# Electric power

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Electric Power is the rate, per unit time, at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second.

## Contents

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 electric power grid. Electric energy is usually sold by the kilowatt hour (1 kW·h = 3.6 MJ) which is the product of the power in kilowatts multiplied by running time in hours. Electric utilities measure energy using an electricity meter, which keeps a running total of the electric energy delivered to a customer.

Electric power can be delivered over long distances by transmission lines and used for applications such as motion, light or heat with high efficiency. [1]

## 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 (voltage) difference of V is

${\displaystyle P={\text{work done per unit time}}={\frac {VQ}{t}}=VI\,}$

where

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

## Explanation

Electric power is transformed to other forms of energy when electric charges move through an electric potential (voltage) difference, which occurs in electrical components in electric circuits. From the standpoint of electric power, components in an electric circuit can be divided into two categories:

• Passive devices or loads: When electric charges move through a potential difference from a higher to a lower voltage, that is when conventional current (positive charge) moves from the positive (+) terminal to the negative (−) terminal, work is done by the charges on the device. The potential energy of the charges due to the voltage between the terminals is converted to kinetic energy in the device. These devices are called passive components or loads; they 'consume' electric power from the circuit, converting it to other forms of energy such as mechanical work, heat, light, etc. Examples are electrical appliances, such as light bulbs, electric motors, and electric heaters. In alternating current (AC) circuits the direction of the voltage periodically reverses, but the current always flows from the higher potential to the lower potential side.
• Active devices or power sources: If the charges are moved by an 'exterior force' through the device in the direction from the lower electric potential to the higher, (so positive charge moves from the negative to the positive terminal), work will be done on the charges, and energy is being converted to electric potential energy from some other type of energy, such as mechanical energy or chemical energy. Devices in which this occurs are called active devices or power sources; such as electric generators and batteries.

Some devices can be either a source or a load, depending on the voltage and current through them. For example, a rechargeable battery acts as a source when it provides power to a circuit, but as a load when it is connected to a battery charger and is being recharged, or a generator as a power source and a motor as a load.

### 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 (Ohmic, or linear) loads, Joule's law can be combined with Ohm's law (V = I·R) to produce alternative expressions for the amount of power that is dissipated:

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

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 real power P in watts consumed by a device is given by

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

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 is the phase angle between the current and voltage sine waves

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:

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

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 θ between them:

${\displaystyle {\mbox{(real power)}}={\mbox{(apparent power)}}\cos \theta }$
${\displaystyle {\mbox{(reactive power)}}={\mbox{(apparent power)}}\sin \theta }$

The ratio of real power to apparent power is called power factor 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.

### 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 must be replaced by a more complex calculation, the integral of the cross-product of the electrical and magnetic field vectors over a specified area, thus:

${\displaystyle P=\int _{S}(\mathbf {E} \times \mathbf {H} )\cdot \mathbf {dA} .\,}$

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

## 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: electricity 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 power 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. [2] Since the invention of the first battery (or "voltaic pile") 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, [3] with 6% annual growth. There are two types of batteries: primary batteries (disposable batteries), which are designed to be used once and discarded, and secondary batteries (rechargeable batteries), which are designed to be recharged and used multiple times. Batteries come in many sizes, from miniature 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.

### Electric power industry

The electric power industry provides the production and delivery of power, in sufficient quantities to areas that need electricity, through a grid connection. The grid distributes electrical energy to customers. Electric power is generated by central power stations or by distributed generation. The electric power industry has gradually been trending towards deregulation – with emerging players offering consumers competition to the traditional public utility companies. [4]

## Use

Electric power, produced from central generating stations and distributed over an electrical transmission grid, is widely used in industrial, commercial and consumer applications. The per capita electric power consumption of a country correlates with its industrial development. [5] 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 source of energy for building space heating. Use of electric power for pumping water ranges from individual household wells to irrigation projects and energy storage projects.

## Notes

1. Smith, Clare (2001). Environmental physics. London, United Kingdom: Routledge. ISBN   0-415-20191-8.
2. "battery" (def. 4b), Merriam-Webster Online Dictionary (2009). Retrieved 25 May 2009.
3. Power Shift: DFJ on the lookout for more power source investments Archived 2005-12-01 at the Wayback Machine . Draper Fisher Jurvetson. Retrieved 20 November 2005.
4. The Opportunity of Energy Group-Buying EnPowered, April 18, 2016,
5. Ignacio J. Pérez-Arriaga (ed), Regulation of the Power Sector, Springer Science & Business Media, 2014 ISBN   1447150341, page 8

## Related Research Articles

Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. In early days, electricity was considered as being unrelated to magnetism. Later on, many experimental results and the development of Maxwell's equations indicated that both electricity and magnetism are from a single phenomenon: electromagnetism. Various common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges and many others.

Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points. The difference in electric potential between two points in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named volt. In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule per 1 coulomb. The official SI definition for volt uses power and current, where 1 volt = 1 watt per 1 ampere. This definition is equivalent to the more commonly used 'joules per coulomb'. Voltage or electric potential difference is denoted symbolically by V, but more often simply as V, for instance in the context of Ohm's or Kirchhoff's circuit laws.

The volt is the derived unit for electric potential, electric potential difference (voltage), and electromotive force. It is named after the Italian physicist Alessandro Volta (1745–1827).

In electrical engineering, the power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit, and is a dimensionless number in the closed interval of −1 to 1. A power factor of less than one indicates the voltage and current are not in phase, reducing the average product of the two. Real power is the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the product of RMS current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power. A negative power factor occurs when the device generates power, which then flows back towards the source.

Electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage is applied. The term complex impedance may be used interchangeably.

Alternating current (AC) is an electric current which periodically reverses direction, in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug kitchen appliances, televisions, fans and electric lamps into a wall socket. A common source of DC power is a battery cell in a flashlight. The abbreviations AC and DC are often used to mean simply alternating and direct, as when they modify current or voltage.

Direct current (DC) is the unidirectional flow of an electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or even through a vacuum as in electron or ion beams. The electric current flows in a constant direction, distinguishing it from alternating current (AC). A term formerly used for this type of current was galvanic current.

A rectifier is an electrical device that converts alternating current (AC), which periodically reverses direction, to direct current (DC), which flows in only one direction.

Electromotive force, is the electrical action produced by a non-electrical source. A device that converts other forms of energy into electrical energy, such as a battery or generator, provides an emf as its output. Sometimes an analogy to water "pressure" is used to describe electromotive force.

The output impedance of an electrical network is the measure of the opposition to current flow (impedance), both static (resistance) and dynamic (reactance), into the load network being connected that is internal to the electrical source. The output impedance is a measure of the source's propensity to drop in voltage when the load draws current, the source network being the portion of the network that transmits and the load network being the portion of the network that consumes.

In power engineering, the power-flow study, or load-flow study, is a numerical analysis of the flow of electric power in an interconnected system. A power-flow study usually uses simplified notations such as a one-line diagram and per-unit system, and focuses on various aspects of AC power parameters, such as voltages, voltage angles, real power and reactive power. It analyzes the power systems in normal steady-state operation.

In physics and engineering, a phasor, is a complex number representing a sinusoidal function whose amplitude (A), angular frequency (ω), and initial phase (θ) are time-invariant. It is related to a more general concept called analytic representation, which decomposes a sinusoid into the product of a complex constant and a factor that encapsulates the frequency and time dependence. The complex constant, which encapsulates amplitude and phase dependence, is known as phasor, complex amplitude, and sinor or even complexor.

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 inductors and capacitors may result in periodic reversals of the direction of energy flow.

The wattmeter is an instrument for measuring the electric power in watts of any given circuit. Electromagnetic wattmeters are used for measurement of utility frequency and audio frequency power; other types are required for radio frequency measurements.

A capacitor is a device that stores electrical energy in an electric field. It is a passive electronic component with two terminals.

A load bank is a device which develops an electrical load, applies the load to an electrical power source and converts or dissipates the resultant power output of the source. A load bank includes load elements with protection, control, metering and accessory devices required for operation. Load banks can either be permanently installed at a facility and permanently connected to a power source or portable versions can be used for testing power sources such as standby generators and batteries. Load banks are the best way to replicate, prove and verify the real-life demands on critical power systems.

A permanent magnet synchronous generator is a generator where the excitation field is provided by a permanent magnet instead of a coil. The term synchronous refers here to the fact that the rotor and magnetic field rotate with the same speed, because the magnetic field is generated through a shaft mounted permanent magnet mechanism and current is induced into the stationary armature.

Leading and lagging current are phenomena that occur as a result of alternating current. In a circuit with alternating current, the value of voltage and current vary sinusoidally. In this type of circuit, the terms lead, lag, and in phase are used to describe current with reference to voltage. Current is in phase with voltage when there is no phase shift between the sinusoids describing their time varying behavior. This generally occurs when the load drawing the current is resistive.

In electrical engineering, the passive sign convention (PSC) is a sign convention or arbitrary standard rule adopted universally by the electrical engineering community for defining the sign of electric power in an electric circuit. The convention defines electric power flowing out of the circuit into an electrical component as positive, and power flowing into the circuit out of a component as negative. So a passive component which consumes power, such as an appliance or light bulb, will have positive power dissipation, while an active component, a source of power such as an electric generator or battery, will have negative power dissipation. This is the standard definition of power in electric circuits; it is used for example in computer circuit simulation programs such as SPICE.

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