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Encyclopedia > Alternating current
City lights viewed in a motion blurred exposure. The AC blinking causes the lines to be dotted rather than continuous.

An alternating current (AC) is an electrical current whose magnitude and direction vary cyclically, as opposed to direct current, whose direction remains constant. The usual waveform of an AC power circuit is a sine wave, as this results in the most efficient transmission of energy. However in certain applications different waveforms are used, such as triangular or square waves. Image File history File links Download high resolution version (2048x1536, 707 KB) The city lights of Prince George, British Columbia, motion-blurred by waving the camera during the exposure. ... Image File history File links Download high resolution version (2048x1536, 707 KB) The city lights of Prince George, British Columbia, motion-blurred by waving the camera during the exposure. ... This amusement ride moved during the exposure. ... In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ... The magnitude of a mathematical object is its size: a property by which it can be larger or smaller than other objects of the same kind; in technical terms, an ordering of the class of objects to which it belongs. ... Direct current (DC or continuous current) is the continuous flow of electricity through a conductor such as a wire from high to low potential. ... Waveform quite literally means the shape and form of a signal, such as a wave moving across the surface of water, or the vibration of a plucked string. ... Usually hidden from the unaided eye, the blinking of (non-incandescent) lighting powered by AC mains is revealed in this motion-blurred long exposure of city lights. ... In trigonometry, an ideal sine wave is a waveform whose graph is identical to the generalized sine function y = Asin[ω(x − α)] + C, where A is the amplitude, ω is the angular frequency (2π/P where P is the wavelength), α is the phase shift, and C is the...

Used generically, AC refers to the form in which electricity is delivered to businesses and residences. However, audio and radio signals carried on electrical wire are also examples of alternating current. In these applications, an important goal is often the recovery of information encoded (or modulated) onto the AC signal. Electricity (from New Latin Ä“lectricus, amberlike) is a general term for a variety of phenomena resulting from the presence and flow of electric charge. ... An audio frequency (abbreviation: AF) is any frequency from about 20 hertz to about 20 kilohertz, which is the approximate range of sound frequencies that is audible to humans. ... For other uses, see Wire (disambiguation). ... The ASCII codes for the word Wikipedia represented in binary, the numeral system most commonly used for encoding computer information. ... For the musical use of modulation, see modulation (music). ...

Westinghouse Early AC System 1887 (U.S. Patent 373,035 )

William Stanley, Jr. designed one of the first practical devices to transfer AC power efficiently between isolated circuits. Using pairs of coils wound on a common iron core, his design, called an induction coil, was an early precursor of the modern transformer. The system used today was devised in the late nineteenth century by Nikola Tesla, who subsequently sold his patent to George Westinghouse. Lucien Gaulard, John Dixon Gibbs, Carl Wilhelm Siemens and others contributed subsequently to this field. AC systems overcame the limitations of the direct current system used by Thomas Edison to distribute electricity efficiently over long distances. The practical coil circuits were the prototypes for the modern transformers William Stanley, Jr. ... An induction coil or spark coil (archaically known as a Ruhmkorff coil) is a type of disruptive discharge coil. ... For other uses, see Transformer (disambiguation). ... Nikola Tesla (Serbian Cyrillic: ) (10 July 1856 â€“ 7 January 1943) was a inventor, physicist, mechanical engineer, and electrical engineer. ... This article does not cite any references or sources. ... Lucien Gaulard (1850 - November 26, 1888) invented devices for the transmission of alternating current electrical energy. ... Wilhelm Siemens Carl Wilhelm Siemens (en: Charles William Siemens) (April 4, 1823 â€“ November 19, 1883) was a German engineer. ... Direct current (DC or continuous current) is the continuous flow of electricity through a conductor such as a wire from high to low potential. ... Edison redirects here. ...

The first modern commercial power plant using three-phase alternating current was at the Mill Creek hydroelectric plant near Redlands, California in 1893 designed by Almirian Decker. Decker's design incorporated 10,000 volt three-phase transmission and established the standards for the complete system of generation, transmission and motors used today. Redlands is a city in San Bernardino County, California, United States. ...

