4055:. 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.
4178:
1298:, 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
4150:
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. 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
1271:
4142:, and DĂ©ri had performed the experiments; 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
157:
2192:
1096:
133:
4379:
4365:
36:
3504:
2713:
1711:
4107:
4084:
1364:, 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
3172:
2397:
4146:). 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.
1521:. 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. This tendency of alternating current to flow predominantly in the periphery of conductors reduces the effective cross-section of the conductor. This increases the effective AC
3778:
3910:, that is 460 RW. During the course of one cycle (two cycle as the power) the voltage rises from zero to 325 V, the power from zero to 460 RW, and both falls through zero. Next, the voltage descends to reverse direction, -325 V, but the power ascends again to 460 RW, and both returns to zero.
4268:
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
1669:
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
1372:
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
1342:
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
4149:
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
1653:
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
1330:
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
1497:
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
1632:
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.
1426:
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
1099:
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,
1352:
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
4216:
generator's voltage of 500 volts was converted into 3000 volts, and then the voltage was stepped down to 500 volts by six
Westinghouse transformers. With this setup, the Westinghouse company successfully powered thirty 100-volt incandescent bulbs in twenty shops along the main street of Great
1335:. 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
3499:{\displaystyle {\begin{aligned}v(t)&=V_{\text{peak}}\sin(\omega t)\\i(t)&={\frac {v(t)}{R}}={\frac {V_{\text{peak}}}{R}}\sin(\omega t)\\p(t)&=v(t)i(t)={\frac {(V_{\text{peak}})^{2}}{R}}\sin ^{2}(\omega t)={\frac {(V_{\text{peak}})^{2}}{2R}}\ (1-\cos(2\omega t))\end{aligned}}}
2708:{\displaystyle {\begin{aligned}V_{\text{rms}}&={\sqrt {{\frac {1}{T}}\int _{0}^{T}^{2}dt}}}\\&=V_{\text{peak}}{\sqrt {{\frac {1}{2T}}\int _{0}^{T}dt}}}\\&=V_{\text{peak}}{\sqrt {{\frac {1}{2T}}\int _{0}^{T}{dt}}}\\&={\frac {V_{\text{peak}}}{\sqrt {2}}}\end{aligned}}}
1427:
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
4269:
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
3938:
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
3617:
1537:
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
4030:
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
1347:
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.
4203:
held an option on the US rights for the Ganz ZBD transformers, requiring
Westinghouse to pursue alternative designs on the same principles. George Westinghouse had bought Gaulard and Gibbs' patents for $ 50,000 in February 1886. He assigned to
1517:. 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 â 60 Hz), non-uniform distribution of current still occurs in sufficiently thick
4169:
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:
4002:
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
1353:
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
4066:
in 1886 for the London
Electric Supply Corporation (LESCo) including alternators of his own design and open core transformer designs with serial connections for utilization loads - similar to Gaulard and Gibbs. In 1890, he designed
1308:(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
1612:
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.
1331:
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
5369:. [Excerpt taken from YMER 1941, hÀfte 2.Utgiven av SÀllskapet för antropologi och geografi: Meddelande frÄn Upsala univeristets geografiska institution, N:o 29, published by Esselte ab, Stockholm 1941 no. 135205]
2387:
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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.
4822:
4137:
of
Budapest, determined that open-core devices were impractical, as they were incapable of reliably regulating voltage. BlĂĄthy had suggested the use of closed cores, Zipernowsky had suggested the use of
5212:
3611:
4337:
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
1212:
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.
2792:
1357:
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.
3177:
2402:
1481:
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
1803:
1073:
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
3843:
3773:{\displaystyle P_{\text{peak}}={\frac {(V_{\text{rms}})^{2}}{R}}{\frac {(V_{\text{peak}})^{2}}{(V_{\text{rms}})^{2}}}={\text{P}}_{\text{average}}{\sqrt {2}}^{2}={\text{2}}P_{\text{average}}.}
2933:
4885:
1455:
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
1525:
of the conductor, since resistance is inversely proportional to the cross-sectional area. A conductor's AC resistance is higher than its DC resistance, causing a higher energy loss due to
1263:
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
3908:
3012:
4318:. Decker's design incorporated 10 kV three-phase transmission and established the standards for the complete system of generation, transmission and motors used in USA today. The
1207:
4161:
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
3558:
1542:. 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
1258:
2049:
2019:
4199:
in Pittsburgh, Pennsylvania, on January 8, 1886. The new firm became active in developing alternating current (AC) electric infrastructure throughout the United States. The
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3808:
1837:
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2103:
1927:
2221:
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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
3070:, 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
1124:
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 (
4720:
1989:
1863:
1322:, 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°
5364:
3068:
2270:
4208:
the task of redesigning the Gaulard and Gibbs transformer for commercial use in United States. On March 20, 1886, Stanley conducted a demonstrative experiment in
4811:
3036:
2290:
1949:
1891:
714:
5194:
1267:, and transformed down to tens of kilovolts to be transmitted on lower level lines, and finally transformed down to 100 V â 240 V for domestic use.
