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{{Redirect|Potential difference|other uses|Potential|other uses of Voltage|Voltage (disambiguation)}}
{{Infobox physical quantity
|bgcolour = {default}
|name = Voltage
|image = [[File:AA AAA AAAA A23 battery comparison-1.jpg|frameless]]
|caption = [[Battery (electricity)|Batteries]] are sources of voltage in many [[Electrical network|electric circuits]]
|unit = [[volt]]
|symbols = {{math|''V''}} , {{math|∆''V''}} , {{math|''E''}}
}}

{{Electromagnetism}}
'''Voltage''', '''electrical potential difference''', '''electric tension''' or '''electric pressure''' (denoted {{math|∆''V''}}) and measured in units of [[electric potential]]: [[volt]]s, or [[joule]]s per [[Coulomb|coulomb]] is the electric potential difference between two points, or the difference in [[electric potential energy]] of a unit [[electric charge|charge]] transported between two points.<ref>[http://electrochem.cwru.edu/ed/dict.htm#v08 "Voltage"], ''Electrochemistry Encyclopedia''</ref> Voltage is equal to the [[work (physics)|work]] done per [[Test charge|unit charge]] against a static [[electric field]] to move the charge between two points. A voltage may represent either a source of energy ([[electromotive force]]), or lost, used, or stored energy ([[voltage drop|potential drop]]). A [[voltmeter]] can be used to measure the voltage (or potential difference) between two points in a system; usually a common reference potential such as the [[ground (electricity)|ground]] of the system is used as one of the points.  Voltage can be caused by static electric fields, by [[electric current]] through a [[magnetic field]], by time-varying magnetic fields, or some combination of these three.<ref>Demetrius T. Paris and F. Kenneth Hurd, ''Basic Electromagnetic Theory'', McGraw-Hill, New York 1969, ISBN 0-07-048470-8, pp. 512, 546</ref><ref>P. Hammond, ''Electromagnetism for Engineers'', p. 135, Pergamon Press 1969 {{OCLC|854336}}.</ref>

[[File:Opfindelsernes bog3 fig282.png|thumb|right|The electric field around the rod exerts a force on the charged pith ball, in an [[electroscope]]]]
[[File:Electrostatic definition of voltage.svg|thumb|right|In a static field, the work is independent of the path]]

==Definition==
Given two points in the space, called A and B, voltage is the difference of electric potentials between those two points. From the definition of electric potential it follows that:

:<math>\Delta V_{BA} = V_B - V_A = - \int_{r_0}^{B} \vec{E} \cdot d\vec{l} - \left( - \int_{r_0}^{A} \vec{E} \cdot d\vec{l} \right) </math>
::::<math> = \int_{B}^{r_0} \vec{E} \cdot d\vec{l} + \int_{r_0}^{A} \vec{E} \cdot d\vec{l} = \int_{B}^{A} \vec{E} \cdot d\vec{l}</math>

Voltage is electric potential energy per unit charge, measured in joules per coulomb ( = volts). It is often referred to as "electric potential", which then must be distinguished from electric potential energy by noting that the "potential" is a "per-unit-charge" quantity. Like mechanical potential energy, the zero of potential can be chosen at any point, so the difference in voltage is the quantity which is physically meaningful. The difference in voltage measured when moving from point A to point B is equal to the work which would have to be done, per unit charge, against the electric field to move the charge from A to B. The voltage between the two ends of a path is the total energy required to move a small electric charge along that path, divided by the magnitude of the charge.  Mathematically this is expressed as the [[line integral]] of the  [[electric field]] and the time rate of change of magnetic field along that path. In the general case, both a static (unchanging) electric field and a dynamic (time-varying) electromagnetic field must be included in determining the voltage between two points.

Historically this quantity has also been called "tension"<ref>{{Cite encyclopedia | title = Tension | url = http://www.collinslanguage.com/results.aspx?context=3&reversed=False&action=define&homonym=0&text=tension | encyclopedia = CollinsLanguage}}</ref> and "pressure". Pressure is now obsolete but tension is still used, for example within the phrase "[[High voltage|high tension]]" (HT) which is commonly used in thermionic valve ([[vacuum tube]]) based electronics.

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. Current can flow from lower voltage to higher voltage, but only when a [[electromotive force|source of energy]] is present to "push" it against the opposing electric field. For example, inside a [[Battery_(electricity)|battery]], chemical reactions provide the energy needed for current to flow from the negative to the positive terminal.