Alternating current circuit theory evolved rapidly in the latter part of the 19th and early 20th century. Notable contributors to the theoretical basis of alternating current calculations include Charles Steinmetz, James Clerk Maxwell, Oliver Heaviside, and many others. Calculations in unbalanced three-phase systems were simplified by the symmetrical components methods discussed by Charles Legeyt Fortescue in 1918. Charles Proteus Steinmetz (April 9, 1865_October 26, 1923) was born in Breslau, Silesia, Germany. ... James Clerk Maxwell (13 June 1831 â€“ 5 November 1879) was a Scottish mathematician and theoretical physicist. ... Oliver Heaviside (May 18, 1850 â€“ February 3, 1925) was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, developed techniques for applying Laplace transforms to the solution of differential equations, reformulated Maxwells field equations in terms of electric and... In electrical engineering, the method of Symmetrical components is used to simplify analysis of unbalanced three phase power systems. ... Charles LeGeyt Fortescue (1876-1936) was born in York Factory, in what is now Manitoba where the Hayes River enters Hudson Bay. ...

## Transmission, distribution, and domestic power supply

AC power can be increased or decreased in voltage with a transformer. Use of a higher voltage leads to significantly more efficient transmission of power. The power losses in a conductor are a product of the square of the current and the resistance of the conductor, described by the formula $P=I^2 cdot R ,!$. This means that when transmitting a fixed power on a given wire, if the current is doubled, the power loss will be four times greater. 11kV/400V-230V transformer in an older suburb of Wellington, New Zealand Electricity distribution is the penultimate stage in the delivery (before retail) of electricity to end users. ... For other uses, see Transformer (disambiguation). ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ...

Since the power transmitted is equal to the product of the current, the voltage and the cosine of the phase difference φ (P = IVcosφ), the same amount of power can be transmitted with a lower current by increasing the voltage. Therefore it is advantageous when transmitting large amounts of power to distribute the power with high voltages (often hundreds of kilovolts). The power factor of an AC electric power system is defined as the ratio of the real power to the apparent power, and is a number between 0 and 1. ...

However, high voltages also have disadvantages, the main ones being the increased insulation required, and generally increased difficulty in their safe handling. In a power plant, power is generated at a convenient voltage for the design of a generator, and then stepped up to a high voltage for transmission. Near the loads, the transmission voltage is stepped down to the voltages used by equipment. Consumer voltages vary depending on the country and size of load, but generally motors and lighting are built to use up to a few hundred volts between phases. A power station (also power plant) is a facility for the generation of electric power. ... This article is about machines that produce electricity. ...

The utilization voltage delivered to equipment such as lighting and motor loads is standardized, with an allowable range of voltage over which equipment is expected to operate. Standard power utilization voltages and percentage tolerance vary in the different mains power systems found in the world. // Plugs. ...

Modern high-voltage, direct-current electric power transmission systems contrast with the more common alternating-current systems as a means for the bulk transmission of electrical power over long distances. HVDC systems tend to be more expensive and less efficient than transformers. Transmission with high voltage direct current was not feasible when Edison, Westinghouse and Tesla were designing their power systems, since there was then no way to economically convert AC power to DC and back again at the necessary voltages. HVDC or high-voltage, direct current electric power transmission systems contrast with the more common alternating-current systems as a means for the bulk transmission of electrical power. ... Edison redirects here. ... This article does not cite any references or sources. ... Nikola Tesla (Serbian Cyrillic: ) (10 July 1856 â€“ 7 January 1943) was a inventor, physicist, mechanical engineer, and electrical engineer. ...

Three-phase electrical generation is very common. Three separate coils in the generator stator are physically offset by an angle of 120° to each other. Three current waveforms are produced that are equal in magnitude and 120° out of phase to each other. In electrical engineering, three-phase electric power systems have at least three conductors carrying voltage waveforms that are 2Ï€/3 radians (120Â°,1/3 of a cycle) offset in time. ... The stator is the fixed part of a rotating machine. ...

