Alternating Current
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Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to
direct current Direct current (DC) is one-directional flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or eve ...
(DC) which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug
kitchen 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 functions such as cooking, cleaning and food preservation. Appliances are divided into three ty ...
s, televisions, fans and electric lamps into a
wall socket AC power plugs and sockets connect electric equipment to the alternating current (AC) mains electricity power supply in buildings and at other sites. Electrical plugs and sockets differ from one another in voltage and electric current, current ...
. A common source of DC power is a
battery cell An electrochemical cell is a device capable of either generating electrical energy from chemical reactions or using electrical energy to cause chemical reactions. The electrochemical cells which generate an electric current are called voltaic o ...
in a flashlight. The abbreviations ''AC'' and ''DC'' are often used to mean simply ''alternating'' and ''direct'', as when they modify ''
current Currents, Current or The Current may refer to: Science and technology * Current (fluid), the flow of a liquid or a gas ** Air current, a flow of air ** Ocean current, a current in the ocean *** Rip current, a kind of water current ** Current (stre ...
'' or ''
voltage Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
''. The usual
waveform In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electro ...
of alternating current in most electric power circuits is a 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 electronic device or system that strengthens the electrical signal from a pickup on an electric guitar, bass guitar, or acoustic guitar so that it can produce sound through one or more loudspeakers, which ar ...
s, different waveforms are used, such as triangular waves or square waves.
Audio Audio most commonly refers to sound, as it is transmitted in signal form. It may also refer to: Sound * Audio signal, an electrical representation of sound *Audio frequency, a frequency in the audio spectrum * Digital audio, representation of sou ...
and
radio Radio is the technology of signaling and 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 called a transmit ...
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 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, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
may be increased or decreased with a
transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
. This allows the power to be transmitted through
power line An overhead power line is a structure used in electric power transmission and distribution to transmit electrical energy across large distances. It consists of one or more uninsulated electrical cables (commonly multiples of three for three-p ...
s efficiently at
high voltage High voltage electricity refers to electrical potential large enough to cause injury or damage. In certain industries, ''high voltage'' refers to voltage above a certain threshold. Equipment and conductors that carry high voltage warrant spec ...
, which reduces the energy lost as heat due to resistance 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 (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 electricity generation, generation of electric power. Power stations are generally connected to an el ...
, energy is generated at a convenient voltage for the design of a
generator Generator may refer to: * Signal generator, electronic devices that generate repeating or non-repeating electronic signals * Electric generator, a device that converts mechanical energy to electrical energy. * Generator (circuit theory), an eleme ...
, 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, voltages and frequencies they commonly use for providing electrical power to low voltage appliances, equipment, and lighting typically found in homes an ...
found in the world.
High-voltage direct-current A high-voltage direct current (HVDC) electric power transmission system (also called a power superhighway or an electrical superhighway) uses direct current (DC) for electric power transmission, in contrast with the more common alternating curre ...
(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, 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 Three-phase electric power (abbreviated 3φ) is a common type of alternating current used in electricity generation, Electric power transmission, transmission, and Electric power distribution, distribution. It is a type of polyphase system empl ...
electrical generation is very common. The simplest way is to use three separate coils in the generator stator, 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 and mathematics, the phase of a periodic function F of some real variable t (such as time) is an angle-like quantity representing the fraction of the cycle covered up to t. It is denoted \phi(t) and expressed in such a scale that it ...
to each other. If coils are added opposite to these (60° spacing), they generate the same phases with reverse
polarity Polarity may refer to: Science *Electrical polarity, direction of electrical current *Polarity (mutual inductance), the relationship between components such as transformer windings * Polarity (projective geometry), in mathematics, a duality of ord ...
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 A harmonic is a wave with a frequency that is a positive integer multiple of the '' fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', ...
. 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 In electrical engineering, single-phase electric power (abbreviated 1φ) is the distribution of alternating current electric power using a system in which all the voltages of the supply vary in unison. Single-phase distribution is used when loads ...
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 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 Third Wire Productions Inc. is a C corporation based in Austin, Texas, United States; it is an independent software development company founded in 1999 to create multimedia entertainment, such as Amateur flight simulation, amateur flight simulat ...
, 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, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. Quantitatively, the impedance of a two-terminal circuit element is the ratio of the com ...
path to ground sufficient to carry any fault current for as long as it takes for the system to clear the fault. This low impedance path allows the maximum amount of fault current, 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 of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that on ...
