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Alternating current (AC) is an
electric current An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, ...
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 (math ...
(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 Electrical energy is energy derived as a result of movement of electrically charged particles. When used loosely, ''electrical energy'' refers to energy that has been conve ...
is delivered to businesses and residences, and it is the form of
electrical energy Electrical energy is energy derived as a result of movement of electrically charged particles. When used loosely, ''electrical energy'' refers to energy that has been converted ''from'' electric potential energy. This energy is supplied by the comb ...
that consumers typically use when they plug
kitchen appliance A home appliance, also referred to as a domestic appliance, an electric appliance or a household appliance, is a machine which assists in household A household consists of one or several persons who live in the same dwelling and share meals. I ...
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 cur ...
. A common source of DC power is a battery cell in a
flashlight A flashlight (American English, US, Canadian English, Canada) or torch (British English, UK, Australian English, Australia) is a portable hand-held electric light. Formerly, the light source typically was a miniature incandescent light bulb, b ...

flashlight
. 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 ...

voltage
''. The usual
waveform In electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons The electron is a subatomic particle In physical sciences, subatomic part ...
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 Time is the indefinite continued sequence, progress of existence and ev ...

sine wave
, 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 that strengthens the weak electrical signal from a on an , , or so that it can produce sound through one or more s, which are typically housed in a wooden . A guitar amplifier may be a standalone wood or met ...
s, different waveforms are used, such as
triangular waves
triangular waves
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 A unit of time is any particular time Tim ...

square wave
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 communicating Communication (from Latin ''communicare'', meaning "to share") is the act of developing Semantics, meaning among Subject (philosophy), entities or Organization, groups through the use ...
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 informatio ...

modulation
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 ...

voltage
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 ...

transformer
. 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 ...

power line
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 plant A power station, also referred to as a power plant and sometimes generating station or generating plant, is an industrial facility for the generation A generation is "all of the people born and living Living or The Living may refer to: ...

power plant
, 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, electric pressure or electric tension is the difference in electric potential The electric poten ...
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 Electrical energy is energy derived as a result of movement of electrically charged particles. When used loosely, ''electrical energy'' refers to energy that has been convert ...

electric power transmission
, 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 generator In electricity generation, a generator is a device that converts motive power ( mechanical energy) into electrical power for use in an external circuit. So ...
, 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 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. "Ph ...
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 Ground and neutral are circuit conductors used in alternating current electrical systems. The ground circuit is connected to earth, and neutral circuit is usually connected to ground. As the neutral point of an electrical supply system is often co ...
. 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 A harmonic is any member of the harmonic series Harmonic series may refer to either of two related concepts: *Harmonic series (mathematics) *Harmonic series (music) {{Disambig .... The term is employed in various disciplines, including music ...
. 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 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 ...
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 engineering is an engineering discipline concerned with the study, design, and application of equipment, devices, and systems which use electricity, electronics, and electromagnetism. It emerged as an ident ...
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 Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action ...

Hertz
. Some countries have a mixture of 50 Hz and 60 Hz supplies, notably
electricity power transmission in Japan
electricity power transmission in Japan
. A low frequency eases the design of electric motors, particularly for hoisting, crushing and rolling applications, and commutator-type
traction motor A traction motor is an electric motor used for propulsion of a vehicle, such as locomotive File:R707-loco-victorian-railways.jpg, upright=1.2, An Victorian Railways R class, R class steam locomotive number R707 as operated by the Victorian Railwa ...
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 that transports people or cargo. Vehicles include wagons, bicycles, motor veh ...

railway
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 An incandescent light bulb, incandescent lamp or incandescent light globe is an with a wire heated until it glows. The filament is enclosed in a glass bulb with a vacuum or inert gas to protect the filament from . Current is supplied to the ...

incandescent light bulb
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 (, ; german: Österreich ), officially the Republic of Austria (german: Republik Österreich, links=no, ), is a landlocked A landlocked country is a country that does not have territory connected to an ocean or whose coastli ...

Austria
,
Germany ) , image_map = , map_caption = , map_width = 250px , capital = Berlin Berlin (; ) is the and by both area and population. Its 3,769,495 inhabitants, as of 31 December 2019 makes it the , according to population within city l ...

Germany
,
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 Norwegian (Norwegian: ''norsk'') is a Nort ...

Norway
,
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 fo ...

Sweden
and
Switzerland , french: Suisse(sse), it, svizzero/svizzera or , rm, Svizzer/Svizra , government_type = Federalism, Federal semi-direct democracy under an assembly-independent Directorial system, directorial republic , leader_title1 = Fe ...

