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 {{Short description|the rate per unit of time at which electrical energy is transferred by an electric circuit}}
[[File:NIGU_Strain_tower.JPG|thumb|Electric power is transmitted on [[Overhead power line|overhead lines]] like these, and also on underground [[high-voltage cable]]s.]]
'''Electric power''' is the rate, per unit time, at which [[electrical energy]] is transferred by an [[electric circuit]]. The [[SI]] unit of [[power (physics)|power]] is the [[watt]], one [[joule]] per [[second]].

Electric power is usually produced by [[electric generator]]s, but can also be supplied by  sources such as [[Battery (electricity)|electric batteries]].   It is usually supplied to businesses and homes (as domestic [[mains electricity]]) by the [[electric power industry]] through an [[electric power grid]]. Electric energy is usually sold by the [[kilowatt hour]] (1 kW·h = 3.6 MJ) which is the product of the  power in kilowatts multiplied by running time in hours.  Electric utilities measure power using an [[electricity meter]], which keeps a running total of the electric energy delivered to a customer.

Electrical power provides a low [[entropy]] form of energy and can be [[electric power transmission|carried long distances]] and converted into other forms of energy such as [[electric motor|motion]], [[electric light|light]] or [[electric heat|heat]] with high [[electrical efficiency|energy efficiency]].<ref name="smith-2001">
{{cite book | last1 = Smith | first1 = Clare | title = Environmental physics | date = 2001 | publisher = [[Routledge]] | location = London, United Kingdom | isbn = 0-415-20191-8}}</ref>

==Definition==
Electric power, like [[power (physics)|mechanical power]], is the rate of doing [[work (electrical)|work]], measured in [[watt]]s, and represented by the letter ''P''. The term ''wattage'' is used colloquially to mean "electric power in watts."  The electric power in [[watt]]s produced by an [[electric current]] ''I'' consisting of a [[electric charge|charge]] of ''Q'' coulombs every ''t'' seconds passing through an [[electric potential]] ([[voltage]]) difference of ''V'' is
:<math>P = \text{work done per unit time} = \frac {VQ}{t} = VI \,</math>
where
:''Q'' is electric charge in [[coulomb]]s
:''t'' is time in [[second]]s
:''I'' is electric current in [[ampere]]s
:''V'' is electric potential or voltage in [[volt]]s

==Explanation==
[[File:Electric load animation 2.gif|thumb|upright=0.6|Animation showing electric load]]

Electric power is transformed to other forms of energy when [[electric charge]]s move through an [[electric potential]] ([[voltage]]) difference, which occurs in [[electrical component]]s in electric circuits.  From the standpoint of electric power, components in an electric circuit can be divided into two categories:  
*'''Passive devices''' or '''loads''':  When electric charges move through a potential difference from a higher to a lower voltage, that is when [[conventional current]] (positive charge) moves from the positive (+)  terminal to the negative (−) terminal, [[work (physics)|work]] is done by the charges on the device. The [[potential energy]] of the charges due to the voltage between the terminals is converted to [[kinetic energy]] in the device. These devices are called ''[[Passivity (engineering)|passive]]'' components or ''loads''; they 'consume' electric power from the circuit, converting it to other forms of energy such as [[mechanical work]], heat, light, etc.  Examples are [[electrical appliance]]s, such as [[light bulb]]s, [[electric motor]]s, and [[electric heater]]s.  In [[alternating current]] (AC) circuits the direction of the voltage periodically reverses, but the current always flows from the higher potential to the lower potential side.

[[File:Electric power source animation 2.gif|thumb|upright=0.6|Animation showing power source]]
*'''Active devices''' or '''power sources''': If the charges are moved by an 'exterior force' through the device in the direction from the lower electric potential to the higher, (so positive charge moves from the negative to the positive terminal), [[work (physics)|work]] will be done ''on'' the charges, and energy is being converted to electric [[potential energy]] from some other type of energy, such as [[mechanical energy]] or [[chemical energy]]. Devices in which this occurs are called ''[[Passivity (engineering)|active]]'' devices or ''power sources''; such as [[electric generator]]s and [[electric battery|batteries]].  
Some devices can be either a source or a load, depending on the voltage and current through them.  For example, a [[rechargeable battery]] acts as a source when it provides power to a circuit, but as a load when it is connected to a battery charger and is being recharged, or a generator as a power source and a motor as a load.