. Some countries have a mixture of 50 Hz and 60 Hz supplies, notably 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 locomotives, electric or hydrogen vehicles, elevators or electric multiple unit. Traction motors are used in electrically powered rail vehicles ( electric multiple ...
s for applications such as
railway Rail transport (also known as train transport) is a means of transport that transfers passengers and goods on wheeled vehicles running on rails, which are incorporated in tracks. In contrast to road transport, where the vehicles run on a pre ...
s. However, low frequency also causes noticeable flicker in arc lamps and
incandescent light bulb An incandescent light bulb, incandescent lamp or incandescent light globe is an electric light with a wire filament heated until it glows. The filament is enclosed in a glass bulb with a vacuum or inert gas to protect the filament from oxid ...
s. The use of lower frequencies also provided the advantage of lower transmission 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, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ...
,
Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...
,
Norway Norway, officially the Kingdom of Norway, is a Nordic country in Northern Europe, the mainland territory of which comprises the western and northernmost portion of the Scandinavian Peninsula. The remote Arctic island of Jan Mayen and t ...
,
Sweden Sweden, formally the Kingdom of Sweden,The United Nations Group of Experts on Geographical Names states that the country's formal name is the Kingdom of SwedenUNGEGN World Geographical Names, Sweden./ref> is a Nordic country located on ...
and
Switzerland ). Swiss law does not designate a ''capital'' as such, but the federal parliament and government are installed in Bern, while other federal institutions, such as the federal courts, are in other cities (Bellinzona, Lausanne, Luzern, Neuchâtel ...
. 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 systems were often powered by 400 Hz or 415 Hz for benefits of
ripple Ripple may refer to: Science and technology * Capillary wave, commonly known as ripple, a wave traveling along the phase boundary of a fluid ** Ripple, more generally a disturbance, for example of spacetime in gravitational waves * Ripple (electri ...
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 homogeneous electrically conducting wire. An alternating current of any frequency is forced away from the wire's center, toward its outer surface. This is because an alternating current (which is the result of the acceleration of
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
) creates electromagnetic waves (a phenomenon known as
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) li ...
). Electric conductors are not conducive to electromagnetic waves (a perfect electric conductor prohibits all electromagnetic waves within its boundary), so a wire that is made of a non-perfect conductor (a conductor with finite, rather than infinite, electrical conductivity) pushes the alternating current, along with their associated electromagnetic fields, away from the wire's center. The phenomenon of alternating current being pushed away from the center of the conductor is called skin effect, and a direct current does not exhibit this effect, since a direct current does not create electromagnetic waves. 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 Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the co ...
s. The skin depth is the thickness at which the current density is reduced by 63% (a reduction of one neper). Even at relatively low frequencies used for power transmission (50 Hz – 60 Hz), non-uniform distribution of current still occurs in sufficiently thick conductors. For example, the skin depth of a copper conductor is approximately 8.57 mm at 60 Hz, so high current conductors are usually hollow to reduce their mass and cost. Since the current tends to flow in the periphery of conductors, the effective cross-section of the conductor is reduced. This increases the effective AC resistance of the conductor, since resistance is inversely proportional to the cross-sectional area. The AC resistance is often 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 through a conductor produces heat. Joule's first law (also just Joule's law), also known in countries of former US ...
(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. 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 two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a 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 electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the ...
current (up to hundreds of kilohertz), such as switch-mode
power supplies A power supply is an electrical device that supplies electric power to an electrical load. The main purpose of a power supply is to convert electric current from a source to the correct voltage, current, and frequency to power the load. As a res ...
and
radio frequency Radio frequency (RF) is the oscillation rate of an alternating electric current or voltage or of a magnetic, electric or electromagnetic field or mechanical system in the frequency range from around to around . This is roughly between the ...
transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the 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 charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
under periodic
acceleration In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...
, which causes radiation of 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 used for communications in which two conductors of a single circuit are twisted together for the purposes of improving electromagnetic compatibility. Compared to a single conductor or an untwisted ba ...
. This reduces losses from
electromagnetic radiation In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) li ...
and inductive coupling. 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 cables are commonly used at
audio frequencies An audio frequency or audible frequency (AF) is a periodic function, periodic vibration whose frequency is human hearing range, audible to the average human. The International System of Units, SI unit of frequency is the hertz (Hz). It is the pr ...
and above for convenience. A coaxial cable has a conductive wire inside a conductive tube, separated by a
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
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 with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ra ...
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 waves or sound, with minimal loss of energy by restricting the transmission of energy to one direction. Without the physical constraint of a waveguide, wave intensities de ...
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 waves or sound, with minimal loss of energy by restricting the transmission of energy to one direction. Without the physical constraint of a waveguide, wave intensities de ...
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, but rather by means of a ''guided'' electromagnetic field. 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 on the wave, such as two adjacent crests, t ...
