Alternating current

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Alternating current (green curve). The horizontal axis measures time (it also represents zero voltage/current) ; the vertical, current or voltage.


The usual waveform 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 amplifiers, different waveforms are used, such as triangular waves or square waves. Audio and radio 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[edit]

A schematic representation of long distance electric power transmission. From left to right: G=generator, U=step up transformer, V=voltage at beginning of transmission line, Pt=power entering transmission line, I=current in wires, R=total resistance in wires, Pw=power lost in transmission line, Pe=power reaching the end of the transmission line, D=step down transformer , C=consumers.

Electrical energy is distributed as alternating current because AC voltage may be increased or decreased with a transformer. This allows the power to be transmitted through power lines efficiently at high voltage, 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 () in the wire are a product of the square of the current ( I ) and the resistance (R) of the wire, described by the formula:

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.


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.

Three-phase high voltage transmission lines use alternating currents to distribute power over long distances between electric generation plants and consumers. The lines in the picture are located in eastern Utah.





AC power supply frequencies[edit]


Effects at high frequencies[edit]



Techniques for reducing AC resistance[edit]


Techniques for reducing radiation loss[edit]


Twisted pairs[edit]


Coaxial cables[edit]

Coaxial cables are commonly used at audio frequencies and above for convenience. A coaxial cable has a conductive wire inside a conductive tube, separated by a 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 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 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 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 of the alternating current to be transmitted, so they are feasible only at microwave frequencies. In addition to this mechanical feasibility, electrical resistance of the non-ideal metals forming the walls of the waveguide causes dissipation of power (surface currents flowing on lossy conductors dissipate power). At higher frequencies, the power lost to this dissipation becomes unacceptably large.

Fiber optics[edit]


Mathematics of AC voltages[edit]

A sinusoidal alternating voltage.
  1. Peak, also amplitude,
  2. Peak-to-peak,
  3. Effective value,
  4. Period




  • is the peak voltage (unit: volt),
  • is the angular frequency (unit: radians per second).
    The angular frequency is related to the physical frequency, (unit: hertz), which represents the number of cycles per second, by the equation .
  • is the time (unit: second).



The relationship between voltage and the power delivered is:

where represents a load resistance.


Power oscillation

Root mean square voltage[edit]

Below an AC waveform (with no DC component) is assumed.

The RMS voltage is the square root of the mean over one cycle of the square of the instantaneous voltage.

  • For an arbitrary periodic waveform of period :
  • For a sinusoidal voltage:
  • For a triangle waveform centered about zero
  • For a square waveform centered about zero

Examples of alternating current[edit]


For 230 V AC, the peak voltage is therefore , 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[edit]




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 'electric candles' (arc lamps) of his own design,[6][7] used to keep the failure of one lamp from disabling the entire circuit.[6] 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.[8]





In the autumn of 1884, Károly Zipernowsky, Ottó Bláthy and Miksa Déri (ZBD), three engineers associated with the Ganz Works of Budapest, determined that open-core devices were impractical, as they were incapable of reliably regulating voltage.[10] 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.[9] 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). The new transformers were 3.4 times more efficient than the open-core bipolar devices of Gaulard and Gibbs.[11] The Ganz factory in 1884 shipped the world's first five high-efficiency AC transformers.[12] 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.[12]

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).[13][14] 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.[15][16] Bláthy had suggested the use of closed cores, Zipernowsky had suggested the use of parallel shunt connections, and Déri had performed the experiments;[17] The other essential milestone was the introduction of 'voltage source, voltage intensive' (VSVI) systems'[18] by the invention of constant voltage generators in 1885.[19] In early 1885, the three engineers also eliminated the problem of eddy current losses with the invention of the lamination of electromagnetic cores.[20] Ottó Bláthy also invented the first AC electricity meter.[21][22][23][24]

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 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.[25] The reliability of the AC technology received impetus after the Ganz Works electrified a large European metropolis: Rome in 1886.[25]

Westinghouse Early AC System 1887
(US patent 373035)

In the UK, 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.[26] In 1890 he designed their power station at Deptford[27] 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.[28]

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. Stanley also worked on engineering and adapting European designs such as the Gaulard and Gibbs transformer for US entrepreneur George Westinghouse who started building AC systems in 1886. The spread of Westinghouse and other AC systems triggered a push back in late 1887 by Thomas Edison (a proponent of direct current) who attempted to discredit alternating current as too dangerous in a public campaign called the "war of the currents". In 1888 alternating current systems gained further viability with introduction of a functional AC motor, something these systems had lacked up till then. The design, an induction motor, was independently invented by Galileo Ferraris and Nikola Tesla (with Tesla's design being licensed by Westinghouse in the US). This design was further developed into the modern practical three-phase form by Mikhail Dolivo-Dobrovolsky, Charles Eugene Lancelot Brown.[29] 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.[30] In 1891, a second transmission system was installed in Telluride Colorado.[31] 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, 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 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 11.5 kilometers (7.1 mi) 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.[32][33] Calculations in unbalanced three-phase systems were simplified by the symmetrical components methods discussed by Charles Legeyt Fortescue in 1918.

See also[edit]


  3. ^ "The Basics of 400-Hz Power Systems". Electrical Construction & Maintenance (EC&M) Magazine. March 1, 1995.
  4. ^ "Pixii Machine invented by Hippolyte Pixii, National High Magnetic Field Laboratory". Archived from the original on 2008-09-07. Retrieved 2012-03-23.
  6. ^ a b "Stanley Transformer". Los Alamos National Laboratory; University of Florida. Archived from the original on 2009-01-19. Retrieved Jan 9, 2009.
  10. ^ Hughes (1993), p. 95.
  19. ^ Hughes (1993), p. 96.
  20. ^ Electrical Society of Cornell University (1896). Proceedings of the Electrical Society of Cornell University. Andrus & Church. p. 39.
  23. ^ The Electrician, Volume 50. 1923
  25. ^ a b "Ottó Bláthy, Miksa Déri, Károly Zipernowsky". IEC Techline. Archived from the original on September 30, 2007. Retrieved Apr 16, 2010.
  26. ^ Hughes (1993), p. 98.
  27. ^ Ferranti Timeline Archived 2015-10-03 at the Wayback MachineMuseum of Science and Industry (Accessed 22-02-2012)
  28. ^ Hughes (1993), p. 208.
  29. ^ Arnold Heertje, Mark Perlman 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
  30. ^ "Electric Transmission of Power". General Electric Review. XVIII. 1915.
  31. ^ "Electric Transmission of Power". General Electric. XVIII. 1915.
  32. ^ Grattan-Guinness, I. (September 19, 2003). Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences. JHU Press. ISBN 978-0-8018-7397-3 – via Google Books.
  33. ^ Suzuki, Jeff (August 27, 2009). Mathematics in Historical Context. MAA. ISBN 978-0-88385-570-6 – via Google Books.

Further reading[edit]


External links[edit]