4570:
687:
5408:
5381:
4503:
4334:
was 11.5 kilometers (7.1 mi) long on wooden towers, and the municipal distribution grid 3000 V/110 V included six transforming stations.
3560:
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:
5276:
5478:
4403:
699:
5110:
5496:
2297:
4889:
1959:
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
136:
Alternating current (green curve). The horizontal axis measures time (it also represents zero voltage/current); the vertical, current or voltage.
3967:
to his device to produce the (then) more commonly used direct current. The earliest recorded practical application of alternating current is by
4553:
1674:
of the alternating current to be transmitted, so they are feasible only at microwave frequencies. In addition to this mechanical feasibility,
5270:
1312:, as there was then no economically viable way to step the voltage of DC down for end user applications such as lighting incandescent bulbs.
1290:
High voltages have disadvantages, such as the increased insulation required, and generally increased difficulty in their safe handling. In a
3107:
5137:
4277:, which was 14 miles away. Meanwhile, the possibility of transferring electrical power from a waterfall at a distance was explored at the
4241:(with Tesla's design being licensed by Westinghouse in the US). This design was independently further developed into the modern practical
2834:
1702:, which are a form of dielectric waveguides, can be used. For such frequencies, the concepts of voltages and currents are no longer used.
1549:, reducing losses in flexible conductors carrying very high currents at lower frequencies, and in the windings of devices carrying higher
3526:
2108:
1407:
A low frequency eases the design of electric motors, particularly for hoisting, crushing and rolling applications, and commutator-type
950:
719:
5029:
1588:. Energy that is radiated is lost. Depending on the frequency, different techniques are used to minimize the loss due to radiation.
729:
4221:(a proponent of direct current), who attempted to discredit alternating current as too dangerous in a public campaign called the "
100:
3566:
3979:
for electrotherapeutic triggering of muscle contractions. Alternating current technology was developed further by the Hungarian
72:
1423:. The use of lower frequencies also provided the advantage of lower transmission losses, which are proportional to frequency.
554:
4933:
5418:
5391:
5253:
4791:
4470:
569:
564:
191:
1047:, whose positive half-period corresponds with positive direction of the current and vice versa (the full period is called a
4728:
4311:
4011:, Budapest, Hungary, began manufacturing equipment for electric lighting and, by 1883, had installed over fifty systems in
579:
79:
53:
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2722:
4967:
4261:
1077:
of an AC carrier signal. These currents typically alternate at higher frequencies than those used in power transmission.
17:
4288:
fall at HÀllsjön, Smedjebackens kommun, where a small iron work had been located, was selected. In 1893, a three-phase
1748:
3813:
1396:
1215:
The power transmitted is equal to the product of the current and the voltage (assuming no phase difference); that is,
5309:
5284:
5226:
4665:
4537:
4196:
2895:
181:
119:
86:
4991:
American Society for Engineering Education. Conference â 1995: Annual Conference Proceedings, Volume 2, (PAGE: 1848)
4007:(arc lamps) of his own design, used to keep the failure of one lamp from disabling the entire circuit. In 1878, the
1502:, and a direct current does not exhibit this effect, since a direct current does not create electromagnetic waves.
449:
5185:
4319:
4051:
in 1884. However, these early induction coils with open magnetic circuits are inefficient at transferring power to
5518:
4209:
3875:
364:
5500:". The history of various frequencies and interconversion schemes in the US at the beginning of the 20th century
2957:
68:
4582:
4574:
4062:, who had been developing AC generators and transformers in London since 1882, redesigned the AC system at the
943:
709:
186:
57:
1326:
to each other. If coils are added opposite to these (60° spacing), they generate the same phases with reverse
4507:
4250:
4200:
4154:
losses with the invention of the lamination of electromagnetic cores. OttĂł BlĂĄthy also invented the first AC
724:
429:
5475:
4418:
4044:
1650:
1638:
1391:
varies by country and sometimes within a country; most electric power is generated at either 50 or 60
1382:
1163:
589:
329:
196:
1628:
and above for convenience. A coaxial cable has a conductive wire inside a conductive tube, separated by a
319:
5466:
5114:
4413:
4326:(42 Hz, 550 kW each) and the transformers were produced and installed by the Hungarian company
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1344:
1336:
1309:
1305:
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1086:
882:
757:
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dissipate power). At higher frequencies, the power lost to this dissipation becomes unacceptably large.
