# Electric power

Electric power

Electric power is defined as the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt.

When electric current flows in a circuit, it can transfer energy to do mechanical or thermodynamic work. Devices convert electrical energy into many useful forms, such as heat (electric heaters), light (light bulbs), motion (electric motors), sound (loudspeaker) or chemical changes. Electricity can be produced mechanically by generation, or chemically, or by direct conversion from light in photovoltaic cells, also it can be stored chemically in batteries.

Mathematics of electric power

Circuits

Electric power, like mechanical power, is represented by the letter "P" in electrical equations. The term "wattage" is used colloquially to mean "electric power in watts."

Direct current

In direct current resistive circuits, instantaneous electrical power is calculated using Joule's Law, which is named after the British physicist James Joule, who first showed that heat and mechanical energy were interchangeable.:$P = V I ,$

where:$P$ is the power (watt or W):$V$ is the potential difference (volt or V):$I$ is the current (ampere or A)

For example::$2,mbox\left\{A\right\} cdot 12,mbox\left\{V\right\} = 24,mbox\left\{W\right\} ,$.

Joule's law can be combined with Ohm's law to produce two more equations::$P = I^2 R, = frac\left\{V^2\right\}\left\{R\right\} ,$

where:$R$ is the resistance (Ohm or Ω).

For example::$\left(2,mbox\left\{A\right\}\right)^2 cdot 6,Omega = 24,mbox\left\{W\right\} ,$

and:$frac\left\{\left(12,mbox\left\{V\right)\right\}^2\right\}\left\{6,Omega\right\} = 24,mbox\left\{W\right\} ,$

Alternating current

In 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 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::$mbox\left\{\left(apparent power\right)\right\}^2 = mbox\left\{\left(real power\right)\right\}^2 + mbox\left\{\left(reactive power\right)\right\}^2$

Real and reactive powers can also be calculated directly from the apparent power, when the current and voltage are both sinusoids with a known phase angle between them:

:$mbox\left\{\left(real power\right)\right\} = mbox \left\{\left(apparent power\right)\right\} * cos mbox \left\{\left(theta\right)\right\}$

:$mbox\left\{\left(reactive power\right)\right\} = mbox \left\{\left(apparent power\right)\right\} * sin mbox \left\{\left(theta\right)\right\}$

The ratio of real power to apparent power is called power factor and is a number always between 0 and 1.

In space

Electrical power flows wherever electric and magnetic fields exist 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 vector cross-product of the electrical and magnetic fields over a specified area, thus::$mathbf\left\{P\right\} = int_S mathbf\left\{E\right\} imes mathbf\left\{H\right\} cdot mathbf\left\{dA\right\}. ,$

The result is a scalar since it is the "surface integral" of the "Poynting vector".

ee also

*AC power
*EGRID
*World energy resources and consumption
*Rural electricity

Power generation

*Electricity generation
*Energy development
*Nuclear Power
*Fossil fuel power plant

References

* [http://www.eei.org/industry_issues/industry_overview_and_statistics/nonav_key_facts/index.htm Key Facts About the Electric Power Industry, Edison Electric Institute website]
* [http://www.nerc.com/~filez/blackout.html Reports on August 2003 Blackout, North American Electric Reliability Council website]
* cite book
last = Croft
first = Terrell
coauthors = Summers, Wilford I.
title = American Electricans' Handbook
url = http://books.mcgraw-hill.com/getbook.php?isbn=0071377352
edition = Eleventh Edition
year = 1987
publisher = McGraw Hill
location = New York
id = ISBN 0-070-13932-6

* cite book
last = Fink
first = Donald G.
coauthors = Beaty, H. Wayne
title = Standard Handbook for Electrical Engineers
url = http://books.mcgraw-hill.com/getbook.php?isbn=0070220050
edition = Eleventh Edition
year = 1978
publisher = McGraw Hill
location = New York
id = ISBN 0-070-20974-X

* [http://www.sengpielaudio.com/calculator-ohm.htm Electric power calculations]

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