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.
See also
Power generation
References
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