If the load on a three-phase system is balanced equally among the phases, no current flows through the neutral point. Even in the worst-case unbalanced (linear) load, the neutral current will not exceed the highest of the phase currents. It is noteworthy that non-linear loads (e.g. computers) may require an oversized neutral bus and neutral conductor in the upstream distribution panel to handle harmonics. Harmonics can cause neutral conductor current levels to exceed that of one or all phase conductors. Ground or earth in a mains (AC power) electrical wiring system is a conductor that exists primarily to help protect against faults. ... In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integral multiple of the fundamental frequency. ...

For three-phase at utilization voltages a four-wire system is often used. When stepping down three-phase, a transformer with a Delta primary and a Star secondary is often used so there is no need for a neutral on the supply side.

For smaller customers (just how small varies by country and age of the installation) only a single phase and the neutral or two phases and the neutral are taken to the property. For larger installations all three phases and the neutral are taken to the main distribution panel. From the three-phase main panel, both single and three-phase circuits may lead off. The generation of AC electric power is commonly three phase, in which the waveforms of three supply conductors are offset from one another by 120°. These three conductors are commonly housed in a single conduit (e. ...

Three-wire single phase systems, with a single centre-tapped transformer giving two live conductors, is a common distribution scheme for residential and small commercial buildings in North America. This arrangement is sometimes incorrectly referred to as "two phase". A similar method is used for a different reason on construction sites in the UK. Small power tools and lighting are supposed to be supplied by a local center-tapped transformer with a voltage of 55V between each power conductor and the earth. This significantly reduces the risk of electric shock in the event that one of the live conductors becomes exposed through an equipment fault whilst still allowing a reasonable voltage for running the tools. A split phase electricity distribution system is a 3-wire single-phase distribution system, commonly used in North America for single-family residential and light commercial (up to about 100 kVA) applications. ... Sign warning of possible electric shock hazard An electric shock can occur upon contact of a humans body with any source of voltage high enough to cause sufficient current flow through the muscles or hair. ...

A third wire, called the bond wire, is often connected between non-current carrying metal enclosures and earth ground. This conductor provides protection from electrical shock due to accidental contact of circuit conductors with the metal chassis of portable appliances and tools. Bonding all non-current carrying metal parts into one complete system ensures there is always a low impedance path to ground sufficient to carry any fault current for as long as it takes for the system to clear the fault. This low impedance path allows the maximum amount of fault current to flow, causing the overcurrent protection device (Breakers, fuses) to trip or burn out as quickly as possible, returning the electrical system to a safe state. All bond wires are bonded to ground at the main service panel, as is the Neutral/Identified Conductor if present. Ground or earth in a mains (AC power) electrical wiring system is a conductor that exists primarily to provide a low impedance path to the earth to prevent the buildup of voltages, static or transient (lightning), that may result in undue hazards to connected equipment or persons, and which in...

## AC power supply frequencies

The frequency of the electrical system varies by country; most electric power is generated at either 50 or 60 Hz. See List of countries with mains power plugs, voltages and frequencies. Some countries have a mixture of 50 Hz and 60 Hz supplies, notably Japan. The waveform of 230 volt, 50 Hz compared with 110 V, 60 Hz. ... The terms line voltage/frequency or mains voltage/frequency commonly refer to the electrical voltage and frequency used in the low voltage parts (in particular wall sockets) of an alternating current electricity supply network. ...

