**Electric power** is the rate at which electric energy is transferred by an electric circuit. The

SISi, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

unit of power is the watt.

### 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

resistiveThe electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

circuits, electrical power is calculated using Joule's law:

where

*P* is the electric power,

*V* the potential difference, and

*I* the

electric currentElectric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

.

In the case of resistive (Ohmic, or linear) loads, Joule's law can be combined with

Ohm's lawOhm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...

(

*I* =

*V/R*) to produce alternative expressions for the dissipated power:

where

*R* is the

electrical resistanceThe electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

.

#### Alternating current

In

alternating currentPower in an electric circuit is the rate of flow of energy past a given point of the circuit. In alternating current circuits, energy storage elements such as inductance and capacitance may result in periodic reversals of the direction of energy flow...

circuits, energy storage elements such as

inductanceIn electromagnetism and electronics, inductance is the ability of an inductor to store energy in a magnetic field. Inductors generate an opposing voltage proportional to the rate of change in current in a circuit...

and

capacitanceIn electromagnetism and electronics, capacitance is the ability of a capacitor to store energy in an electric field. Capacitance is also a measure of the amount of electric potential energy stored for a given electric potential. A common form of energy storage device is a parallel-plate capacitor...

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 TheoremIn mathematics, the Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle...

, the relationship among real, reactive and apparent power is:

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:

The ratio of real power to apparent power is called

power factorThe power factor of an AC electric power system is defined as the ratio of the real power flowing to the load over the apparent power in the circuit, and is a dimensionless number between 0 and 1 . Real power is the capacity of the circuit for performing work in a particular time...

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.

### In space

Electrical power 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

integralIntegration is an important concept in mathematics and, together with its inverse, differentiation, is one of the two main operations in calculus...

of the

cross-productIn mathematics, the cross product, vector product, or Gibbs vector product is a binary operation on two vectors in three-dimensional space. It results in a vector which is perpendicular to both of the vectors being multiplied and normal to the plane containing them...

of the electrical and magnetic field vectors over a specified area, thus:

The result is a scalar since it is the

*surface integral*In mathematics, a surface integral is a definite integral taken over a surface ; it can be thought of as the double integral analog of the line integral...

of the

*Poynting vector*In physics, the Poynting vector can be thought of as representing the directional energy flux density of an electromagnetic field. It is named after its inventor John Henry Poynting. Oliver Heaviside and Nikolay Umov independently co-invented the Poynting vector...

.

## See also

- High voltage cable
A high voltage cable - also called HV cable - is used for electric power transmission at high voltage. High voltage cables of differing types have a variety of applications in instruments, ignition systems, AC and DC power transmission...

- AC power
Power in an electric circuit is the rate of flow of energy past a given point of the circuit. In alternating current circuits, energy storage elements such as inductance and capacitance may result in periodic reversals of the direction of energy flow...

- EGRID
- Electric energy consumption
- Rural electrification
Rural electrification is the process of bringing electrical power to rural and remote areas. Electricity is used not only for lighting and household purposes, but it also allows for mechanization of many farming operations, such as threshing, milking, and hoisting grain for storage; in areas...

### Power generation

- Electricity generation
Electricity generation is the process of generating electric energy from other forms of energy.The fundamental principles of electricity generation were discovered during the 1820s and early 1830s by the British scientist Michael Faraday...

- Energy development
Energy development is the effort to provide sufficient primary energy sources and secondary energy forms for supply, cost, impact on air pollution and water pollution, mitigation of climate change with renewable energy....

- Nuclear Power
Nuclear power is the use of sustained nuclear fission to generate heat and electricity. Nuclear power plants provide about 6% of the world's energy and 13–14% of the world's electricity, with the U.S., France, and Japan together accounting for about 50% of nuclear generated electricity...

- Fossil fuel power plant
A fossil-fuel power station is a power station that burns fossil fuels such as coal, natural gas or petroleum to produce electricity. Central station fossil-fuel power plants are designed on a large scale for continuous operation...

- Geothermal Power
Geothermal energy is thermal energy generated and stored in the Earth. Thermal energy is the energy that determines the temperature of matter. Earth's geothermal energy originates from the original formation of the planet and from radioactive decay of minerals...

## External links