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 reciprocal quantity is , measuring the ease with which an electric current passes. Electrical resistance shares some conceptual paralle ...
of the non-ideal metals forming the walls of the waveguide causes
dissipation In thermodynamics, dissipation is the result of an irreversible process that takes place in homogeneous thermodynamic systems. In a dissipative process, energy ( internal, bulk flow kinetic, or system potential) transforms from an initial form to ...
of power (surface currents flowing on lossy conductors 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 in the waveguide walls become large. Instead, fiber optics, which are a form of dielectric waveguides, can be used. For such frequencies, the concepts of voltages and currents are no longer used.


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 type of key on computer keyboards * Function model, a structured representation of processes in a system * Function object or functor or functionoid, a concept of object-oriente ...
of time by the following equation: :v(t) = V_\text\sin(\omega t), where * V_\text is the peak voltage (unit:
volt The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). It is named after the Italian physicist Alessandro Volta (1745–1827). Defi ...
), * \omega is the
angular frequency In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...
(unit:
radians per second The radian per second (symbol: rad⋅s−1 or rad/s) is the unit of angular velocity in the International System of Units (SI). The radian per second is also the SI unit of angular frequency, commonly denoted by the Greek letter ''ω'' (omega). ...
). The angular frequency is related to the physical frequency, f (unit:
hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that on ...
), 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) is the unit of time in the International System of Units (SI), historically defined as of a day – this factor derived from the division of the day first into 24 hours, then to 60 minutes and finally to 60 seconds ...
). 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 (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 In signal processing, 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 ...
(with no
DC component DC, D.C., D/C, Dc, or dc may refer to: Places * Washington, D.C. (District of Columbia), the capital and the federal territory of the United States * Bogotá, Distrito Capital, the capital city of Colombia * Dubai City, as distinct from th ...
) is assumed. The RMS voltage is the square root of the
mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value (magnitude and sign) of a given data set. For a data set, the '' ari ...
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 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 an abstract concept that refers to that which has the power to inform. At the most fundamental level information pertains to the interpretation of that which may be sensed. Any natural process that is not completely random ...
, 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 easily heard directly. A telephone converts sound, typically and most efficiently the human voice, into e ...
and
cable television Cable television is a system of delivering television programming to consumers via radio frequency (RF) signals transmitted through coaxial cables, or in more recent systems, light pulses through fibre-optic cables. This contrasts with bro ...
. 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 In telecommunications and signal processing, baseband is the range of frequencies occupied by a signal that has not been modulated to higher frequencies. Baseband signals typically originate from transducers, converting some other variable int ...
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 was an annual mobile technology-focused overnight hack day event held in London from 2008 to 2016. The two-day event would include practical and educational talks and a hacking competition. Sponsors of the event have included the B ...
.


History

The first
alternator An alternator is an electrical generator that converts mechanical energy to electrical energy in the form of alternating current. For reasons of cost and simplicity, most alternators use a rotating magnetic field with a stationary armature.Gor ...
to produce alternating current was a
dynamo "Dynamo Electric Machine" (end view, partly section, ) A dynamo is an electrical generator that creates direct current using a commutator. Dynamos were the first electrical generators capable of delivering power for industry, and the foundati ...
electric generator based on
Michael Faraday Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic inducti ...
's principles constructed by the French instrument maker
Hippolyte Pixii Hippolyte Pixii (1808–1835) was an instrument maker from Paris, France. In 1832 he built an early form of alternating current electrical generator, based on the principle of electromagnetic induction discovered by Michael Faraday. Mohamed A. El- ...
in 1832. Pixii later added a 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 Guillaume-Benjamin-Amand Duchenne (de Boulogne) (September 17, 1806 in Boulogne-sur-Mer – September 15, 1875 in Paris) was a French neurologist who revived Galvani's research and greatly advanced the science of electrophysiology. The era of m ...
, 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 stimulators for neurological dise ...
. In 1855, he announced that AC was superior to
direct current Direct current (DC) is one-directional flow of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or eve ...
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, England. His Italian father, Cesare, was a ...
,
Lucien Gaulard Lucien Gaulard (16 July 1850 – 26 November 1888) invented devices for the transmission of alternating current electrical energy. Biography Gaulard was born in Paris, France in 1850. A power transformer developed by Gaulard of France and John ...
, 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 inventor of the induction motor although he never patented his work. Many ...
. In 1876, Russian engineer
Pavel Yablochkov Pavel Nikolayevich Yablochkov (also transliterated as Jablochkoff; russian: Павел Николаевич Яблочков) ( – ) was a Russian electrical engineer, businessman and the inventor of the Yablochkov candle (a type of electric ...