A low frequency eases the design of low speed electric motors, particularly for hoisting, crushing and rolling applications, and commutator-type traction motors for applications such as railways, but also causes a noticeable flicker in incandescent lighting and objectionable flicker of fluorescent lamps. 16⅔ Hz power is still used in some European rail systems, such as in Austria, Germany, Norway, Sweden and Switzerland. The use of lower frequencies also provided the advantage of lower impedance losses, which are proportional to frequency. The original Niagara Falls generators were built to produce 25 Hz power, as a compromise between low frequency for traction and heavy induction motors, while still allowing incandescent lighting to operate (although with noticeable flicker); most of the 25 Hz residential and commercial customers for Niagara Falls power were converted to 60 Hz by the late 1950's, although some 25 Hz industrial customers still existed as of the start of the 21st century. Traction motor typically refers to those motors that are used to power the driving wheels of a railroad locomotive, electrical multi-unit train (such as a subway or light rail vehicle train), or a tram. ... This is the top-level page of WikiProject trains Rail tracks Rail transport refers to the land transport of passengers and goods along railways or railroads. ... Fluorescent lamps Assorted types of fluorescent lamps. ...

Off-shore,military, textile industry, marine, computer mainframe, aircraft, and spacecraft applications sometimes use 400 Hz, for benefits of reduced weight of apparatus or higher motor speeds. For other uses, see Mainframe. ...

## Effects at high frequencies

A direct, constant current flows uniformly throughout the cross-section of the (uniform) wire that carries it. With alternating current of any frequency, the current is forced towards the outer surface of the wire, and away from the center. This is because an electric charge which accelerates (as is the case of an alternating current) radiates electromagnetic waves, and materials of high conductivity (the metal which makes up the wire) do not allow propagation of electromagnetic waves. This phenomenon is called skin effect. This box:      Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... Electromagnetic radiation or EM radiation is a combination (cross product) of oscillating electric and magnetic fields perpendicular to each other, moving through space as a wave, effectively transporting energy and momentum. ... Not to be confused with electrical conductance, a measure of an objects or circuits ability to conduct an electric current between two points, which is dependent on the electrical conductivity and the geometric dimensions of the conducting object. ... The skin effect is the tendency of an alternating electric current (AC) to distribute itself within a conductor so that the current density near the surface of the conductor is greater than that at its core. ...

At very high frequencies the current no longer flows in the wire, but effectively flows on the surface of the wire, within a thickness of a few skin depths. The skin depth is the thickness at which the current density is reduced by 63%. Even at relatively low frequencies used for high power transmission (50–60 Hz), non-uniform distribution of current still occurs in sufficiently thick conductors. For example, the skin depth of a copper conductor is approximately 8.57 mm at 60 Hz, so high current conductors are usually hollow to reduce their mass and cost. When an electromagnetic wave interacts with a conductive material, mobile charges within the material are made to oscillate back and forth with the same frequency as the impinging fields. ... In science and engineering, conductors are materials that contain movable charges of electricity. ...

Since the current tends to flow in the periphery of conductors, the effective cross-section of the conductor is reduced. This increases the effective AC resistance of the conductor, since resistance is inversely proportional to the cross-sectional area in which the current actually flows. The AC resistance often is many times higher than the DC resistance, causing a much higher energy loss due to ohmic heating (also called I2R loss). Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... In electronics, and in physics more broadly, Joule heating or ohmic heating refers to the increase in temperature of a conductor as a result of resistance to an electrical current flowing through it. ...

### Techniques for reducing AC resistance

For low to medium frequencies, conductors can be divided into stranded wires, each insulated from one other, and the individual strands specially arranged to change their relative position within the conductor bundle. Wire constructed using this technique is called Litz wire. This measure helps to partially mitigate skin effect by forcing more equal current flow throughout the total cross section of the stranded conductors. Litz wire is used for making high Q inductors, reducing losses in flexible conductors carrying very high currents at power frequencies, and in the windings of devices carrying higher radio frequency current (up to hundreds of kilohertz), such as switch-mode power supplies and radio frequency transformers. Litz wire is a special type of wire used in electronics. ... The Q factor or quality factor is a measure of the quality of a resonant system. ... An inductor is a passive electrical device employed in electrical circuits for its property of inductance. ... It has been suggested that this article or section be merged with Radio waves. ... A wall wart style variable DC power supply with its cover removed. ... It has been suggested that this article or section be merged with Radio waves. ... For other uses, see Transformer (disambiguation). ...