4423:
4246:
1349:
1318:
electrical generation is very common. The simplest way is to use three separate coils in the generator
1315:
1221:
382:
2024:
1994:
1339:. Harmonics can cause neutral conductor current levels to exceed that of one or all phase conductors.
974:
that periodically reverses direction and changes its magnitude continuously with time, in contrast to
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1815:
1601:
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4914:. Budapest University of Technology and Economics, National Technical Information Centre and Library
4306:, becoming the first commercial application. In 1893, Decker designed the first American commercial
3077:
2081:
1900:
4350:
4225:". In 1888, alternating current systems gained further viability with introduction of a functional
2202:
2185:
2054:
1694:
At frequencies greater than 200 GHz, waveguide dimensions become impractically small, and the
1373:
are bonded to ground at the main service panel, as is the neutral/identified conductor if present.
434:
5489:
4605:
4217:
Barrington. The spread of Westinghouse and other AC systems triggered a push back in late 1887 by
867:
369:
5528:
5055:
2797:
1596:
At frequencies up to about 1 GHz, pairs of wires are twisted together in a cable, forming a
1478:
1420:
1127:
747:
274:
264:
259:
93:
46:
872:
842:
5440:
History and Reflections on the Way Things Were: Mill Creek Power Plant â Making History with AC
5218:
4783:
4346:
4068:
2717:
1739:
1498:
phenomenon of alternating current being pushed away from the center of the conductor is called
694:
464:
239:
5243:
4578:
4487:
4460:
4438:
4110:
The prototype of the ZBD transformer on display at the Széchenyi Istvån Memorial Exhibition,
4072:
3964:
3510:
1962:
1848:
1675:
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1585:
1522:
1486:
1154:
1121:
792:
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419:
409:
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1670:
the fields to the space outside the waveguide. Waveguides have dimensions comparable to the
1100:
Pe=power reaching the end of the transmission line, D=step-down transformer, C=consumers.
5033:
4778:
Creating the Twentieth Century: Technical Innovations of 1867â1914 and Their Lasting Impact
4619:
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284:
219:
5456:
4911:
4177:
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2246:
156:
8:
4818:
4692:
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4345:, and many others. Calculations in unbalanced three-phase systems were simplified by the
4222:
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3522:
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1279:
877:
857:
852:
659:
644:
529:
394:
324:
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1734:
Alternating currents are accompanied (or caused) by alternating voltages. An AC voltage
1633:
Coaxial cables have acceptably small losses for frequencies up to about 5 GHz. For
5155:
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4776:
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5222:
5159:
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4015:. Their AC systems used arc and incandescent lamps, generators, and other equipment.
4004:
1866:
1494:
1388:
1327:
1275:
989:
985:
812:
4871:
4850:
Halacsy, A. A.; Von Fuchs, G. H. (April 1961). "Transformer Invented 75 Years Ago".
4504:"Pixii Machine invented by Hippolyte Pixii, National High Magnetic Field Laboratory"
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224:
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980:(DC), which flows only in one direction. Alternating current is the form in which
5482:
5383:
Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences
4863:
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4012:
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4812:"Electrostatics and Electrodynamics at Pest University in the Mid-19th Century"
4162:
4075:, showing the way to integrate older plants into a universal AC supply system.
4036:
3988:
3976:
3972:
1543:
1477:
A direct current flows uniformly throughout the cross-section of a homogeneous
1408:
1395:. Some countries have a mixture of 50 Hz and 60 Hz supplies, notably
1354:
1270:
981:
976:
807:
802:
624:
514:
439:
389:
339:
312:
269:
244:
214:
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5150:
4888:. Institute for Developing Alternative Energy in Latin America. Archived from
4278:
5512:
5071:
4384:
4218:
4166:
2826:
2382:{\displaystyle V_{\text{rms}}={\sqrt {{\frac {1}{T}}\int _{0}^{T}{^{2}dt}}}.}
2179:
1695:
1621:
1609:
1526:
1332:
1058:
1001:
997:
922:
907:
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832:
544:
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359:
344:
249:
5302:
Evolving Technology and Market Structure: Studies in Schumpeterian Economics
4130:
4096:
5462:
4238:
4151:
3513:
sine, and its fundamental frequency is double of the one of the voltage's.
