View source for Volt-ampere

{{short description|SI unit of apparent power in an electrical circuit}}
{{technical|date=December 2019}}
{{Infobox unit
| bgcolor      = 
| name         = volt-ampere
| image        = Cmplxpower.svg
| caption      = [[Apparent power]] (<math>|S|</math>) is the magnitude of the vector sum of [[real power]] vector (<math>P</math>) and [[reactive power]] vector (<math>Q</math>); <math>\varphi</math> is the phase shift between voltage and current.
| standard     = [[SI units]]
| quantity     = [[Apparent power]]
| symbol       = V⋅A
| symbol2      = 
| namedafter   = 
| extralabel   = 
| extradata    = 
| units1       = SI base units
| inunits1     = 1 kg⋅m<sup>2</sup>⋅s<sup>−3</sup>
}}
The '''volt-ampere''' ([[International System of Units|SI symbol]]: '''VA''',<ref name = dir /> sometimes '''V&sdot;A''' or '''V&nbsp;A''') is the [[unit of measurement]] for [[apparent power]] in an [[electrical circuit]]. It is the product of the [[Root mean square AC voltage|root mean square voltage]] (in [[volts]]) and the [[Root-Mean-Square Current|root mean square current]] (in [[amperes]]).<ref>Ciletti, M. D., Irwin, J. D., Kraus, A. D., Balabanian, N., Bickard, T. A., and Chan, S. P. (1993). Linear circuit analysis. In ''Electrical Engineering Handbook,'' edited by R. C. Dorf. Boca Raton: CRC Press. (pp.82–87)</ref> Volt-amperes are usually used for analyzing [[alternating current]] (AC) circuits. In [[direct current]] (DC) circuits, this product is equal to the [[real power]], measured in [[watt]]s.<ref>''IEEE 100 : the authoritative dictionary of IEEE standards terms.-7th ed.'' {{ISBN|0-7381-2601-2}}, page 14</ref> The volt-ampere is dimensionally equivalent to the [[watt]]: in [[SI units]], 1&nbsp;V&sdot;A = 1&nbsp;W. VA rating is most used for generators and transformers, and other power handling equipment, where loads may be reactive (inductive or capacitive).

== Formulation ==
For a simple [[electrical circuit]] running on [[direct current]], the electrical current and voltage are constant. In that case, the [[real power]] (''P'', measured in [[watt]]s) is the product of the current (''I'', measured in [[amperes]]) and the voltage from one side of the circuit to the other (''V'', measured in [[volts]]):

:<math>P = I \cdot V</math>

For [[alternating current]], both the voltage and current are oscillating. Instantaneous power is still the product of instantaneous current and instantaneous voltage, but if both of those are ideal sine waves driving a purely resistive load (like an incandescent light bulb), average power becomes (with subscripts designating average (av), [[Amplitude#Peak_amplitude|peak amplitude]] (pk) and [[root mean square]] (rms)):

:<math>P_\text{av} = {I_\text{pk} \cdot V_\text{pk} \over 2} = I_\text{rms} \cdot V_\text{rms}</math>

More generally, when voltage and current are not in phase, these products no longer represent average power but a new apparent power, measured in volt-amperes:<ref>{{citation | last1=Schavemaker | first1=P. | last2=van der Sluis | first2=L.| title=Electrical Power System Essentials | publisher=Wiley | publication-place=Chichester, England ; Hoboken, NJ | date=2008 | isbn=978-0-470-51027-8 | oclc=193911699 | page=35}}</ref>

:<math>|S| = I_\text{rms} \cdot V_\text{rms}</math>

== Usage ==
The relationship between real power and apparent power is described by the [[power factor]]. With a purely resistive load, they are the same: the apparent power is equal to the real power. Where a reactive (capacitive or inductive) component is present in the load, the apparent power is greater than the real power as voltage and current are no longer in phase.  In the limiting case of a purely reactive load, current is drawn but no power is dissipated in the load.

Some devices, including [[uninterruptible power supplies]] (UPSs), have ratings both for maximum volt-amperes and maximum watts. A common [[SI prefix|prefixed]] derived unit is "kilovolt-ampere" (symbol kVA). The VA rating is limited by the maximum permissible current, and the watt rating by the power-handling capacity of the device. When a UPS powers equipment which presents a [[electrical reactance|reactive]] load with a low power factor, neither limit may safely be exceeded.<ref>[http://www.apc.com/us/en/faqs/FA157485/ ''Watt Ratings Differs from Volt Amp Ratings''] APC</ref> For example, a (large) UPS system rated to deliver 400,000 volt-amperes (400 kVA) at 220 volts can deliver a current of 1818 amperes (these are RMS values).

VA ratings are also often used for transformers; maximum output current is then VA rating divided by nominal output voltage.<ref>{{cite web|title=Transformers and VA Ratings|url=https://yorkcentraltechtalk.wordpress.com/2012/06/27/transformers-and-va-ratings/|date=2012-06-27|access-date=13 December 2016}}</ref> Transformers with the same sized core usually have the same VA rating.

The convention of using the volt-ampere to distinguish apparent power from real power is allowed by the SI standard.<ref>{{cite web|url=http://www.bipm.org/en/publications/si-brochure/section5-3-2.html|title=SI Brochure|edition=8th |archive-url=https://web.archive.org/web/20190329203216/https://www.bipm.org/utils/common/pdf/si_brochure_8_en.pdf |archive-date=March 29, 2019}}</ref>{{Page needed|date=February 2022}}

== Volt-ampere reactive {{anchor|Reactive}} ==
In electric power [[Electric power transmission|transmission]] and [[Electric power distribution|distribution]], '''volt-ampere reactive''' ('''var''') is a unit of measurement of [[AC_power#Active,_reactive,_and_apparent_power|reactive power]]. Reactive power exists in an AC circuit when the current and voltage are not in phase. The term ''var'' was proposed by the Romanian [[electrical engineer]] [[Constantin Budeanu]] and introduced in 1930 by the [[International Electrotechnical Commission|IEC]] in [[Stockholm]], which has adopted it as the unit for [[electrical reactance|reactive]] power.

Special instruments called ''varmeters'' are available to measure the reactive power in a circuit.<ref name=":0">{{Cite book|title=Electrical Machines, Drives and Power Systems|last=Wildi|first=Theodore|publisher=Pearson|year=2002|isbn=978-0-13-093083-5|pages=137}}</ref>

The unit "var" is allowed by the  [[International System of Units]] (SI) even though the unit var is representative of a form of power.<ref>[https://www.bipm.org/en/publications/si-brochure/section2-2-2.html SI Brochure, 8th ed.]</ref> Per EU [[directive 80/181/EEC]] (the "metric directive"), the correct symbol is lower-case "var",<ref name = dir>[http://eur-lex.europa.eu/LexUriServ/LexUriServ.do?uri=OJ:L:1980:039:0040:0050:EN:PDF#page=6 Council Directive on units of measurements 80/181/EEC] Chapter 1.2.3., p. 6: "Special names for the unit of power: the name volt–ampere (symbol ‘VA’) when it is used to express the apparent power of alternating electric current, and var (symbol ‘var’) when it is used to express reactive electric power."</ref> although the spellings "Var" and "VAr" are commonly seen, and "VAR" is widely used throughout the power industry.

== References ==
{{Reflist}}
* {{FS1037C}}

[[Category:Electricity]]
[[Category:Units of power]]