===Passive sign convention===
{{main|Passive sign convention}}
Since electric power can flow either into or out of a component, a convention is needed for which direction represents positive power flow. Electric power flowing ''out'' of a circuit ''into'' a component is arbitrarily defined to have a positive sign, while power flowing ''into'' a circuit from a component is defined to have a negative sign. Thus passive components have positive power consumption, while power sources have negative power consumption.   This is called the ''[[passive sign convention]]''.

===Resistive circuits===
In the case of [[resistive]] (Ohmic, or linear) loads, Joule's law can be combined with [[Ohm's law]] (''V'' = ''I·R'') to produce alternative expressions for the amount of power that is dissipated:

:<math>P = I V = I^2 R = \frac{V^2}{R},</math>

where ''R'' is the [[electrical resistance]].

===Alternating current===
{{Main|AC power}}
In [[AC power|alternating current]] circuits, energy storage elements such as [[inductance]] and [[capacitance]] may result in periodic reversals of the direction of energy flow. The portion of power flow that, averaged over a complete cycle of the AC waveform, results in net transfer of energy in one direction is known as [[real power]] (also referred to as active power). That portion of power flow due to stored energy, that returns to the source in each cycle, is known as [[reactive power]]. The real power '''''P''''' in watts consumed by a device is given by
:<math>P = {1 \over 2}V_p I_p \cos \theta = V_{\rm rms}I_{\rm rms} \cos \theta \,</math>
where
:'''''V'''''<sub>p</sub> is the peak voltage in volts
:'''''I'''''<sub>p</sub> is the peak current in amperes
:'''''V'''''<sub>rms</sub> is the [[root-mean-square]] voltage in volts
:'''''I'''''<sub>rms</sub> is the [[root-mean-square]] current in amperes
:'''''θ''''' is the [[phase angle]] between the current and voltage sine waves

[[File:Power Triangle 01.svg|thumb|Power triangle: The components of [[AC power]]]]

The relationship between real power, reactive power and apparent power can be expressed by representing the quantities as vectors. Real power is represented as a horizontal vector and reactive power is represented as a vertical vector. The apparent power vector is the hypotenuse of a right triangle formed by connecting the real and reactive power vectors. This representation is often called the ''power triangle''. Using the [[Pythagorean Theorem]], the relationship among real, reactive and apparent power is:
:<math>\mbox{(apparent power)}^2 = \mbox{(real power)}^2 + \mbox{(reactive power)}^2</math>

Real and reactive powers can also be calculated directly from the apparent power, when the current and voltage are both [[Sine wave|sinusoid]]s with a known phase angle θ between them:

:<math>\mbox{(real power)} = \mbox {(apparent power)}\cos \theta</math>

:<math>\mbox{(reactive power)} = \mbox {(apparent power)}\sin \theta</math>

The ratio of real power to apparent power is called [[power factor]] and is a number always between 0 and 1. Where the currents and voltages have non-sinusoidal forms, power factor is generalized to include the effects of distortion.

===Electromagnetic fields===
{{unreferenced section|date=November 2012}}
Electrical energy flows wherever electric and magnetic fields exist together and fluctuate in the same place. The simplest example of this is in electrical circuits, as the preceding section showed. In the general case, however, the simple equation ''P'' = ''IV'' must be replaced by a more complex calculation, the [[integral]] of the [[cross product|cross-product]] of the electrical and magnetic field [[vector (geometric)|vectors]] over a specified area, thus:
:<math>
P = \int_S (\mathbf{E} \times \mathbf{H}) \cdot \mathbf{dA}. \,
</math>

The result is a scalar since it is the ''[[surface integral]]'' of the ''[[Poynting vector]]''.

==Generation==
{{main|Electricity generation}}
The fundamental principles of much electricity generation were discovered during the 1820s and early 1830s by the British scientist [[Michael Faraday]].  His basic method is still used today: electricity is generated by the movement of a loop of wire, or disc of copper between the poles of a [[magnet]].

For [[electric utility|electric utilities]], it is the first process in the delivery of electricity to consumers. The other processes, electricity [[Electric power transmission|transmission]], [[Electric power distribution|distribution]], and electrical power storage and recovery using [[Pumped-storage hydroelectricity|pumped-storage]] methods are normally carried out by the [[electric power industry]].

Electricity is mostly generated at a [[power station]] by electromechanical [[electrical generator|generators]], driven by [[heat engine]]s heated by [[combustion]], [[geothermal power]] or [[nuclear fission]]. Other generators are driven by the [[kinetic energy]] of flowing water and wind. There are many other technologies that are used to generate electricity such as [[photovoltaic]] solar panels.