Technically, in a material the electric field is not the only factor determining charge flow, and different materials naturally develop electric potential differences at equilibrium ([[Galvani potential]]s). The electric potential of a material is not even a well defined quantity, since it varies on the subatomic scale. A more convenient definition of 'voltage' can be found instead in the concept of [[Fermi level]]. In this case the voltage between two bodies is the [[thermodynamic work]] required to move a unit of charge between them. This definition is practical since a real voltmeter actually measures this work, not differences in electric potential.

==Hydraulic analogy==
{{Main|Hydraulic analogy}}

A simple analogy for an [[electric circuit]] is water flowing in a closed circuit of [[pipework]], driven by a mechanical [[pump]].  This can be called a "water circuit".  Potential difference between two points corresponds to the [[fluid pressure|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]]. Similarly, work can be done by an [[electric current]] driven by the potential difference provided by a [[electric battery|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]]. 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]] multiplied by the [[volume]] of water moved. Similarly, in an electrical circuit, the work done to move electrons or other charge-carriers is equal to "electrical pressure" 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#Definition|Electric power]]".)

== Applications==
[[File:US Navy 110315-N-0278E-002 High-voltage electricians from Naval Facilities Engineering Command (NAVFAC) Hawaii reconfigure electrical circuitry and.jpg|thumb|upright|left|Working on [[high voltage]] power lines]]
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]] 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 (electricity)|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]] 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]] (AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added  for [[direct current]] (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==

[[File:9VBatteryWithMeter.jpg|thumb|[[Multimeter]] set to measure voltage]]
Instruments for measuring voltages include the [[voltmeter]], the [[Potentiometer (measuring instrument)|potentiometer]], and the [[oscilloscope]]. The voltmeter works by measuring the current through a fixed resistor, which, according to [[Ohm's Law]], is proportional to the voltage across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in a [[bridge circuit]]. The cathode-ray oscilloscope works by amplifying the voltage and using it to deflect an [[electron]] beam from a straight path, so that the deflection of the beam is proportional to the voltage.

==Typical voltages==
A common voltage for [[Battery (electricity)|flashlight batteries]] is 1.5&nbsp;volts (DC). 
A common voltage for [[Automotive battery|automobile batteries]] is 12&nbsp;volts (DC).

Common voltages supplied by power companies to consumers are 110 to 120 volts (AC) and 220 to 240&nbsp;volts (AC). The voltage in [[electric power transmission]] lines used to distribute electricity from power stations can be several hundred times greater than consumer voltages, typically 110 to 1200&nbsp;kV (AC).

The voltage used in [[overhead line]]s to power railway locomotives is between 12&nbsp;kV and 50&nbsp;kV (AC).

==Galvani potential versus electrochemical potential==
{{main|Galvani potential|Electrochemical potential|Fermi level}}
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 the different atomic environments.<ref>{{cite book|url=http://books.google.com/books?id=09QI-assq1cC&pg=PA22 |title=Fundamentals of electrochemistry|first= Vladimir Sergeevich|last= Bagotskii|page=22|isbn=978-0-471-70058-6|year=2006}}</ref>
The quantity measured by a voltmeter is called [[electrochemical potential]] or [[Fermi level]] divided by electron charge, while the pure unadjusted [[electrostatic potential]] is sometimes called [[Galvani potential]].
The terms "voltage" and "electric potential" are a bit ambiguous in that, in practice, they can refer to ''either'' of these in different contexts.

==See also==
{{Portal|Electronics}}
*[[Alternating current]] (AC)
*[[Direct current]] (DC)
*[[Electric potential]]
*[[Electric shock]]
*[[Electrical measurements]]
*[[Electrochemical potential]]
*[[Fermi level]]
*[[High voltage]]
*[[Mains electricity]] (an article about domestic power supply voltages)
*[[Mains electricity by country]] (list of countries with mains voltage and frequency)
*[[Ohm's law]]
*[[Open-circuit voltage]]
*[[Phantom voltage]]

==References==
<references/>

==External links==
{{Wiktionary}}
*[http://www.sengpielaudio.com/calculator-ohm.htm Electrical voltage ''V'', amperage ''I'', resistivity ''R'', impedance ''Z'', wattage ''P'']
*[http://www.ndt-ed.org/EducationResources/HighSchool/Electricity/voltage.htm Elementary explanation of voltage at NDT Resource Center]

[[Category:Electromagnetism]]
[[Category:Electrical systems]]
[[Category:Physical quantities]]