### Techniques for reducing radiation loss

As written above, an alternating current is made of electric charge under periodic acceleration, which causes radiation of electromagnetic waves. Energy that is radiated represents a loss. Depending on the frequency, different techniques are used to minimize the loss due to radiation. This box:      Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... Acceleration is the time rate of change of velocity and/or direction, and at any point on a velocity-time graph, it is given by the slope of the tangent to the curve at that point. ... This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... Electromagnetic radiation or EM radiation is a combination (cross product) of oscillating electric and magnetic fields perpendicular to each other, moving through space as a wave, effectively transporting energy and momentum. ...

#### Twisted pairs

At frequencies up to about 1 GHz, wires are paired together in cabling to form a twisted pair in order to reduce losses due to electromagnetic radiation and inductive coupling. A twisted pair must be used with a balanced signalling system, where the two wires carry equal but opposite currents. The result is that each wire in the twisted pair radiates a signal that is effectively cancelled by the other wire, resulting in almost no electromagnetic radiation. 25 Pair Color Code Chart 10BASE-T UTP Cable Twisted pair cabling is a common form of wiring in which two conductors are wound around each other for the purposes of cancelling out electromagnetic interference known as crosstalk. ... This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... In electronics, inductive coupling refers to the transfer of energy from one circuit component to another through a shared magnetic field. ...

#### Waveguides

Waveguides are similar to coax cables, as both consist of tubes, with the biggest difference being that the waveguide has no inner conductor. Waveguides can have any arbitrary cross section, but rectangular cross sections are the most common. With waveguides, the energy is no longer carried by an electric current, but by a guided electromagnetic field. Waveguides have dimensions comparable to the wavelength of the alternating current to be transmitted, so they are only feasible at microwave frequencies. This box:      This page is about waveguides for electromagnetic wave propagation at microwave and radio wave frequencies. ... This box:      Electric current is the flow (movement) of electric charge. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... For other uses, see Wavelength (disambiguation). ...

#### Fiber optics

At frequencies greater than 200 GHz, waveguide dimensions become impractically small, and the ohmic losses in the waveguide walls become large. Instead, fiber optics, which are a form of dielectric waveguides, can be used. For such frequencies, the concepts of voltages and currents are no longer used. In electronics, and in physics more broadly, Joule heating or ohmic heating refers to the increase in temperature of a conductor as a result of resistance to an electrical current flowing through it. ... Fiber Optic strands An optical fiber in American English or fibre in British English is a transparent thin fiber for transmitting light. ...

## Mathematics of AC voltages

A sine wave, over one cycle (360°). The dashed line represents the root mean square (RMS) value at about 0.707

Alternating currents are accompanied (or caused) by alternating voltages. In English the initialism AC is commonly and somewhat confusingly used for both. An AC voltage v can be described mathematically as a function of time by the following equation: Image File history File links Sine_wave. ... Image File history File links Sine_wave. ... In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ... This article is about functions in mathematics. ...

$v(t)=V_mathrm{peak}cdotsin(omega t)$,

where

• $displaystyle V_{rm peak}$ is the peak voltage (unit: volt),
• $displaystyle omega$ is the angular frequency (unit: radians per second)
• The angular frequency is related to the physical frequency, $displaystyle f$, which represents the number of oscillations per second (unit = hertz), by the equation $omega = 2,pi, f$.
• $displaystyle t$ is the time (unit: second).

The peak-to-peak value of an AC voltage is defined as the difference between its positive peak and its negative peak. Since the maximum value of $displaystyle sin(x)$ is +1 and the minimum value is −1, an AC voltage swings between $displaystyle+V_{rm peak}$ and $displaystyle-V_{rm peak}$. The peak-to-peak voltage, usually written as $displaystyle V_{rm pp}$ or $displaystyle V_{rm P-P}$, is therefore $V_{rm peak} - left(-V_{rm peak}right) = 2 times V_{rm peak}$. Josephson junction array chip developed by NIST as a standard volt. ... It has been suggested that this article or section be merged into Angular velocity. ... Angular frequency is a measure of how fast an object is rotating In physics (specifically mechanics and electrical engineering), angular frequency Ï‰ (also called angular speed) is a scalar measure of rotation rate. ... This article is about the SI unit of frequency. ... This article is about the unit of time. ...

