simplified ''V'', or ''U'', for instance in the context of or
Kirchhoff's circuit laws Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuit An electrical network is an interconnection of electronic compon ...
. Electric potential differences between points can be caused by the build up of
electric charge Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respectively). Like c ...
(e.g., a
capacitor A capacitor is a device that stores electric charge in an electric field. It is a passivity (engineering), passive electronic component with two terminal (electronics), terminals. The effect of a capacitor is known as capacitance. While som ...

), and from an
electromotive force In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is c ...
(e.g.,
electromagnetic induction Electromagnetic or magnetic induction is the production of an electromotive force In electromagnetism and electronics, electromotive force (emf, denoted \mathcal and measured in volts) is the electrical action produced by a non-electrical sour ...

in generator,
inductors An inductor, also called a coil, choke, or reactor, is a incremental passivity, passive two-terminal electronic component, electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically c ...

, and
transformers ''Transformers'' is a produced by American toy company and Japanese toy company . It follows the battles of sentient, living autonomous robots, often the s and the s, who can transform into other forms, such as vehicles and animals. The franc ...

). 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 that accumulates in certain solid materials—such as s, certain s, and biological matter such as bone, , and various s—in response to applied . The word ''piezoelectricity'' means electricity resulting from pressu ...

, and heat-induced electromotive force across metal-metal junctions. These latter processes at microscopic level have the physical origins previously mentioned. A
voltmeter A voltmeter is an instrument used for measuring 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 ne ...

can be used to measure the voltage (or potential difference) between two points in a system. Often a common reference potential such as the
ground Ground may refer to: * Soil File:Stagnogley.JPG, Surface-water-Gley soil, gley developed in glacial till, Northern Ireland. Soil is a mixture of organic matter, minerals, gases, liquids, and organisms that together support life. Earth's body ...
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

There are multiple useful ways to define voltage, including the standard definition mentioned earlier. 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 Electric charge is the physical property of matter t ...
in a wire or
resistor A resistor is a that implements as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to , active elements, and terminate s, among other uses. High-power resistors that can dissipat ...

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 ''High Tension'' (French: ''Haute Tension'', ; released in the United Kingdom as ''Switchblade Romance'') is a 2003 French slasher film directed by Alexandre Aja, co-written with Grégory Levasseur, and starring Cécile de France, Maïwenn, and ...

" (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 An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστή ...
) based electronics.

## Definition in electrostatics

In
electrostatics Electrostatics is a branch of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related enti ...
, the voltage increase from point $\mathbf_A$ to some point $\mathbf_B$ is given by the change in
electrostatic 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 ...
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 Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
of the
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically-charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' ' ...

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 A conservative force is a force In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (phy ...
in those cases.This follows from the Maxwell-Faraday equation: $\nabla\times\mathbf=-\frac$ If there are changing magnetic fields in some
simply connected In topology s, which have only one surface and one edge, are a kind of object studied in topology. In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric objec ...
region, then the
curl Curl or CURL may refer to: Science and technology * Curl (mathematics) In vector calculus Vector calculus, or vector analysis, is concerned with derivative, differentiation and integral, integration of vector fields, primarily in 3-dimension ...
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 meaning and value of potential differences will depend on the choice of
gauge Gauge (US: , UK: or ) may refer to: Measurement * Gauge (instrument) A gauge, in science Science (from the Latin word ''scientia'', meaning "knowledge") is a systematic enterprise that Scientific method, builds and Taxonomy (general), o ...
. 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 te ...
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 The field of electronics is a branch of physics and electrical enginee ...

,
lumped element model The lumped-element model (also called lumped-parameter model, or lumped-component model) simplifies the description of the behaviour of spatially distributed physical systems into a topology s, which have only one surface and one edge, are a k ...
s 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 In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is ca ...
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 spe ...

, electric potential difference, and
electromotive force In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is c ...
. 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 A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in ...

(1745–1827), who invented the
voltaic pile –zinc Zinc is a chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all have the sa ...

, possibly the first chemical
battery Battery may refer to: Energy source * Electric battery, an electrochemical device to provide electrical power ** Automotive battery, a device to provide power to certain functions of an automobile ** List of battery types * Energy storage, inclu ...
.

# Hydraulic analogy

A simple analogy for an
electric circuit An electrical network is an interconnection of electrical component An electronic component is any basic discrete device or physical entity in an electronic system used to affect electrons or their associated fields. Electronic componen ...

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 proces ...