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 '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 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 component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the 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
power transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer's c ...
developed by
Lucien Gaulard Lucien Gaulard (16 July 1850 – 26 November 1888) invented devices for the transmission of alternating current electrical energy. Biography Gaulard was born in Paris, France in 1850. A power transformer developed by Gaulard of France and John ...
and
John Dixon Gibbs John Dixon Gibbs (1834–1912) was a British engineer and financier who, together with Lucien Gaulard, is often credited as the co-inventor of the AC step-down transformer. The transformer was first demonstrated in 1883 at London's Royal Aquarium ...
was demonstrated in London in 1881, and attracted the interest of Westinghouse. They also exhibited the invention in
Turin Turin ( , Piedmontese language, Piedmontese: ; it, Torino ) is a city and an important business and cultural centre in Northern Italy. It is the capital city of Piedmont and of the Metropolitan City of Turin, and was the first Italian capital ...
in 1884. However these early induction coils with open magnetic circuits are inefficient at transferring power to 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 Károly Zipernowsky (born as Carl Zipernowsky, 4 April 1853 in Vienna – 29 November 1942 in Budapest) was an Austrian-born Hungarian electrical engineer. He invented the transformer with his colleagues (Miksa Déri and Ottó Bláthy) at t ...
,
Ottó Bláthy Ottó Titusz Bláthy (11 August 1860 – 26 September 1939) was a Hungarian electrical engineer. In his career, he became the co-inventor of the modern electric transformer, the tension regulator, the AC watt-hour meter. motor capacitor f ...
and
Miksa Déri Miksa Déri (27 October 1854 November, Bács, Kingdom of Hungary, (now: Bač, Serbia) – 3 March 1938) was a Hungarian electrical engineer, inventor, power plant builder. He contributed with his partners Károly Zipernowsky and Ottó Bláth ...
(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
toroidal cores Toroidal describes something which resembles or relates to a torus or toroid: Mathematics *Torus *Toroid, a surface of revolution which resembles a torus *Toroidal polyhedron *Toroidal coordinates, a three-dimensional orthogonal coordinate system ...
). 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 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 Eddy currents (also called Foucault's currents) are loops of electrical current induced within conductors by a changing magnetic field in the conductor according to Faraday's law of induction or by the relative motion of a conductor in a magnet ...
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 of electric charge. An electrochemical cell is a prime example of DC power. Direct current may flow through a conductor such as a wire, but can also flow through semiconductors, insulators, or eve ...
system. In 1886, the ZBD engineers designed the world's first
power station A power station, also referred to as a power plant and sometimes generating station or generating plant, is an industrial facility for the generation of electric power. Power stations are generally connected to an electrical grid. Many p ...
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 , established_title = Founded , established_date = 753 BC , founder = King Romulus (legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...
in 1886. In the UK,
Sebastian 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, England. His Italian father, Cesare, was ...
, 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 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. William Stanley Jr. (November 28, 1858 – May 14, 1916) was an American physicist born in Brooklyn, New York. During his career, he obtained 129 patents covering a variety of electric devices. In 1913, he also patented an all-steel vacuum bottl ...
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 component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
. Stanley also worked on engineering and adapting European designs such as the Gaulard and Gibbs transformer for US entrepreneur
George Westinghouse George Westinghouse Jr. (October 6, 1846 – March 12, 1914) was an American entrepreneur and engineer based in Pennsylvania who created the railway air brake and was a pioneer of the electrical industry, receiving his first patent at the age ...
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 Thomas Alva Edison (February 11, 1847October 18, 1931) was an American inventor and businessman. He developed many devices in fields such as electric power generation, mass communication, sound recording, and motion pictures. These inventio ...
(a proponent of direct current) who attempted to discredit alternating current as too dangerous in a public campaign called the "
war of the currents The war of the currents was a series of events surrounding the introduction of competing electric power transmission systems in the late 1880s and early 1890s. It grew out of two lighting systems developed in the late 1870s and early 1880s; arc ...
". In 1888, alternating current systems gained further viability with introduction of a functional
AC motor An AC motor is an electric motor driven by an alternating current (AC). The AC motor commonly consists of two basic parts, an outside stator having coils supplied with alternating current to produce a rotating magnetic field, and an inside rotor ...
, 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 inventor of the induction motor although he never patented his work. Many ...
and
Nikola Tesla Nikola Tesla ( ; ,"Tesla"
''
three-phase Three-phase electric power (abbreviated 3φ) is a common type of alternating current used in electricity generation, Electric power transmission, transmission, and Electric power distribution, distribution. It is a type of polyphase system empl ...
form by
Mikhail Dolivo-Dobrovolsky Mikhail Osipovich Dolivo-Dobrovolsky (russian: Михаи́л О́сипович Доли́во-Доброво́льский; german: Michail von Dolivo-Dobrowolsky or ''Michail Ossipowitsch Doliwo-Dobrowolski''; – ) was a Russian Empire ...
