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## PowerPedia:Electric power

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:For delivered electrical power see: There was an error working with the wiki: Code[8].

Electric power is defined as the amount of There was an error working with the wiki: Code[1] done by an Electric current in a unit There was an error working with the wiki: Code[9].

#### Explanation

When a current flows in a circuit with Electrical resistance, it does work. Devices can be made that convert this work into There was an error working with the wiki: Code[2] (Electric motors). In our modern society, electrical power or Electricity is a term not just for physical work but also for a There was an error working with the wiki: Code[10] of modern There was an error working with the wiki: Code[11].

When a loss of electrical power occurs over a large region of a country, whether by the actions of people or nature, it is a disaster. There was an error working with the wiki: Code[3], because of the necessity of electrical power.

#### Mathematics of electric power

##### In circuits

Electric power, like mechanical power, is represented by the letter P in electrical equations, and is measured in units called Watts (symbol W), named after Scottish engineer There was an error working with the wiki: Code[12]. The term wattage is used colloquially to mean 'electric power in watts'.

In Electrical resistance circuits, instantaneous electrical power is calculated using There was an error working with the wiki: Code[13], which is named after the British physicist There was an error working with the wiki: Code[14], who first showed that electrical and mechanical energy were interchangeable.

:P=IV\,

where

:P = power in Watts

:I = current in Amperes

:V = potential difference in Volts

For example: 2 amperes &times 12 volts = 24 watts.

Joule's law can be combined with There was an error working with the wiki: Code[15] to produce two more equations:

:P = I^2R\,

and

:P = \frac {V^2} {R}

where

:R = resistance in ohms.

For example:

:(2 amperes)2 &times 6 ohms = 24 watts

and

:(12 volts)2 / 6 ohms = 24 watts.

In There was an error working with the wiki: Code[4] circuits, energy storage elements such as There was an error working with the wiki: Code[16] and There was an error working with the wiki: Code[17] 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 There was an error working with the wiki: Code[18]. That portion of power flow due to stored energy, that returns to the source in each cycle, is known as There was an error working with the wiki: Code[19].

The unit for reactive power is given the special name VAR, which stands for volt-amperes-reactive. In reactive circuits, the watt unit (symbol W) is generally reserved for the real power component. The There was an error working with the wiki: Code[20] of the real power and the reactive power is called the There was an error working with the wiki: Code[21]. Apparent power is conventionally expressed in volt-amperes (V·A) since it is the simple multiple of rms voltage and current.

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 There was an error working with the wiki: Code[22], the relationship among real, reactive and apparent power is shown to be:

: ({real\ power}/W)^2 + ({reactive\ power}/VAR)^2 = ({apparent\ power}/VA)^2. \,

##### 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 There was an error working with the wiki: Code[5] There was an error working with the wiki: Code[6] of the electrical and magnetic fields over a specified area, thus:

:{P} = \int_S {E} \times {H} \cdot {dA}

The result of this integral is a vector, since power has both magnitude and direction. The There was an error working with the wiki: Code[23] describes the energy flux (J·m?2·s?1) of an electromagnetic field. It is named after its inventor John Henry Poynting. Oliver Heaviside independently co-discovered the Poynting vector. It points in the direction of energy flow and its magnitude is the power per unit area crossing a surface which is normal to it. For example, the Poynting vector near an ideally conducting wire is parallel to the wire axis - so electric energy is flowing in space outside of the wire. The Poynting vector becomes tilted toward wire for a resistive wire, indicating that energy flows from the e/m field into the wire, producing resistive Joule heating in the wire.

#### Power factor

The ratio between real power and apparent power in a circuit is called the There was an error working with the wiki: Code[24]. Where the waveforms are purely There was an error working with the wiki: Code[25], the power factor is the There was an error working with the wiki: Code[26] of the There was an error working with the wiki: Code[27] (?) between the current and voltage sinusoid waveforms. Equipment data sheets and nameplates often will abbreviate power factor as "\cos \phi" for this reason.

Power factor equals unity (1) when the voltage and current are in phase, and is zero when the current leads or lags the voltage by 90 degrees. Power factor must be specified as leading or lagging. For two systems transmitting the same amount of real power, the system with the lower power factor will have higher circulating currents due to energy that returns to the source from energy storage in the load. These higher currents in a practical system may produce higher losses and reduce overall transmission efficiency. A lower power factor circuit will have a higher apparent power and higher losses for the same amount of real power transfer.

Capacitive circuits cause reactive power with the current waveform leading the voltage wave by 90 degrees, while inductive circuits cause reactive power with the current waveform lagging the voltage waveform by 90 degrees. The result of this is that capacitive and inductive circuit elements tend to cancel each other out. By convention, capacitors are said to generate reactive power whilst inductors are said to consume it (this probably comes from the fact that most real-life loads are inductive and so reactive power has to be supplied to them from There was an error working with the wiki: Code[28] capacitors).

In Electric power transmission and distribution, significant effort is made to control the reactive power flow. This is typically done automatically by switching inductors (also commonly called reactors) or capacitor banks in and out, by adjusting generator excitation, and by other means. There was an error working with the wiki: Code[29]s may use There was an error working with the wiki: Code[30]s which measure reactive power to financially penalize customers with low power factor loads (especially larger customers).

##### Kilowatt-hour

When paired with a unit of time the term watt is used for expressing energy consumption. For example, a There was an error working with the wiki: Code[7], is the amount of Energy expended by a one kilowatt device over the course of one hour it equals 3.6 megajoules. A megawatt day (MWd or MW·d) is equal to 86.4 GJ. These units are often used in the context of power plants and home energy bills.

#### References and external articles

Rama Corporation Engineering Guide - A free 35-page PDF displaying power and wattage requirements, energy calculations and material properties is made available by this 50-year old electrical heater manufacturer. (Thanks Congress:Member:Robert L. Pritchett)

Reports on August 2003 Blackout, North American Electric Reliability Council website

Croft, Terrell, Summers, Wilford I., American Electricans' Handbook, Eleventh Edition, McGraw Hill, New York, 1987. ISBN 0-07-013932-6

Fink,Donald G., Beaty, H. Wayne, Standard Handbook for Electrical Engineers Eleventh Edition, McGraw Hill, New York, 1978. ISBN 0-07-020974-X

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