2819:
2228:
1699:
1597:
1577:
1554:
1323:
1117:
902:
797:
762:
704:
639:
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404:
279:
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4242:
4100:
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1679:
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1459:
systems were often powered by 400 Hz or 415 Hz for benefits of
1444:
1291:
1278:
use alternating currents to distribute power over long distances between
1109:
1062:
1005:
822:
674:
504:
166:
5490:
Professor Mark Csele's tour of the 25 Hz Rankine generating station
5366:
Elektrifieringens utveckling i Sverige, en ekonomisk-geografisk översikt
5012:
4099:), inventors of the first high efficiency, closed-core shunt connection
1095:
1080:
4296:
4134:
4008:
3980:
3952:
3930:. Information signals are carried over a wide range of AC frequencies.
3533:
value is 230 V. This means that the time-averaged power delivered
1671:
1629:
1514:
1153:) in the wire are a product of the square of the current ( I ) and the
1113:
1074:
1049:
993:
539:
5097:
Official gazette of the United States Patent Office: Volume 50. (1890)
4331:
4071:
and converted the Grosvenor Gallery station across the Thames into an
1282:
plants and consumers. The lines in the picture are located in eastern
4632:
4302:
3934:
telephone signals have a frequency of about 3 kHz, close to the
3923:
3156:{\displaystyle P_{\text{average}}={\frac {{V_{\text{rms}}}^{2}}{R}}.}
1897:), which represents the number of cycles per second, by the equation
1634:
1539:
1493:). Electric conductors are not conducive to electromagnetic waves (a
1044:
862:
837:
649:
171:
5497:
The Frequency Changer Era: Interconnecting Systems of Varying Cycles
4257:
in Sweden on the other, though Brown favoured the two-phase system.
2876:{\displaystyle V_{\text{rms}}={\frac {V_{\text{peak}}}{\sqrt {3}}}.}
35:
4852:
IEEE Transactions of the American Institute of Electrical Engineers
4485:
4393:
4364:
4291:
4226:
4111:
3940:
3935:
2946:
2195:
A sine wave, over one cycle (360°). The dashed line represents the
2163:{\displaystyle V_{\text{peak}}-(-V_{\text{peak}})=2V_{\text{peak}}}
1546:
1416:
1104:
Electrical energy is distributed as alternating current because AC
1040:
614:
609:
229:
132:
4229:, something these systems had lacked up till then. The design, an
4043:
was demonstrated in London in 1881, and attracted the interest of
3955:
to produce alternating current was an electric generator based on
1678:
of the non-ideal metals forming the walls of the waveguide causes
1463:
reduction while using smaller internal AC to DC conversion units.
1294:, energy is generated at a convenient voltage for the design of a
5076:
Student paper read on January 24, 1896, at the Students' Meeting.
4378:
4213:
4115:
1432:
1428:
1412:
1105:
1032:
984:
is delivered to businesses and residences, and it is the form of
584:
4657:
Networks of Power: Electrification in Western Society, 1880â1930
4458:
1991:
is +1 and the minimum value is â1, an AC voltage swings between
1952:
1873:). The angular frequency is related to the physical frequency,
1710:
1440:
1436:
1319:
669:
176:
4165:
system. In 1886, the ZBD engineers designed the world's first
2191:
5272:
The Smart Grid Enabling Energy Efficiency and Demand Response
4660:. Baltimore: The Johns Hopkins University Press. p. 96.
4408:
4284:
4048:
2951:
The relationship between voltage and the power delivered is:
1894:
1392:
4330:. The transmission line from the power plant to the City of
4106:
1043:
of alternating current in most electric power circuits is a
5138:"A Contrarian History of Early Electric Power Distribution"
5015:
Proceedings of the Electrical Society of Cornell University
4958:
4327:
4322:
in Croatia was set in operation on 28 August 1895. The two
4171:
4083:
3606:{\displaystyle V_{\text{peak}}={\sqrt {2}}\ V_{\text{rms}}}
2238:
over one cycle of the square of the instantaneous voltage.
1840:
1553:
current (up to hundreds of kilohertz), such as switch-mode
1415:. However, low frequency also causes noticeable flicker in
1283:
4528:
Licht, Sidney Herman (1967). "History of Electrotherapy".
