TheInfoList

Alternating current (AC) is an
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving part ...
which periodically reverses direction and changes its magnitude continuously with time in contrast to
direct current Direct current (DC) is one-directional flow Flow may refer to: Science and technology * Flow (fluid) or fluid dynamics, the motion of a gas or liquid * Flow (geomorphology), a type of mass wasting or slope movement in geomorphology * Flow (mathe ...
(DC) which flows only in one direction. Alternating current is the form in which
electric power 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 The watt (symbol: W) is a unit of Power (physics), power or radiant flux. In the International Sy ...
is delivered to businesses and residences, and it is the form of
electrical energy Electrical energy is energy derived from electric potential energy or kinetic energy. When used loosely, ''electrical energy'' refers to energy that has been converted ''from'' electric potential energy. This energy is supplied by the combination ...
that consumers typically use when they plug
kitchen appliance A typical Hoosier cabinet of the 1920s A kitchen is a room or part of a room used for cooking Cooking or cookery is the art, science, and craft of using heat to Outline of food preparation, prepare food for consumption. Cooking techniques a ...
s, televisions, fans and electric lamps into a
wall socket AC power plugs and sockets connect electric equipment to the alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct cu ...
. A common source of DC power is a battery cell in a
flashlight A flashlight, ( US) torch, or torchlight ( UK) is a portable hand-held electric light. Formerly, the light source typically was a miniature incandescent light bulb but these have been displaced by light-emitting diodes (LEDs) since the mid-2 ...

. The abbreviations ''AC'' and ''DC'' are often used to mean simply ''alternating'' and ''direct'', as when they modify ''
current Currents or The Current may refer to: Science and technology * Current (fluid) A current in a fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an applied shear stress, or external force. ...
'' or ''
voltage Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is the ...

''. The usual
waveform A waveform generated by a synthesizer In electronics, acoustics, and related fields, the waveform of a signal is the shape of its Graph of a function, graph as a function of time, independent of its time and Magnitude (mathematics), magnitud ...
of alternating current in most electric power circuits is a
sine wave A sine wave or sinusoid is any of certain mathematical curves that describe a smooth periodic oscillation Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or b ...

, whose positive half-period corresponds with positive direction of the current and vice versa. In certain applications, like
guitar amplifier A guitar amplifier (or amp) is an electronic device or system that strengthens the weak electrical signal from a pickup on an electric guitar An electric guitar is a guitar The guitar is a fretted musical instrument that typically h ...
s, different waveforms are used, such as or
square wave A square wave is a non-sinusoidal periodic waveform in which the amplitude alternates at a steady frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also referred to as temporal frequency, which ...

s.
Audio Audio most commonly refers to sound In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion ( ...
and
radio Radio is the technology of signaling and telecommunication, communicating using radio waves. Radio waves are electromagnetic waves of frequency between 30 hertz (Hz) and 300 gigahertz (GHz). They are generated by an electronic device ...
signals carried on electrical wires are also examples of alternating current. These types of alternating current carry information such as sound (audio) or images (video) sometimes carried by
modulation In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains information ...

of an AC carrier signal. These currents typically alternate at higher frequencies than those used in power transmission.

# Transmission, distribution, and domestic power supply

Electrical energy is distributed as alternating current because AC
voltage Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is the ...

may be increased or decreased with a
transformer A transformer is a passive electrical device that transfers electrical energy from one electrical circuit to another, or multiple Electrical network, circuits. A varying current in any one coil of the transformer produces a varying magnetic flux ...