Switzerland
. 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 pair of IBM mainframes. On the left is the IBM z Systems z13. On the right is the IBM LinuxONE Rockhopper.">IBM_LinuxONE.html" ;"title="IBM z Systems z13. On the right is the IBM LinuxONE">IBM z Systems z13. On the right is the IBM LinuxONE R ...
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 c ...
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 The United States Navy Reserve (USNR), known as the Un ...

waves
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. ...

electromagnetic radiation
that cancel the propagation of electricity toward the center of materials with high conductivity. This phenomenon is called
skin effect Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor Conductor or conduction may refer to: Music * Conductor (music), a person who leads a musical ensemble like, for example, an or ...

skin effect
. 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 ...

skin depth
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 ...

ohmic heating
(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 passive Passive may refer to: * Passive voice, a grammatical voice common in many languages, see also Pseudopassive (disambiguation), Pseudopassive * Passive language, a language from whi ...

inductor
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 Oscillation is the repetitive variation, typically in time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible p ...
current (up to hundreds of kilohertz), such as switch-mode
power supplies#REDIRECT Power supply#REDIRECT Power supply A power supply is an electrical device that supplies electric power to an electrical load. The primary function of a power supply is to convert electric current from a source to the correct voltage, ele ...

power supplies
and
radio frequency Radio frequency (RF) is the oscillation Oscillation is the repetitive variation, typically in time Time is the indefinite continued sequence, progress of existence and event (philosophy), events that occur in an apparently irreversible p ...
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 ...

transformer
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 c ...
under periodic
acceleration In mechanics Mechanics (Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approx ...

acceleration
, 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 ...

radiation
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 ...

electromagnetic waves
. 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 Electronic circuit, circuit are twisted together for the purposes of improving electromagnetic compatibility. Compared to a Single-ended signaling, single conductor o ...

twisted pair
. 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. ...

electromagnetic radiation
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 consisting of an inner surrounded by a concentric conducting , with the two separated by a ( material); many coaxial cables also have a protective outer sheath or jacket. The term ' refers t ...
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 i ...

dielectric
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 ...

microwave
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 particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, ...
, but rather by means of a ''guided''
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field Field may refer to: Expanses of open ground * Field (agriculture), an area of land used for agricultural purposes * Airfield, an aerodrome that lacks the in ...
. Although
surface currents
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 adja ...

wavelength
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 An electric current is a stream of charged particle In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epi ...
of the non-ideal metals forming the walls of the waveguide causes
dissipation In , dissipation is the result of an that takes place in homogeneous . In a dissipative process, (, bulk flow , or system ) from an initial form to a final form, where the capacity of the final form to do is less than that of the initial form. ...
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
ohmic losses
ohmic losses
in the waveguide walls become large. Instead,
fiber optics An optical fiber (or fibre in ) is a flexible, made by () or plastic to a diameter slightly thicker than that of a . Optical fibers are used most often as a means to transmit light between the two ends of the fiber and find wide usage in ...
, 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(t) = V_\text\sin(\omega t), where * V_\text is the peak voltage (unit:
volt The volt is the derived unit for electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work (physics), work energy needed to move a ...

volt
), * \omega is the
angular frequency In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succ ...
(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 ...
). 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 Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action ...

hertz
), 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 continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, th ...
). 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(x) 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 - (-V_\text) = 2 V_\text.


Power

The relationship between voltage and the power delivered is: :p(t) = \frac where R represents a load resistance. Rather than using instantaneous power, p(t), 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(t) &= V_\text\sin(\omega t) \\ i(t) &= \frac = \frac\sin(\omega t) \\ P(t) &= v(t)i(t) = \frac\sin^2(\omega t) \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, especially in statistics. For a data set, the ''arithmetic mean'', also known as arithmetic average, is a central value of a finite set of numbers: specifically, the sum of the values divided by ...
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 Data (; ) are individual facts A fact is something that is truth, true. The usual test for a statement of fact is verifiability—that is whether it can be demonstrated to c ...

information
, as in the cases of
telephone A telephone is a telecommunication Telecommunication is the transmission of information by various types of technologies over wire A wire is a single usually cylindrical A cylinder (from Greek Greek may refer to: Greece Anyt ...

telephone
and
cable television Cable television is a system of delivering television Television, sometimes shortened to TV or telly, is a telecommunication Media (communication), medium used for transmitting moving images in grayscale, black-and-white or in color, ...
. 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 In signal processing Signal processing is an electrical engineering subfield that focuses on analysing, modifying, and synthesizing signals such as audio signal processing, sound, image processing, images, and scien ...

baseband
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
over the air
over the air
.


History

The first
alternator An alternator is an electrical generator In electricity generation Electricity generation is the process of generating electric power from sources of primary energy. For electric utility, utilities in the electric power industry, it is the s ...

alternator
to produce alternating current was a
dynamo A dynamo is an that creates using a . Dynamos were the first electrical generators capable of delivering power for industry, and the foundation upon which many other later devices were based, including the , the , and the . Today, the simple ...

dynamo
electric generator based on
Michael Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical method of acquiring knowledge ...