5442:, IEEE Power Engineering Review, February 1997, pp. 22â24
3959:'s principles constructed by the French instrument maker
1654:
current, waveguides cannot deliver energy by means of an
1567:
5486:". Edison's Miracle of Light, American Experience. (PBS)
4310:
power plant using alternating currentâthe hydroelectric
4191:
Building on the advancement of AC technology in Europe,
1532:
3521:
To illustrate these concepts, consider a 230 V AC
1505:
At very high frequencies, the current no longer flows
1343:
varies by country and age of the installation) only a
4904:
4743:
3878:
3851:
3816:
3789:
3620:
3569:
3539:
3175:
3110:
3080:
3047:
3024:
2960:
2898:
2837:
2800:
2725:
2400:
2300:
2278:
2249:
2205:
2111:
2084:
2057:
2027:
1997:
1965:
1937:
1903:
1879:
1851:
1818:
1751:
1513:
the surface of the wire, within a thickness of a few
1224:
1166:
1130:
1081:
Transmission, distribution, and domestic power supply
27:
Electric current that periodically reverses direction
4994:
4755:
4360:
2787:{\displaystyle \sin ^{2}(x)={\frac {1-\cos(2x)}{2}}}
1572:
As written above, an alternating current is made of
4701:
60:. Unsourced material may be challenged and removed.
5060:Journal of the Institution of Electrical Engineers
4775:
3902:
3864:
3837:
3802:
3772:
3605:
3552:
3516:
3498:
3155:
3093:
3062:
3030:
3006:
2927:
2875:
2810:
2786:
2707:
2381:
2284:
2264:
2215:
2162:
2097:
2070:
2043:
2013:
1983:
1943:
1921:
1885:
1857:
1831:
1798:{\displaystyle v(t)=V_{\text{peak}}\sin(\omega t)}
1797:
1252:
1201:
1145:
1112:. This allows the power to be transmitted through
5268:
5013:Electrical Society of Cornell University (1896).
4845:
4843:
4530:Therapeutic Electricity and Ultraviolet Radiation
5510:
5379:
5293:
5210:
5178:
4849:
4459:N. N. Bhargava & D. C. Kulshreshtha (1983).
3975:. In 1855, he announced that AC was superior to
3845:, which is about 325 V, and the peak power
3838:{\displaystyle 230{\text{ V}}\times {\sqrt {2}}}
5136:Brusso, Barry; Allerhand, Adam (January 2021).
5135:
5105:
5103:
2928:{\displaystyle V_{\text{rms}}=V_{\text{peak}}.}
2051:. The peak-to-peak voltage, usually written as
1120:, which reduces the energy lost as heat due to
5299:
4840:
4697:. London: E. & F. N. Spon. pp. 35â41.
3529:around the world. It is so called because its
1698:in the waveguide walls become large. Instead,
1466:
1376:
5304:. University of Michigan Press. p. 138.
5193:. Tinicum Township Historical Society. 1993.
5111:"OttĂł BlĂĄthy, Miksa DĂ©ri, KĂĄroly Zipernowsky"
3509:For this reason, AC power's waveform becomes
1705:
944:
5100:
4966:. U.S. Patent 352 105, issued Nov. 2, 1886.
4878:
4647:
4603:
4486:National Electric Light Association (1915).
1682:of power (surface currents flowing on lossy
988:that consumers typically use when they plug
5380:Grattan-Guinness, I. (September 19, 2003).
4782:. Oxford: Oxford University Press. p.
4725:Museum of Science and Industry (Manchester)
4133:(ZBD), three engineers associated with the
3913:
3903:{\displaystyle 230\times R\times W\times 2}
2173:
1157:(R) of the wire, described by the formula:
5187:History of Tinicum Township (PA) 1643â1993
4926:
4886:"Hungarian Inventors and Their Inventions"
4803:
4552:: CS1 maint: location missing publisher (
4465:. Tata McGraw-Hill Education. p. 90.
3007:{\displaystyle p(t)={\frac {v^{2}(t)}{R}}}
2234:The RMS voltage is the square root of the
951:
937:
155:
5362:
5149:
5047:
4936:. Hungarian Patent Office. Archived from
4690:
4686:
4684:
4631:
1246:
1195:
120:Learn how and when to remove this message
5027:
4959:Zipernowsky, K.; DĂ©ri, M.; BlĂĄthy, O.T.
4565:
4563:
4532:(2 ed.). New Haven. pp. 1â70.