. This allows the power to be transmitted through
power line An overhead power line is a structure used in electric power transmission and distributionDistribution may refer to: Mathematics *Distribution (mathematics) Distributions, also known as Schwartz distributions or generalized functions ...

s efficiently at high voltage, which reduces the energy lost as heat due to
resistance Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''Th ...
of the wire, and transformed to a lower, safer, voltage for use. Use of a higher voltage leads to significantly more efficient transmission of power. The power losses ($P_$) in the wire are a product of the square of the current ( I ) and the
resistance Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''Th ...
(R) of the wire, described by the formula: :$P_ = I^2 R \, .$ This means that when transmitting a fixed power on a given wire, if the current is halved (i.e. the voltage is doubled), the power loss due to the wire's resistance will be reduced to one quarter. The power transmitted is equal to the product of the current and the voltage (assuming no phase difference); that is, :$P_ = IV \, .$ Consequently, power transmitted at a higher voltage requires less loss-producing current than for the same power at a lower voltage. Power is often transmitted at hundreds of kilovolts on pylons, and transformed down to tens of kilovolts to be transmitted on lower level lines, and finally transformed down to 100 V – 240 V for domestic use. High voltages have disadvantages, such as the increased insulation required, and generally increased difficulty in their safe handling. In a
power plantPower Station or The Power Station may refer to: * Power station, a facility for the generation of electricity Music * The Power Station (band), a 1980s supergroup ** The Power Station (album), ''The Power Station'' (album), a 1985 album by The Pow ...

, energy 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 somewhat 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. The 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 Mains electricity by country includes a list of countries and territories, with the plugs, voltage Voltage, electric potential difference, electromotive force emf, electric pressure or electric tension is the difference in electric pote ...
found in the world. High-voltage direct-current (HVDC) electric power transmission systems have become more viable as technology has provided efficient means of changing the voltage of DC power. Transmission with high voltage direct current was not feasible in the early days of
electric power transmission Electric power transmission is the bulk movement of electrical energy from a power generation, generating site, such as a power plant, to an electrical substation. The interconnected lines which facilitate this movement are known as a ''transmiss ...
, as there was then no economically viable way to step down the voltage of DC for end user applications such as lighting incandescent bulbs.
Three-phase In electrical engineering, three-phase electric power systems have at least three conductors carrying alternating voltages that are offset in time by one-third of the period. A three-phase system may be arranged in delta (∆) or star (Y) (also ...
electrical generation is very common. The simplest way is to use three separate coils in the generator
stator The stator is the stationary part of a rotary system, found in electric generators, electric motors, sirens, mud motors or biological rotors. Energy flows through a stator to or from the rotating component of the system. In an electric mo ...
, physically offset by an angle of 120° (one-third of a complete 360° phase) to each other. Three current waveforms are produced that are equal in magnitude and 120°
out of phase In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through Spa ...
to each other. If coils are added opposite to these (60° spacing), they generate the same phases with reverse polarity and so can be simply wired together. In practice, higher "pole orders" are commonly used. For example, a 12-pole machine would have 36 coils (10° spacing). The advantage is that lower rotational speeds can be used to generate the same frequency. For example, a 2-pole machine running at 3600 rpm and a 12-pole machine running at 600 rpm produce the same frequency; the lower speed is preferable for larger machines. 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. Non-linear loads (e.g. the switch-mode power supplies widely used) may require an oversized neutral bus and neutral conductor in the upstream distribution panel to handle
harmonics of a vibrating string are harmonics. A harmonic is any member of the harmonic series (music), harmonic series. The term is employed in various disciplines, including music, physics, acoustics Acoustics is a branch of physics Physics ...
. Harmonics can cause neutral conductor current levels to exceed that of one or all phase conductors. For three-phase at utilization voltages a four-wire system is often used. When stepping down three-phase, a transformer with a Delta (3-wire) primary and a Star (4-wire, center-earthed) 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 Image:Single-phase-pole-transformer-d335.jpg, 173px, A single-phase polemount stepdown transformer in Canada. One supply phase (phase-to-neutral) from the utility is converted to split-phase for the customers. In electrical engineering, single-phas ...
and neutral, or two phases and neutral, are taken to the property. For larger installations all three phases and neutral are taken to the main distribution panel. From the three-phase main panel, both single and three-phase circuits may lead off. Three-wire single-phase systems, with a single center-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 55 V between each power conductor and earth. This significantly reduces the risk of
electric shock Electrical injury is a physiological reaction caused by electric current passing through the body. The injury depends on the density of the current, tissue resistance and duration of contact. Very small currents may be imperceptible or produce a ...
in the event that one of the live conductors becomes exposed through an equipment fault whilst still allowing a reasonable voltage of 110 V between the two conductors for running the tools. A third wire, called the bond (or earth) wire, is often connected between non-current-carrying metal enclosures and earth ground. This conductor provides protection from electric 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
electrical impedance In electrical engineering, electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage Voltage, electric potential difference, electromotive force emf, electric pressure or electric tension i ...
path to ground sufficient to carry any
fault Fault commonly refers to: *Fault (geology), planar rock fractures showing evidence of relative movement *Fault (law), blameworthiness or responsibility Fault(s) may also refer to: Arts, entertainment, and media * "Fault", a song by Taproot from ...
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, causing the overcurrent protection device (breakers, fuses) to trip or burn out as quickly as possible, bringing 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.