, driven by a mechanical
pump A pump is a device that moves fluids (s or es), or sometimes , by mechanical action, typically converted from electrical energy into hydraulic energy. Pumps can be classified into three major groups according to the method they use to move the fl ...

. This can be called a "water circuit". The potential difference between two points corresponds to the 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 A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', ...

. Similarly, work can be done by an
electric current An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, ...
driven by the potential difference provided by a
battery Battery may refer to: Energy source * Electric battery, an electrochemical device to provide electrical power ** Automotive battery, a device to provide power to certain functions of an automobile ** List of battery types * Energy storage, inclu ...
. 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 An internal combustion engine (ICE or IC engine) is a heat engine In thermodynamics Thermodynamics ...
. 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 In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space ...

drop" (compare p.d.) multiplied by the
volume Volume is a scalar quantity expressing the amount Quantity or amount is a property that can exist as a multitude Multitude is a term for a group of people who cannot be classed under any other distinct category, except for their shared fact ...

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, per unit time, at which electrical energy Electrical energy is energy derived as a result of movement of electrically charged particles. When used loosely, ''electrical energy'' refers to energy that has been conve ...

".)

# 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 potential difference, 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 Voltage drop is the decrease of electrical potential along the path of a current flowing in an electrical circuitCircuit may refer to: Science and technology Electrical engineering * Electrical circuit, a complete electrical network with a ...

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: * Soil File:Stagnogley.JPG, Surface-water-Gley soil, gley developed in glacial till, Northern Ireland. Soil is a mixture of organic matter, minerals, gases, liquids, and organisms that together support life. Earth's body ...
). 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 In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For instance, a vector field in the plane can be visualised as a collection of arrows with ...

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 Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuit An electrical network is an interconnection of electronic compon ...
alternating current Alternating current (AC) is 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 ...
(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 Flow may refer to: Science and technology * Flow (fluid) or fluid dynamics, the motion of a gas or liquid * Flow (geomorphology), a type of mass wasting or slope movement in geomorphology * Flow (math ...
(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 The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work (physics), work energy ne ...

, the
potentiometer A potentiometer is a three- terminal resistor A resistor is a passive two-terminal electrical component that implements electrical resistance In electronics and electromagnetism, the electrical resistance of an object is a measure of ...
, and the
oscilloscope model 475A portable analog oscilloscope, a typical instrument of the late 1970s An oscilloscope, previously called an oscillograph, and informally known as a scope or o-scope, CRO (for cathode-ray oscilloscope), or DSO (for the more modern digit ...

. s, 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 In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contai ...

. The cathode-ray oscilloscope works by amplifying the voltage and using it to deflect an
electron The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family, and are general ...

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 Electrical energy is energy derived as a result of movement of electrically charged particles. When used loosely, ''electrical energy'' refers to energy that has been convert ...

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 A voltmeter is an instrument used for measuring 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 ne ...

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 Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential, as a measurable and quantitative phenomenon, and identifiable chemical change, with either electrical potentia ...
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 Thermodynamics is a branch of physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (e ...
) divided by the electron charge and commonly referred to as the voltage difference, while the pure unadjusted
electrostatic 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 ...
(not measurable with a voltmeter) is sometimes called
Galvani potential In electrochemistry Electrochemistry is the branch of physical chemistry concerned with the relationship between electrical potential, as a measurable and quantitative phenomenon, and identifiable chemical change, with either electrical 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 profess ...

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 of Physics'') is a scientific journal In academic publishing Academic publishing is the subfield of publishing Publishing is the activity of making ...
''. Volta meant by this a force that was not an
electrostatic Electrostatics is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in oth ...
force, specifically, an
electrochemical Electrochemistry is the branch of physical chemistry Physical chemistry is the study of macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying ...
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 A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical method of acquiring knowledge ...

in connection with
electromagnetic induction Electromagnetic or magnetic induction is the production of an electromotive force In electromagnetism and electronics, electromotive force (emf, denoted \mathcal and measured in volts) is the electrical action produced by a non-electrical sour ...

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.

*
Electric shock Electrical injury is a physiological reaction caused by 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 ...
*
Mains electricity by country Mains electricity by country includes a list of countries and territories, with the plugs, voltage Voltage, electric potential difference, electromotive force emf, electric pressure or electric tension is the difference in electric pote ...
(list of countries with mains voltage and frequency) *
Open-circuit voltage Black curve: The highest possible open-circuit voltage of a Shockley-Queisser model under unconcentrated sunlight, as a function of the semiconductor bandgap">Shockley-Queisser limit">Shockley-Queisser model under unconcentrated sunlight, as a f ...
* Phantom voltage