Michael Faraday
's principles constructed by the French instrument maker
Hippolyte Pixii An early form of an alternating current electrical generator built by Pixii Hippolyte Pixii (1808–1835) was an instrument maker from Paris, France. In 1832 he built an early form of alternating current Alternating current (AC) is an electric ...
in 1832. Pixii later added a
commutator In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained (), and quantities and their changes ( and ). There is no gene ...
to his device to produce the (then) more commonly used direct current. The earliest recorded practical application of alternating current is by
Guillaume Duchenne Guillaume-Benjamin-Amand Duchenne (de Boulogne) (September 17, 1806 in Boulogne-sur-Mer – September 15, 1875 in Paris) was a French neurologist who revived Luigi Galvani, Galvani's research and greatly advanced the science of electrophysiology. ...
, inventor and developer of
electrotherapy Electrotherapy is the use of electrical energy as a medical treatment. In medicine, the term ''electrotherapy'' can apply to a variety of treatments, including the use of electrical devices such as deep brain stimulation, deep brain stimulators fo ...
. 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 (math ...
for electrotherapeutic triggering of muscle contractions. Alternating current technology was developed further by the Hungarian
Ganz Works The Ganz Works or Ganz ( or , ''Ganz companies'', formerly ''Ganz and Partner Iron Mill and Machine Factory'') was a group of companies operating between 1845 and 1949 in Budapest, Hungary. It was named after Ábrahám Ganz, the founder and the ...
company (1870s), and in the 1880s:
Sebastian Ziani de Ferranti Sebastian Pietro Innocenzo Adhemar Ziani de Ferranti (9 April 1864 – 13 January 1930) was a British electrical engineer and inventor. Personal life Sebastian Ziani de Ferranti was born in Liverpool Liverpool is a City status in the U ...

Sebastian Ziani de Ferranti
,
Lucien Gaulard Lucien Gaulard (16 July 1850 – 26 November 1888) invented devices for the transmission of alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with t ...
, and
Galileo Ferraris Galileo Ferraris (31 October 1847 – 7 February 1897) was an Italian university professor, physicist and electrical engineer, one of the pioneers of AC power system and an inventor of the three-phase induction motor upright=1.15, Cutaway vie ...

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 ...

transformer
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 Lucien Gaulard (16 July 1850 – 26 November 1888) invented devices for the transmission of alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with t ...
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

In the autumn of 1884, Károly Zipernowsky, Ottó Bláthy and Miksa Déri (ZBD), three engineers associated with the
Ganz Works The Ganz Works or Ganz ( or , ''Ganz companies'', formerly ''Ganz and Partner Iron Mill and Machine Factory'') was a group of companies operating between 1845 and 1949 in Budapest, Hungary. It was named after Ábrahám Ganz, the founder and the ...
of Budapest, determined that open-core devices were impractical, as they were incapable of reliably regulating voltage. In their joint 1885 patent applications for novel transformers (later called ZBD transformers), they described two designs with closed magnetic circuits where copper windings were either wound around a ring core of iron wires or else surrounded by a core of iron wires. In both designs, the magnetic flux linking the primary and secondary windings traveled almost entirely within the confines of the iron core, with no intentional path through air (see transformer#Toroidal cores, toroidal cores). The new transformers were 3.4 times more efficient than the open-core bipolar devices of Gaulard and Gibbs. The Ganz factory in 1884 shipped the world's first five high-efficiency AC transformers. This first unit had been manufactured to the following specifications: 1,400 W, 40 Hz, 120:72 V, 11.6:19.4 A, ratio 1.67:1, one-phase, shell form. The ZBD patents included two other major interrelated innovations: one concerning the use of parallel connected, instead of series connected, utilization loads, the other concerning the ability to have high turns ratio transformers such that the supply network voltage could be much higher (initially 1400 V to 2000 V) than the voltage of utilization loads (100 V initially preferred). When employed in parallel connected electric distribution systems, closed-core transformers finally made it technically and economically feasible to provide electric power for lighting in homes, businesses and public spaces. Bláthy had suggested the use of closed cores, Zipernowsky had suggested the use of Shunt (electrical), parallel shunt connections, and Déri had performed the experiments; The other essential milestone was the introduction of 'voltage source, voltage intensive' (VSVI) systems' by the invention of constant voltage generators in 1885. In early 1885, the three engineers also eliminated the problem of eddy current losses with the invention of the lamination of electromagnetic cores. Ottó Bláthy also invented the first AC electricity meter. Student paper read on January 24, 1896, at the Students' Meeting. The AC power system was developed and adopted rapidly after 1886 due to its ability to distribute electricity efficiently over long distances, overcoming the limitations of the
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 (math ...
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 ...

transformer
. 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 Galileo Ferraris (31 October 1847 – 7 February 1897) was an Italian university professor, physicist and electrical engineer, one of the pioneers of AC power system and an inventor of the three-phase induction motor upright=1.15, Cutaway vie ...

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.


See also

* 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 Unit may refer to: Arts and entertainment * UNIT, a fictional military organization in the science fiction television series ''Doctor Who'' * Unit of action ...

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


References


Further reading

* 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


External links

* "''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

{{Authority control Electrical engineering Electric current Electric power AC power,