# AC power supply frequencies

The frequency of the electrical system varies by country and sometimes within a country; most electric power is generated at either 50 or 60
Hertz The hertz (symbol: Hz) is the unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatric ...

. Some countries have a mixture of 50 Hz and 60 Hz supplies, notably . A low frequency eases the design of electric motors, particularly for hoisting, crushing and rolling applications, and commutator-type
traction motorA traction motor is an electric motor used for propulsion of a vehicle, such as locomotives, electric or hydrogen vehicles, elevator An elevator (North American English) or lift (Commonwealth English) is a type of wire rope, cable-assisted, ...
s for applications such as
railway Rail transport (also known as train transport) is a means of transferring passengers and goods on wheeled vehicle A vehicle (from la, vehiculum) is a machine A machine is a man-made device that uses power to apply forces and contro ...

s. However, low frequency also causes noticeable flicker in
arc lamp . The two lamps, used for laser pumping, are very different in the shape of the electrodes, in particular, the cathode (on the left). An arc lamp or arc light is a lamp that produces light by an electric arc An electric arc, or arc discharge, i ...
s and
incandescent light bulb image of the tungsten Tungsten, or wolfram, is a chemical element with the Symbol (chemistry), symbol W and atomic number 74. Tungsten is a rare metal found naturally on Earth almost exclusively as compounds with other elements. It was identif ...

s. 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 1950s, although some 25 Hz industrial customers still existed as of the start of the 21st century. 16.7 Hz power (formerly 16 2/3 Hz) is still used in some European rail systems, such as in
Austria Austria, officially the Republic of Austria, is a landlocked country in the southern part of Central Europe, located on the Eastern Alps. It is composed of nine States of Austria, federated states, one of which is Vienna, Austria's ca ...
,
Germany ) , image_map = , map_caption = , map_width = 250px , capital = Berlin , coordinates = , largest_city = capital , languages_type = Official language , languages = German language, German , demonym = Germans, German , government_ ...

,
Norway Norway, officially the Kingdom of Norway,Names in the official and recognised languages: Bokmål Bokmål (, ; literally "book tongue") is an official written standard for the Norwegian language, alongside Nynorsk. Bokmål is the preferred ...

,
Sweden Sweden ( sv, Sverige ), officially the Kingdom of Sweden ( sv, links=no, Konungariket Sverige ), is a Nordic countries, Nordic country in Northern Europe.The United Nations Group of Experts on Geographical Names states that the country's for ...

and
Switzerland ,german: Schweizer(in),french: Suisse(sse), it, svizzero/svizzera or , rm, Svizzer/Svizra , government_type = Federalism, Federal semi-direct democracy under a multi-party assembly-independent Directorial system, directorial republic , leader_t ...

. Off-shore, military, textile industry, marine, aircraft, and spacecraft applications sometimes use 400 Hz, for benefits of reduced weight of apparatus or higher motor speeds. Computer
mainframe A mainframe computer, informally called a mainframe or big iron, is a computer used primarily by large organizations for critical applications, bulk data processing (such as the census A census is the procedure of systematically enumerating, a ...
systems were often powered by 400 Hz or 415 Hz for benefits of ripple reduction while using smaller internal AC to DC conversion units.