### Power and root mean square

The relationship between voltage and power is:

$displaystyle P(t) = frac{V^2(t)}{R}$ where $displaystyle R$ represents a load resistance

Rather than using instantaneous power, $displaystyle Pleft(tright)$, it is more practical to use a time averaged power (where the averaging is performed over any integer number of cycles). Therefore, AC voltage is often expressed as a root mean square (RMS) value, written as $displaystyle V_{rm rms}$, because In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ...

$displaystyle P_{rm time~averaged} = frac{{V^2}_{rm rms}}{R}$

For a sinusoidal voltage:

$V_mathrm{rms}=frac{V_mathrm{peak}}{sqrt{2}}$

The factor $sqrt{2}$ is called the crest factor, which varies for different waveforms. The crest factor of a waveform is equal to the peak amplitude of a waveform divided by the RMS value. ...

• For a triangle wave form: $V_mathrm{rms}=frac{V_mathrm{peak}}{sqrt{3}}$
• For a square wave form: $displaystyle V_mathrm{rms}=V_mathrm{peak}$

A triangle wave is a waveform named for its triangular shape. ... A square wave is a kind of basic waveform. ...

### Example

To illustrate these concepts, consider a 240 V AC mains supply. It is so called because its Root mean square value is 240 V. This means that the time-averaged power delivered is equivalent to the power delivered by a DC voltage of 240 Volts. To determine the peak voltage (amplitude), we can modify the above equation to: In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. ...

$V_mathrm{peak}=sqrt{2} V_mathrm{rms}$

For our 240 V AC, the peak voltage Vpeak is therefore $displaystyle 240 V timessqrt{2}$, which is about 339 V. The peak-to-peak value $displaystyle V_{P-P}$ of the 240 V AC is double that, at about 679 V.

• Willam A. Meyers, History and Reflections on the Way Things Were: Mill Creek Power Plant - Making History with AC, IEEE Power Engineering Review, February 1997, Pages 22-24

 Electronics Portal

Image File history File links Nuvola_apps_ksim. ... Direct current (DC or continuous current) is the continuous flow of electricity through a conductor such as a wire from high to low potential. ... This is a list of countries and territories, with the plugs, voltages and frequencies they use for providing electrical power to small appliances and some major appliances. ... This article is about plugs and sockets only intended for common domestic (residential) use. ... Electricity (from New Latin Ä“lectricus, amberlike) is a general term for a variety of phenomena resulting from the presence and flow of electric charge. ... Electrical wiring in general refers to insulated conductors used to carry electricity, and associated devices. ... -1... The waveform of 230 volt, 50 Hz compared with 110 V, 60 Hz. ... // In the War of Currents era (sometimes, War of the Currents or Battle of Currents) in the late 1880s, George Westinghouse and Thomas Edison became adversaries due to Edisons promotion of direct current (DC) for electric power distribution over the alternating current (AC) advocated by Westinghouse and Nikola Tesla. ...

Results from FactBites:

 Alternating current - Wikipedia, the free encyclopedia (2633 words) And through the use of alternating current, Charles Proteus Steinmetz of General Electric was able to solve many of the problems associated with electricity generation and transmission. With alternating current of any frequency, the current is forced towards the outer surface of the wire, and away from the center. The current flowing on the inner conductor is equal and opposite to the current flowing on the inner surface of the outer tube.
 Direct current - Wikipedia, the free encyclopedia (480 words) Direct current installations usually have different types of sockets, switches, and fixtures, mostly due to the low voltages used, from those suitable for alternating current. It is usually important with a direct current appliance not to reverse polarity unless the device has a diode bridge to correct for this. High voltage direct current is used for long-distance point-to-point power transmission and for submarine cables, with voltages from a few kilovolts to approximately one megavolt.
More results at FactBites »

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