,
Charles Eugene Lancelot Brown Brown c. 1900 Charles Eugene Lancelot Brown (17 June 1863 – 2 May 1924) was a Swiss businessman and engineer who co-founded Brown, Boveri & Cie (BBC), which later became ASEA Brown Boveri. Biography Brown was born on 17 June 1863 in Winterth ...
, and
Jonas Wenström Jonas Wenström (August 4, 1855 in Hällefors – December 22, 1893 in Västerås) was a Swedish engineer and inventor. the basis for ASEA (later ABB ABB Ltd. is a Swedish- Swiss multinational corporation headquartered in Zürich, Swi ...
. The
Ames Hydroelectric Generating Plant The Ames Hydroelectric Generating Plant, constructed in 1890 near Ophir, Colorado, was one of the first (if not the first) commercial system to produce and transmit alternating current (AC) electricity for industrial use and one of the first AC hy ...
and the original Niagara Falls
Adams Power Plant Adams Power Plant Transformer House in Niagara Falls, New York is a National Historic Landmarked building constructed in 1895. It is the only remaining structure that was part of the historic Edward Dean Adams Power Plant, the first large-scale, a ...
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 William Decker to provide power to the city of
Pomona, California Pomona is a city in Los Angeles County, California. Pomona is located in the Pomona Valley, between the Inland Empire and the San Gabriel Valley. At the 2020 census, the city's population was 151,713. The main campus of California State Pol ...
, which was 14 miles away. In 1893, he designed the first commercial
three-phase Three-phase electric power (abbreviated 3φ) is a common type of alternating current used in electricity generation, Electric power transmission, transmission, and Electric power distribution, distribution. It is a type of polyphase system empl ...
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 Jaruga Hydroelectric Power Plant is a hydroelectric power plant on river Krka, located in Šibenik-Knin County, in central Dalmatia, Croatia. The first European hydroelectric power plant was built in Croatia (many people worked together to make ...
in Croatia was set in operation on 28 August 1895. The two generators (42 Hz, 550 kW each) and the transformers were produced and installed by the Hungarian company
Ganz 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 th ...
. The transmission line from the power plant to the City of
Šibenik Šibenik () is a historic city in Croatia, located in central Dalmatia, where the river Krka flows into the Adriatic Sea. Šibenik is a political, educational, transport, industrial and tourist center of Šibenik-Knin County, and is also the ...
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 Charles Proteus Steinmetz (born Karl August Rudolph Steinmetz, April 9, 1865 – October 26, 1923) was a German-born American mathematician and electrical engineer and professor at Union College. He fostered the development of alternating ...
,
Oliver Heaviside Oliver Heaviside FRS (; 18 May 1850 – 3 February 1925) was an English self-taught mathematician and physicist who invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed ...
, 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 * Heavy-duty power plugs *
Hertz The hertz (symbol: Hz) is the unit of frequency in the International System of Units (SI), equivalent to one event (or cycle) per second. The hertz is an SI derived unit whose expression in terms of SI base units is s−1, meaning that on ...
*
Mains electricity by country Mains electricity by country includes a list of countries and territories, with the plugs, voltages and frequencies they commonly use for providing electrical power to low voltage appliances, equipment, and lighting typically found in homes an ...
*
AC power plugs and sockets AC power plugs and sockets connect electric equipment to the alternating current (AC) mains electricity power supply in buildings and at other sites. Electrical plugs and sockets differ from one another in voltage and electric current, current ...
*
Utility frequency The utility frequency, (power) line frequency (American English) or mains frequency (British English) is the nominal frequency of the oscillations of alternating current (AC) in a wide area synchronous grid transmitted from a power station to t ...
*
War of the currents The war of the currents was a series of events surrounding the introduction of competing electric power transmission systems in the late 1880s and early 1890s. It grew out of two lighting systems developed in the late 1870s and early 1880s; arc ...
*
AC/DC receiver design An AC/DC receiver design is a style of power supply of vacuum tube radio or television receivers that eliminated the bulky and expensive mains transformer. A side-effect of the design was that the receiver could in principle operate from a DC su ...


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

(
PBS The Public Broadcasting Service (PBS) is an American public broadcaster and non-commercial, free-to-air television network based in Arlington, Virginia. PBS is a publicly funded nonprofit organization and the most prominent provider of educat ...
) * "''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