# Effects at high frequencies

A direct current flows uniformly throughout the cross-section of a uniform wire. An alternating current of any frequency is forced away from the wire's center, toward its outer surface. This is because the acceleration of an
electric charge Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respectively). Like ch ...
in an alternating current produces
waves The United States Naval Reserve (Women's Reserve), better known as the WAVES (for Women Accepted for Volunteer Emergency Service), was the women's branch of the United States Naval Reserve during World War II World War II or the S ...
of
electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
that cancel the propagation of electricity toward the center of materials with high conductivity. This phenomenon is called
skin effect s use stranded coils to reduce losses due to the skin effect. Skin effect is the tendency of an alternating current, alternating electric current (AC) to become distributed within a Conductor (material), conductor such that the current density i ...

. 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 depth s use stranded coils to reduce losses due to the skin effect. Skin effect is the tendency of an alternating current, alternating electric current (AC) to become distributed within a conductor such that the current density In electromagnetism ...

s. The skin depth is the thickness at which the current density is reduced by 63%. Even at relatively low frequencies used for power transmission (50 Hz – 60 Hz), non-uniform distribution of current still occurs in sufficiently thick
conductors Conductor or conduction may refer to: Music * Conductor (music), a person who leads a musical ensemble like, for example, an orchestra. * Conductor (album), ''Conductor'' (album), an album by indie rock band The Comas * Conduction, a type of ...
. 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. 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 Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''Th ...
of the conductor, since resistance is inversely proportional to the cross-sectional area. The AC resistance often is many times higher than the DC resistance, causing a much higher energy loss due to
ohmic heating Joule heating, also known as resistive, resistance, or Ohmic heating, is the process by which the passage of an electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical co ...

(also called I2R loss).

## Techniques for reducing AC resistance

For low to medium frequencies, conductors can be divided into stranded wires, each insulated from the others, with the relative positions of individual strands specially arranged within the conductor bundle. Wire constructed using this technique is called
Litz wire Litz wire is a particular type of multistrand wire A wire is a single usually cylindrical, flexible strand or rod of metal. Wires are used to bear mechanical loads or electricity Electricity is the set of physical phenomena associa ...
. This measure helps to partially mitigate skin effect by forcing more equal current throughout the total cross section of the stranded conductors. Litz wire is used for making high-Q
inductor An inductor, also called a coil, choke, or reactor, is a incremental passivity, passive two-terminal electronic component, electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically c ...

s, reducing losses in flexible conductors carrying very high currents at lower frequencies, and in the windings of devices carrying higher
radio frequency Radio frequency (RF) is the oscillation rate of an Alternating_current, alternating electric current or voltage or of a Magnetic_field, magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around ...
current (up to hundreds of kilohertz), such as switch-mode
power supplies A power supply is an electrical device that supplies electric power 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 The watt (symbol: W) is a ...

and
radio frequency Radio frequency (RF) is the oscillation rate of an Alternating_current, alternating electric current or voltage or of a Magnetic_field, magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around ...
transformer A transformer is a passive electrical device that transfers electrical energy from one electrical circuit to another, or multiple Electrical network, circuits. A varying current in any one coil of the transformer produces a varying magnetic flux ...

s.

## Techniques for reducing radiation loss

As written above, an alternating current is made of
electric charge Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respectively). Like ch ...
under periodic
acceleration In mechanics Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objects, more specifically the relationships among force, matter, and motion. Forces applied to objects result in Displacement ( ...
, which causes
radiation upThe international symbol for types and levels of ionizing radiation (radioactivity) that are unsafe for unshielded humans. Radiation, in general, exists throughout nature, such as in light and sound. In physics Physics (from grc ...
of
electromagnetic waves In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through ...
. Energy that is radiated is lost. Depending on the frequency, different techniques are used to minimize the loss due to radiation.

### Twisted pairs

At frequencies up to about 1 GHz, pairs of wires are twisted together in a cable, forming a
twisted pair Twisted pair cabling is a type of wiring in which two conductors of a single circuit are twisted together for the purposes of improving electromagnetic compatibility Electromagnetic compatibility (EMC) is the ability of electrical equipment ...

