# 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 is the difference in electric potential between two points. The difference in electric potential between two points (i.e., voltage) in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named volt.[1] In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule (of work) per 1 coulomb (of charge). The official SI definition for volt uses power and current, where 1 volt = 1 watt (of power) per 1 ampere (of current).[1] This definition is equivalent to the more commonly used 'joules per coulomb'. Voltage or electric potential difference is denoted symbolically by V, but more often simply as V, for instance in the context of Ohm's or Kirchhoff's circuit laws.

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.[2][3] 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

There are multiple useful ways to define voltage, including the standard definition mentioned at the start of this page. There are also other useful definitions of work per charge (see this section).

Roughly speaking, 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) based electronics.

### Definition as potential of electric field

The voltage increase from some point ${\textstyle x_{A}}$ to some point ${\textstyle x_{B}}$ is given by

{\displaystyle {\begin{aligned}\Delta V_{AB}&=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)\\&=-\int _{x_{A}}^{x_{B}}{\vec {E}}\cdot d{\vec {l}}\end{aligned}}}
The electric field around the rod exerts a force on the charged pith ball, in an electroscope

In this case, the voltage increase 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 without causing any acceleration. Mathematically, this is expressed as the line integral of the electric field along that path. Under this definition, the voltage difference between two points is not uniquely defined when there are time-varying magnetic fields since the electric force is not a conservative force in such cases.

In a static field, the work is independent of the path

If this definition of voltage is used, any circuit where there are time-varying magnetic fields[note 1], such as circuits containing inductors, will not have a well-defined voltage between nodes in the circuit. However, if magnetic fields are suitably contained to each component, then the electric field is conservative in the region exterior[note 2] to the components and voltages are well-defined in that region[4]. In this case, the voltage across an inductor, viewed externally, turns out to be

${\displaystyle \Delta V=-L{\frac {dI}{dt}}}$

despite the fact that, internally, the electric field in the coil is zero[4] (assuming it is a perfect conductor).

### Definition via decomposition of electric field

Using the above definition, the electric potential is not defined whenever magnetic fields change with time. In physics, it's sometimes useful to generalize the electric potential by only considering the conservative part of the electric field. This is done by the following decomposition used in electrodynamics:

${\displaystyle {\vec {E}}=-\nabla V-{\frac {\partial {\vec {A}}}{\partial t}}}$

where ${\textstyle {\vec {A}}}$ is the magnetic vector potential. The above decomposition is justified by Helmholtz's theorem.

In this case, the voltage increase from ${\textstyle x_{A}}$ to ${\textstyle x_{B}}$ is given by

{\displaystyle {\begin{aligned}\Delta V_{AB}&=-\int _{x_{A}}^{x_{B}}{\vec {E}}_{\mathrm {conservative} }\cdot d{\vec {l}}\\&=-\int _{x_{A}}^{x_{B}}\left({\vec {E}}+{\frac {\partial {\vec {A}}}{\partial t}}\right)\cdot d{\vec {l}}\\&=-\int _{x_{A}}^{x_{B}}({\vec {E}}-{\vec {E}}_{\mathrm {induced} })\cdot d{\vec {l}}\end{aligned}}}

where ${\textstyle {\vec {E}}_{\mathrm {induced} }}$ is the rotational electric field due to time-varying magnetic fields. In this case, the voltage between points is always uniquely defined.

### Treatment in circuit theory

In circuit analysis and electrical engineering, the voltage across an inductor is not considered to be zero or undefined, as the standard definition would suggest. This is because electrical engineers use a lumped element model to represent and analyze circuits.

When using a lumped element model, it is assumed that there are no magnetic fields in the region surrounding the circuit and that the effects of these are contained in 'lumped elements', which are idealized and self-contained circuit elements used to model physical components[5]. If the assumption of negligible leaked fields is too inaccurate, their effects can be modelled by parasitic components.

In the case of a physical inductor though, the ideal lumped representation is often accurate. This is because the leaked fields of the inductor are generally negligible, especially if the inductor is a toroid. If leaked fields are negligible, we find that

${\displaystyle \int _{\mathrm {exterior} }{\vec {E}}\cdot d{\vec {l}}=-L{\frac {dI}{dt}}}$

is path-independent, and there is a well-defined voltage across the inductor's terminals[4]. This is the reason that measurements with a voltmeter across an inductor are often reasonably independent of the placement of the test leads.

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