Electric power

Power
Common symbols	℘ or P
SI unit	watt (W)
In SI base units	kg⋅m2⋅s−3
Derivations from other quantities	℘ = E/t ℘ = F·v ℘ = U·I ℘ = τ·ω
Dimension	${\displaystyle {\mathsf {L}}^{2}{\mathsf {M}}{\mathsf {T}}^{-3}}$

Electric power is the rate of transfer of

In common parlance, electric power is the production and delivery of electrical energy, an essential public utility in much of the world. Electric power is usually produced by electric generators, but can also be supplied by sources such as electric batteries. It is usually supplied to businesses and homes (as domestic mains electricity) by the electric power industry through an electrical grid.

Electric power can be delivered over long distances by

) difference of V is:

$${\displaystyle {\text{Work done per unit time}}=\wp ={\frac {W}{t}}={\frac {W}{Q}}{\frac {Q}{t}}=VI}$$

where:

• W is work in joules
• t is time in seconds
• Q is electric charge in coulombs
• V is electric potential or voltage in volts
• I is electric current in amperes

I.e.,

watts = volts times amps.

Explanation

Electric power is transformed to other forms of energy when

Active devices (power sources)

If

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

(V = I·R) to produce alternative expressions for the amount of power that is dissipated:

$${\displaystyle \wp =IV=I^{2}R={\frac {V^{2}}{R}}}$$

where R is the

electrical resistance

.

Alternating current without harmonics

In

$${\displaystyle \wp ={1 \over 2}V_{p}I_{p}\cos \theta =V_{\rm {rms}}I_{\rm {rms}}\cos \theta }$$

• V_p is the peak voltage in volts
• I_p is the peak current in amperes
• V_rms is the
  root-mean-square
  voltage in volts
• I_rms is the
  root-mean-square
  current in amperes
• θ = θ_v − θ_i is the phase angle by which the voltage sine wave leads the current sine wave, or equivalently the phase angle by which the current sine wave lags the voltage sine wave

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

$${\displaystyle {\text{(apparent power)}}^{2}={\text{(real power)}}^{2}+{\text{(reactive power)}}^{2}}$$

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 θ between them:

$${\displaystyle {\text{(real power)}}={\text{(apparent power)}}\cos \theta }$$

$${\displaystyle {\text{(reactive power)}}={\text{(apparent power)}}\sin \theta }$$

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

Electromagnetic fields

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 may be replaced by a more complex calculation. The closed

$${\displaystyle \wp =\oint _{\text{area}}(\mathbf {E} \times \mathbf {H} )\cdot d\mathbf {A} .}$$

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

Production

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: electric current is generated by the movement of a loop of wire, or disc of copper between the poles of a magnet.

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

Electricity is mostly generated at a

A

The electric power industry provides the production and delivery of power, in sufficient quantities to areas that need

Electric power, produced from central generating stations and distributed over an electrical transmission grid, is widely used in industrial, commercial, and consumer applications. A country's per capita electric power consumption correlates with its industrial development. [10] 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 furnaces. 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 energy source for building space heating. The use of electric power for pumping water ranges from individual household wells to irrigation and energy storage projects.

See also

• EGRID
• Electric energy consumption
• Electric power system
• High-voltage cable
• Power engineering
• Rural electrification

References

Bibliography

• Reports on August 2003 Blackout, North American Electric Reliability Council website
• Croft, Terrell; Summers, Wilford I. (1987). American Electricians' Handbook (Eleventh ed.). New York:
  ISBN 0-07-013932-6
  .
• ISBN 0-07-020974-X
  .

External links

Wikimedia Commons has media related to Electrical power.

• U.S. Department of Energy: Electric Power