. This reduces losses from
electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
and
inductive coupling In electrical engineering, two conductors are said to be inductively coupled or magnetically coupled when they are configured such that a change in current through one wire induces a voltage across the ends of the other wire through electroma ...
. A twisted pair must be used with a balanced signalling system, so that the two wires carry equal but opposite currents. Each wire in a twisted pair radiates a signal, but it is effectively cancelled by radiation from the other wire, resulting in almost no radiation loss.

### Coaxial cables

Coaxial cable Coaxial cable, or coax (pronounced ) is a type of electrical cable consisting of an inner conductor surrounded by a concentric conducting shield, with the two separated by a dielectric ( insulating material); many coaxial cables also have a p ...
s are commonly used at
audio frequencies An audio frequency or audible frequency (AF) is a periodic vibration Vibration is a mechanical phenomenon whereby oscillation Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point ...
and above for convenience. A coaxial cable has a conductive wire inside a conductive tube, separated by a
dielectric In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is ...
layer. The current flowing on the surface of the inner conductor is equal and opposite to the current flowing on the inner surface of the outer tube. The electromagnetic field is thus completely contained within the tube, and (ideally) no energy is lost to radiation or coupling outside the tube. Coaxial cables have acceptably small losses for frequencies up to about 5 GHz. For
microwave Microwave is a form of electromagnetic radiation In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies mat ...

frequencies greater than 5 GHz, the losses (due mainly to the dielectric separating the inner and outer tubes being a non-ideal insulator) become too large, making
waveguides A waveguide is a structure that guides waves, such as electromagnetic wave Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electr ...
a more efficient medium for transmitting energy. Coaxial cables often use a perforated dielectric layer to separate the inner and outer conductors in order to minimize the power dissipated by the dielectric.

### Waveguides

Waveguides A waveguide is a structure that guides waves, such as electromagnetic wave Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electr ...
are similar to coaxial cables, as both consist of tubes, with the biggest difference being that waveguides have no inner conductor. Waveguides can have any arbitrary cross section, but rectangular cross sections are the most common. Because waveguides do not have an inner conductor to carry a return current, waveguides cannot deliver energy by means of an
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving part ...
, but rather by means of a ''guided''
electromagnetic field An electromagnetic field (also EM field) is a classical (i.e. non-quantum) field produced by accelerating electric charge Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic ...
. Although surface currents do flow on the inner walls of the waveguides, those surface currents do not carry power. Power is carried by the guided electromagnetic fields. The surface currents are set up by the guided electromagnetic fields and have the effect of keeping the fields inside the waveguide and preventing leakage of the fields to the space outside the waveguide. Waveguides have dimensions comparable to the
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase (waves), phase on the wave, such as two adjac ...

of the alternating current to be transmitted, so they are feasible only at microwave frequencies. In addition to this mechanical feasibility,
electrical resistance The electrical resistance of an object is a measure of its opposition to the flow of electric current. Its Multiplicative inverse, reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares so ...
of the non-ideal metals forming the walls of the waveguide causes
dissipation In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is governed ...
of power (surface currents flowing on lossy
conductors Conductor or conduction may refer to: Music * Conductor (music), a person who leads a musical ensemble like, for example, an orchestra. * Conductor (album), ''Conductor'' (album), an album by indie rock band The Comas * Conduction, a type of ...
dissipate power). At higher frequencies, the power lost to this dissipation becomes unacceptably large.

### Fiber optics

At frequencies greater than 200 GHz, waveguide dimensions become impractically small, and the in the waveguide walls become large. Instead,
fiber optics An optical fiber (or fibre in British English British English (BrE) is the standard dialect of the English language English is a West Germanic languages, West Germanic language first spoken in History of Anglo-Saxon England, ea ...
, which are a form of dielectric waveguides, can be used. For such frequencies, the concepts of voltages and currents are no longer used.