A [[battery (electricity)|battery]] is a device consisting of one or more [[electrochemical cell]]s that convert stored chemical [[energy]] into electrical energy.<ref name="Webster">[http://www.merriam-webster.com/dictionary/battery "battery" (def. 4b)], ''Merriam-Webster Online Dictionary'' (2009). Retrieved 25 May 2009.</ref> Since the invention of the first battery (or "[[voltaic pile]]") in 1800 by [[Alessandro Volta]] and especially since the technically improved [[Daniell cell]] in 1836, batteries have become a common power source for many household and industrial applications. According to a 2005 estimate, the worldwide battery industry generates [[United States dollar|US$]]48 [[1000000000 (number)|billion]] in sales each year,<ref>[http://www.dfj.com/cgi-bin/artman/publish/article_141.shtml Power Shift: DFJ on the lookout for more power source investments] {{webarchive|url=https://web.archive.org/web/20051201015849/http://www.dfj.com/cgi-bin/artman/publish/article_141.shtml |date=2005-12-01 }}. ''Draper Fisher Jurvetson''. Retrieved 20 November 2005.</ref> with 6% annual growth. There are two types of batteries: [[Primary battery|primary batteries]] (disposable batteries), which are designed to be used once and discarded, and [[Secondary battery|secondary batteries]] (rechargeable batteries), which are designed to be recharged and used multiple times. Batteries come in many sizes, from miniature cells used to power [[hearing aid]]s and wristwatches to battery banks the size of rooms that provide standby power for [[telephone exchange]]s and computer [[data center]]s.

==Electric power industry==
{{main|Electric power industry}}
The electric power industry provides the production and delivery of power, in sufficient quantities to areas that need [[electricity]], through a [[grid connection]]. The grid distributes electrical energy to customers. Electric power is generated by central [[power station]]s or by [[distributed generation]]. The electric power industry has gradually been trending towards deregulation - with emerging players offering consumers competition to the traditional public utility companies.<ref>[https://www.en-powered.com/blog/the-opportunity-of-energy-group-buying The Opportunity of Energy Group-Buying] ''EnPowered'', April 18, 2016,</ref>

==Use==
Electric power, produced from central generating stations and distributed over an electrical transmission grid, is widely used in industrial, commercial and consumer applications. The per capita electric power consumption of a country correlates with its industrial development. <ref>Ignacio J. Pérez-Arriaga (ed), ''Regulation of the Power Sector'', Springer Science & Business Media, 2014 {{ISBN|1447150341}}, page 8 </ref>  Electric motors power manufacturing machinery and propel subways and railway trains. Electric lighting is the most important form of artificial light. Electrical energy is used directly in processes such as extraction of aluminum from its ores and in production of steel in [[electric arc furnace]]s. Reliable electric power is essential to telecommunications and broadcasting. Electric power is used to provide air conditioning in hot climates, and in some places electric power is an economically competitive source of energy for building space heating. Use of electric power for pumping water ranges from individual household wells to irrigation projects and energy storage projects.

==See also==
{{Portal|Energy}}
* [[EGRID]]
* [[Electric energy consumption]]
* [[Electric power system]]
* [[High-voltage cable]]
* [[Power engineering]]
* [[Rural electrification]]

==Notes==
{{reflist}}

==References==
* [https://web.archive.org/web/20060616214056/http://www.nerc.com/~filez/blackout.html Reports on August 2003 Blackout, North American Electric Reliability Council website]
* {{cite book
 | last = Croft
 | first = Terrell
 |author2=Summers, Wilford I.
 | title = American Electricians' Handbook
 | edition = Eleventh
 | year = 1987
 | publisher = [[McGraw Hill]]
 | location = New York
 | isbn = 0-07-013932-6
}}
* {{cite book
 | last = Fink
 | first = Donald G.
 | authorlink = Donald G. Fink
 |author2=Beaty, H. Wayne
 | title = Standard Handbook for Electrical Engineers
 | edition = Eleventh
 | year = 1978
 | publisher = McGraw Hill
 | location = New York
 | isbn = 0-07-020974-X
}}

==External links==
{{commonscat|Electrical power}}
*[https://www.energy.gov/energysources/electricpower.htm U.S. Department of Energy: Electric Power]
*[http://en.globtek.com/glossary.php#.UvZfsRBdWE8 GlobTek, Inc. Glossary of Electric power Power Supply Terms]
*[https://e-electricity.com Platform of electric sector]
{{Electricity generation}}

{{Authority control}}

[[Category:Electric power| ]]
[[Category:Electromagnetism|Power]]

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