# Electric power: Map

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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.


[[Image:Electricalgrid.jpg|thumb|250px|right|Electrical power is transmitted with overhead lines on pylons like these in Brisbane, Australia.
For underground transmission see high voltage cables.]]

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, electrical power is calculated using Joule's law:
P = V \cdot I \,

where P is the electric power, V the potential difference, and I the electric current.

Joule's law can be combined with Ohm's law (V = RI) to produce alternative expressions for the dissipated power:

P = I^2 R \,
and
P = \frac{V^2}{R},
where R is the electrical resistance.

#### 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{(apparent power)}^2 = \mbox{(real power)}^2 + \mbox{(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 between them:

\mbox{(real power)} = \mbox {(apparent power)} * \cos \mbox {(theta)}

\mbox{(reactive power)} = \mbox {(apparent power)} * \sin \mbox {(theta)}

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

The above theory of reactive power and the power triangle is true only when both the voltage and current is strictly sinusoidal. Therefore is more or less abandoned for low voltage distribution applications where the current normally is rather distorted. It can still be used for high voltage tranmission applications and, with some care, for medium voltage applications where the current normally is less distorted.

### 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 integral of the vector cross-product of the electrical and magnetic fields over a specified area, thus:P = \int_S (\mathbf{E} \times \mathbf{H}) \cdot \mathbf{dA}. \,

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

## References

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