# Mathematics of AC voltages

Alternating currents are accompanied (or caused) by alternating voltages. An AC voltage ''v'' can be described mathematically as a
function Function or functionality may refer to: Computing * Function key A function key is a key on a computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations automatically. Modern comp ...
of time by the following equation: :$v\left(t\right) = V_\text\sin\left(\omega t\right)$, where * $V_\text$ is the peak voltage (unit:
volt The volt (symbol: V) is the SI derived unit, derived unit for electric potential, electric potential difference (voltage), and electromotive force. It is named after the Italian physicist Alessandro Volta (1745–1827). Definition One volt is ...

), * $\omega$ is the
angular frequency Angular frequency omega, ''ω'' (in radians per second), is larger than frequency ''ν'' (in cycles per second, also called Hertz, Hz), by a factor of . This figure uses the symbol ''ν'', rather than ''f'' to denote frequency. In physics, angular ...
(unit:
radians per second The radian per second (symbol: rad⋅s−1 or rad/s) is the SI unit of angular velocity, commonly denoted by the Greek letter ''ω'' (omega). The radian per second is also the SI unit of angular frequency. The radian per second is defined as ...
). The angular frequency is related to the physical frequency, $f$ (unit:
hertz The hertz (symbol: Hz) is the unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatric ...

), which represents the number of cycles per second, by the equation $\omega = 2\pi f$. * $t$ is the time (unit:
second The second (symbol: s, also abbreviated: sec) is the base unit of time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible process, irreversible succession ...
). 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 $\sin\left(x\right)$ is +1 and the minimum value is −1, an AC voltage swings between $+V_\text$ and $-V_\text$. The peak-to-peak voltage, usually written as $V_\text$ or $V_\text$, is therefore $V_\text - \left(-V_\text\right) = 2 V_\text$.

## Power

The relationship between voltage and the power delivered is: :$p\left(t\right) = \frac$ where $R$ represents a load resistance. Rather than using instantaneous power, $p\left(t\right)$, 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 In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
(RMS) value, written as $V_\text$, because :$P_\text = \frac.$ ;Power oscillation: $\begin v\left(t\right) &= V_\text\sin\left(\omega t\right) \\ i\left(t\right) &= \frac = \frac\sin\left(\omega t\right) \\ P\left(t\right) &= v\left(t\right)i\left(t\right) = \frac\sin^2\left(\omega t\right) \end$

## Root mean square voltage

Below an
AC waveform When describing a periodic function A periodic function is a function that repeats its values at regular intervals, for example, the trigonometric functions In mathematics Mathematics (from Ancient Greek, Greek: ) includes the stud ...
(with no
DC component When describing a periodic function in the time domain, the DC bias, DC component, DC offset, or DC coefficient is the mean amplitude of the waveform. If the mean amplitude is zero, there is no DC bias. A waveform with no DC bias is known as a ...
) is assumed. The RMS voltage is the square root of the
mean There are several kinds of mean in mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mat ...
over one cycle of the square of the instantaneous voltage.

## Examples of alternating current

To illustrate these concepts, consider a 230 V AC mains supply used in many countries around the world. It is so called because its
root mean square In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...
value is 230 V. This means that the time-averaged power delivered is equivalent to the power delivered by a DC voltage of 230 V. To determine the peak voltage (amplitude), we can rearrange the above equation to: :$V_\text = \sqrt\ V_\text.$ For 230 V AC, the peak voltage $V_\text$ is therefore $230\text\times\sqrt$, which is about 325 V. During the course of one cycle the voltage rises from zero to 325 V, falls through zero to −325 V, and returns to zero.

# Information transmission

Alternating current is used to transmit
information Information is processed, organised and structured data. It provides context for data and enables decision making process. For example, a single customer’s sale at a restaurant is data – this becomes information when the business is able ...

