# Voltage

Voltage
Batteries are sources of voltage in many electric circuits.
Common symbols
V , V
U , U
SI unitvolt
Derivations from
other quantities
Voltage = Energy / charge
DimensionM L2 T−3 I−1

Voltage, electric potential difference, electric pressure or electric tension (formally denoted V or U, but more often simply as V or U, for instance in the context of Ohm's or Kirchhoff's circuit laws) is the difference in electric potential between two points. The voltage between two points is equal to the work done per unit of charge against a static electric field to move a test charge between two points. This is measured in units of volts (a joule per coulomb); moving 1 coulomb of charge across 1 volt of electric potential requires 1 joule of work.

Electric potential differences between points can be caused by electric charge, by electric current through a magnetic field, by time-varying magnetic fields, or some combination of these three.[1][2] A voltmeter 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 of the system is used as one of the points. A voltage may represent either a source of energy (electromotive force) or lost, used, or stored energy (potential drop).

## Definition

Given two points in space, ${\displaystyle x_{A}}$ and ${\displaystyle x_{B}}$, voltage is the difference in electric potential between those two points. From the definition of electric potential it follows that:

${\displaystyle \Delta V_{BA}=V(x_{B})-V(x_{A})=-\int _{r_{0}}^{x_{B}}{\vec {E}}\cdot d{\vec {l}}-\left(-\int _{r_{0}}^{x_{A}}{\vec {E}}\cdot d{\vec {l}}\right)}$
${\displaystyle =\int _{x_{B}}^{r_{0}}{\vec {E}}\cdot d{\vec {l}}+\int _{r_{0}}^{x_{A}}{\vec {E}}\cdot d{\vec {l}}=\int _{x_{B}}^{x_{A}}{\vec {E}}\cdot d{\vec {l}}}$
The electric field around the rod exerts a force on the charged pith ball, in an electroscope
In a static field, the work is independent of the path

Electric potential is electric potential energy per unit charge, measured in joules per coulomb (volts). "Electric potential" 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 electric potential can be chosen at any point, so the difference in potential, i.e. the voltage, is the quantity which is physically meaningful. The voltage between point A to point B is equal to the work which would have to be done, per unit charge, against or by 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" and "pressure". Pressure is now obsolete but tension is still used, for example within the phrase "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 source of energy is present to "push" it against the opposing electric field. This is the case within any electric power source. For example, inside a battery, chemical reactions provide the energy needed for ion current to flow from the negative to the positive terminal.

The electric field is not the only factor determining charge flow in a material, and different materials naturally develop electric potential differences at equilibrium (Galvani potentials). 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 a difference in electric potential.

Other Languages
العربية: جهد كهربائي
azərbaycanca: Gərginlik (elektrik)
تۆرکجه: وولتاژ
বাংলা: বিভব
Bân-lâm-gú: Tiān-ap
беларуская (тарашкевіца)‎: Напруга
Cymraeg: Foltedd
Esperanto: Elektra tensio
estremeñu: Tensión
فارسی: ولتاژ
한국어: 전압
हिन्दी: विभवांतर
hrvatski: Napon
Bahasa Indonesia: Tegangan listrik
interlingua: Voltage
íslenska: Rafspenna
עברית: מתח חשמלי
қазақша: Кернеу
latviešu: Spriegums
македонски: Напон
മലയാളം: വോൾട്ടത
मराठी: विभवांतर
Bahasa Melayu: Voltan
монгол: Хүчдэл
မြန်မာဘာသာ: ဗို့အား

norsk nynorsk: Elektrisk spenning
ਪੰਜਾਬੀ: ਵੋਲਟੇਜ
پنجابی: وولٹیج
português: Tensão elétrica
Scots: Voltage
Simple English: Voltage
slovenščina: Električna napetost
српски / srpski: Електрични напон
srpskohrvatski / српскохрватски: Električni napon
Basa Sunda: Voltase
suomi: Jännite
Tagalog: Boltahe
татарча/tatarça: Электр көчәнеше
తెలుగు: వోల్టేజ్
اردو: وولٹیج
Tiếng Việt: Hiệu điện thế

ייִדיש: וואלטאזש