Electric power
Electric power is the rate of transfer of electrical energy within a circuit. Its SI unit is the watt, the general unit of power, defined as one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions and billions of watts are called kilowatts, megawatts and gigawatts respectively.
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 by the electric power industry through an electrical grid.
Electric power can be delivered over long distances by transmission lines and used for applications such as motion, light or heat with high efficiency.
Definition
Electric power, like mechanical power, is the rate of doing work, measured in watts, and represented by the letter P. The term wattage is used colloquially to mean "electric power in watts". The electric power in watts produced by an electric current I consisting of a charge of Q coulombs every t seconds passing through an electric potential difference of V is:The voltage between two terminals is defined as the work required to move a unit charge from one terminal to the other against the force of the electric field, so this equation can be derived as
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
Explanation
An often confusing aspect of the terminology is that the direction of electric current is defined as the direction that positive charge flows, but the actual mobile charge carriers in circuits are electrons, which have a negative charge. But a flow of positive charge in one direction is equivalent to an equal flow of negative charge in the other direction. So the electrons in the circuit flow in the opposite direction to the direction of conventional current.
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 resistive loads, the power formula and Joule's first law can be combined with Ohm's law to produce alternative expressions for the amount of power that is dissipated:where R is the electrical resistance.
Alternating current
In alternating current circuits, the polarity of the voltage and the direction of current flow reverses twice each cycle. In resistive circuits, with no reactance, in which the current reverses at the same instant as the voltage reverses, the circuit behaves the same as a DC circuit described above, with power flowing out of sources and consumed by loads.However in circuits with energy storage elements such as inductance and capacitance, in addition to the energy being consumed by resistances, some of the energy flowing into passive components is stored temporarily and returned to the circuit each cycle. This may result in periodic reversals of the direction of energy flow. The portion of energy 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. The amplitude of that portion of energy flow that results in no net transfer of energy but instead oscillates between the source and load in each cycle due to stored energy, is known as the absolute value of reactive power. The product of the RMS value of the voltage wave and the RMS value of the current wave is known as apparent power. The real power P in watts consumed by a device is given by
where
- Vp is the peak voltage in volts
- Ip is the peak current in amperes
- Vrms is the root-mean-square voltage in volts
- Irms is the root-mean-square current in amperes
- θ = θv − θi 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
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 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 surface integral of the cross-product of the electric field intensity and magnetic field intensity vectors gives the total instantaneous power out of the volume: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 power station by electromechanical generators, driven by heat engines heated by combustion, geothermal power or nuclear fission. Other generators are driven by the kinetic energy of flowing water and wind. There are many other technologies that are used to generate electricity such as photovoltaic solar panels.
A battery is a device consisting of one or more electrochemical cells that convert stored chemical energy into electrical energy. Since the invention of the first battery in 1800 by Alessandro Volta and especially since the technically improved Daniell cell in 1836, batteries have become a common power source for many household and industrial applications. According to a 2005 estimate, the worldwide battery industry generates US$48 billion in sales each year, with 6% annual growth. There are two types of batteries: primary batteries, which are designed to be used once and discarded, and secondary batteries, which are designed to be recharged and used multiple times. Batteries are available in many sizes; from miniature button cells used to power hearing aids and wristwatches to battery banks the size of rooms that provide standby power for telephone exchanges and computer data centers.