, as in the cases of
telephone A telephone is a telecommunications device that permits two or more users to conduct a conversation when they are too far apart to be heard directly. A telephone converts sound, typically and most efficiently the human voice, into electronic ...

and
cable television Cable television is a system of delivering television Television (TV), sometimes shortened to tele or telly, is a telecommunication medium used for transmitting moving images in monochrome (black and white), or in color, and in two o ...
. Information signals are carried over a wide range of AC frequencies. POTS telephone signals have a frequency of about 3 kHz, close to the
baseband Baseband is a signal that has a near-zero frequency range, i.e. a spectral magnitude that is nonzero only for frequencies in the vicinity of the origin (termed ''f'' = 0) and negligible elsewhere. In telecommunications and signal processing, ba ...

audio frequency. Cable television and other cable-transmitted information currents may alternate at frequencies of tens to thousands of megahertz. These frequencies are similar to the electromagnetic wave frequencies often used to transmit the same types of information wireless, over the air.

# History

The first alternator to produce alternating current was a dynamo electric generator based on Michael Faraday's principles constructed by the French instrument maker Hippolyte Pixii in 1832. Pixii later added a Commutator (electric), commutator to his device to produce the (then) more commonly used direct current. The earliest recorded practical application of alternating current is by Guillaume Duchenne, inventor and developer of electrotherapy. In 1855, he announced that AC was superior to
direct current Direct current (DC) is one-directional flow Flow may refer to: Science and technology * Flow (fluid) or fluid dynamics, the motion of a gas or liquid * Flow (geomorphology), a type of mass wasting or slope movement in geomorphology * Flow (mathe ...
for electrotherapeutic triggering of muscle contractions. Alternating current technology was developed further by the Hungarian Ganz Works company (1870s), and in the 1880s: Sebastian Ziani de Ferranti, Lucien Gaulard, and Galileo Ferraris. In 1876, Russian engineer Pavel Yablochkov invented a lighting system where sets of induction coils were installed along a high voltage AC line. Instead of changing voltage, the primary windings transferred power to the secondary windings which were connected to one or several Yablochkov candle, 'electric candles' (arc lamps) of his own design, used to keep the failure of one lamp from disabling the entire circuit. In 1878, the Ganz Works, Ganz factory, Budapest, Hungary, began manufacturing equipment for electric lighting and, by 1883, had installed over fifty systems in Austria-Hungary. Their AC systems used arc and incandescent lamps, generators, and other equipment.

## Transformers

Alternating current systems can use
transformer A transformer is a passive electrical device that transfers electrical energy from one electrical circuit to another, or multiple Electrical network, circuits. A varying current in any one coil of the transformer produces a varying magnetic flux ...

s to change voltage from low to high level and back, allowing generation and consumption at low voltages but transmission, possibly over great distances, at high voltage, with savings in the cost of conductors and energy losses. A bipolar open-core Transformer, power transformer developed by Lucien Gaulard and John Dixon Gibbs was demonstrated in London in 1881, and attracted the interest of Westinghouse Electric (1886), Westinghouse. They also exhibited the invention in Turin in 1884. However these early induction coils with open magnetic circuits are inefficient at transferring power to Electrical load, loads. Until about 1880, the paradigm for AC power transmission from a high voltage supply to a low voltage load was a series circuit. Open-core transformers with a ratio near 1:1 were connected with their primaries in series to allow use of a high voltage for transmission while presenting a low voltage to the lamps. The inherent flaw in this method was that turning off a single lamp (or other electric device) affected the voltage supplied to all others on the same circuit. Many adjustable transformer designs were introduced to compensate for this problematic characteristic of the series circuit, including those employing methods of adjusting the core or bypassing the magnetic flux around part of a coil. The direct current systems did not have these drawbacks, giving it significant advantages over early AC systems.

## Pioneers

direct current Direct current (DC) is one-directional flow Flow may refer to: Science and technology * Flow (fluid) or fluid dynamics, the motion of a gas or liquid * Flow (geomorphology), a type of mass wasting or slope movement in geomorphology * Flow (mathe ...
system. In 1886, the ZBD engineers designed the world's first power station that used AC generators to power a parallel-connected common electrical network, the steam-powered Rome-Cerchi power plant. The reliability of the AC technology received impetus after the Ganz Works electrified a large European metropolis: Rome in 1886. In the UK, Sebastian Ziani de Ferranti, Sebastian de Ferranti, who had been developing AC generators and transformers in London since 1882, redesigned the AC system at the Grosvenor Gallery power station in 1886 for the London Electric Supply Corporation (LESCo) including alternators of his own design and transformer designs similar to Gaulard and Gibbs. In 1890 he designed Deptford Power Station, their power station at Deptford and converted the Grosvenor Gallery station across the Thames into an electrical substation, showing the way to integrate older plants into a universal AC supply system. In the U.S., 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
transformer A transformer is a passive electrical device that transfers electrical energy from one electrical circuit to another, or multiple Electrical network, circuits. A varying current in any one coil of the transformer produces a varying magnetic flux ...

. Stanley also worked on engineering and adapting European designs such as the Gaulard and Gibbs transformer for US entrepreneur George Westinghouse who started building AC systems in 1886. The spread of Westinghouse and other AC systems triggered a push back in late 1887 by Thomas Edison (a proponent of direct current) who attempted to discredit alternating current as too dangerous in a public campaign called the "war of the currents". In 1888 alternating current systems gained further viability with introduction of a functional AC motor, something these systems had lacked up till then. The design, an induction motor, was independently invented by Galileo Ferraris and Nikola Tesla (with Tesla's design being licensed by Westinghouse in the US). This design was further developed into the modern practical three-phase form by Mikhail Dolivo-Dobrovolsky, Charles Eugene Lancelot Brown.Arnold Heertje, Mark Perlma
id=qQMOPjUgWHsC&pg=PA138&lpg=PA138&dq=tesla+motors+sparked+induction+motor&source=bl&ots=d0d_SjX8YX&sig=sA8LhTkGdQtgByBPD_ZDalCBwQA&hl=en&sa=X&ei=XoVSUPnfJo7A9gSwiICYCQ&ved=0CEYQ6AEwBA#v=onepage&q=tesla%20motors%20sparked%20induction%20motor&f=false Evolving Technology and Market Structure: Studies in Schumpeterian Economics
page 138
and Jonas Wenström. The Ames Hydroelectric Generating Plant and the original Niagara Falls Adams Power Plant were among the first hydroelectric alternating current power plants. The first long distance transmission of single-phase electricity was from a hydroelectric generating plant in Oregon at Willamette Falls which in 1890 sent power fourteen miles downriver to downtown Portland for street lighting. In 1891, a second transmission system was installed in Telluride Colorado. The San Antonio Canyon Generator was the third commercial single-phase hydroelectric AC power plant in the United States to provide long-distance electricity. It was completed on December 31, 1892, by Almarian Decker, Almarian William Decker to provide power to the city of Pomona, California, which was 14 miles away. In 1893 he designed the first commercial three-phase power plant in the United States using alternating current—the hydroelectric Mill Creek No. 1 Hydroelectric Plant near Redlands, California. Decker's design incorporated 10 kV three-phase transmission and established the standards for the complete system of generation, transmission and motors used today. The Jaruga Hydroelectric Power Plant in Croatia was set in operation on 28 August 1895. The two eElectric generator, generators (42 Hz, 550 kW each) and the transformers were produced and installed by the Hungarian company Ganz. The transmission line from the power plant to the City of Šibenik was long on wooden towers, and the municipal distribution grid 3000 V/110 V included six transforming stations. Alternating current circuit theory developed 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, 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.

* AC power * Electrical wiring * Industrial and multiphase power plugs and sockets, Heavy-duty power plugs *
Hertz The hertz (symbol: Hz) is the unit Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action, a discrete piece of action (or beat) in a theatric ...

* Mains power systems * AC power plugs and sockets * Utility frequency * War of the currents * AC/DC receiver design

# References

* 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, pp. 22–24

* "''AC/DC
What's the Difference
''". Edison's Miracle of Light

(Public Broadcasting Service, PBS) * "''AC/DC
Inside the AC Generator
'". Edison's Miracle of Light, American Experience. (PBS) * Kuphaldt, Tony R., "''Lessons In Electric Circuits

'". March 8, 2003. (Design Science License)

* Blalock, Thomas J., "

'". The history of various frequencies and interconversion schemes in the US at the beginning of the 20th century

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