4176:
4105:
4082:
3918:Alternating current is used to transmit
2190:
2184:For broader coverage of this topic, see
1709:
1269:
1094:
1057:, different waveforms are used, such as
131:
5300:Heertje, Arnold; Perlman, Mark (1990).
5241:
5235:
4462:Basic Electronics & Linear Circuits
4047:. They also exhibited the invention in
3041:Rather than using instantaneous power,
2822:, which varies for different waveforms.
1397:electricity power transmission in Japan
1368:path to ground sufficient to carry any
700:Electromagnetism and special relativity
14:
5511:
5406:
5214:George Westinghouse Powering the World
5000:
4809:
4761:
4749:
4707:
4681:
4653:
1568:Techniques for reducing radiation loss
5053:
5032:. People.clarkson.edu. Archived from
4560:
4527:
1738:can be described mathematically as a
1608:. A twisted pair must be used with a
1533:Techniques for reducing AC resistance
1202:{\displaystyle P_{\rm {w}}=I^{2}R\,.}
1108:may be increased or decreased with a
720:Maxwell equations in curved spacetime
5200:from the original on April 23, 2015.
4773:
4767:
4312:Mill Creek No. 1 Hydroelectric Plant
4026:Alternating current systems can use
3783:For 230 V AC, the peak voltage
1024:, respectively, as when they modify
58:adding citations to reliable sources
29:
5142:IEEE Industry Applications Magazine
4262:Ames Hydroelectric Generating Plant
3983:company (1870s), and in the 1880s:
2243:For an arbitrary periodic waveform
1742:of time by the following equation:
24:
5431:
5344:"Electric Transmission of Power".
5325:"Electric Transmission of Power".
5248:. Algora Publishing. p. 102.
5245:George Westinghouse: Gentle Genius
5017:. Andrus & Church. p. 39.
3553:{\displaystyle P_{\text{average}}}
1389:frequency of the electrical system
1231:
1173:
1137:
1053:). In certain applications, like
25:
5545:
5447:
5410:Mathematics in Historical Context
4934:"BlĂĄthy, OttĂł Titusz (1860â1939)"
4604:De Fonveille, W. (Jan 22, 1880).
4181:Westinghouse Early AC System 1887
1714:A sinusoidal alternating voltage.
1616:
1450:
1253:{\displaystyle P_{\rm {t}}=IV\,.}
5407:Suzuki, Jeff (August 27, 2009).
4377:
4363:
4320:Jaruga Hydroelectric Power Plant
4295:system was used to transfer 400
4273:to provide power to the city of
4233:, was independently invented by
2044:{\displaystyle -V_{\text{peak}}}
2014:{\displaystyle +V_{\text{peak}}}
1591:
1509:the wire, but effectively flows
1402:
34:
5400:
5373:
5356:
5337:
5318:
5262:
5204:
5129:
5091:
5079:
5021:
5006:
4985:
4973:from the original on 2022-10-09
4952:
4828:from the original on 2022-10-09
4713:
4264:and the original Niagara Falls
4069:their power station at Deptford
4064:Grosvenor Gallery power station
4021:
3865:{\displaystyle P_{\text{peak}}}
3803:{\displaystyle V_{\text{peak}}}
3517:Examples of alternating current
1832:{\displaystyle V_{\text{peak}}}
1689:
45:needs additional citations for
5461:". Edison's Miracle of Light,
5113:. IEC Techline. Archived from
4606:"Gas and Electricity in Paris"
4597:
4575:Los Alamos National Laboratory
4521:
4496:
4489:Electrical meterman's handbook
4479:
4452:
3708:
3694:
3683:
3669:
3651:
3637:
3489:
3486:
3474:
3459:
3436:
3422:
3413:
3404:
3376:
3362:
3353:
3347:
3341:
3335:
3322:
3316:
3306:
3297:
3262:
3256:
3240:
3234:
3224:
3215:
3189:
3183:
3094:{\displaystyle V_{\text{rms}}}
3057:
3051:
3038:represents a load resistance.
2995:
2989:
2970:
2964:
2775:
2766:
2745:
2739:
2598:
2595:
2574:
2558:
2488:
2484:
2469:
2449:
2358:
2354:
2348:
2342:
2259:
2253:
2227:Below an AC waveform (with no
2141:
2125:
2098:{\displaystyle V_{\text{P-P}}}
1978:
1972:
1922:{\displaystyle \omega =2\pi f}
1792:
1783:
1761:
1755:
1016:are often used to mean simply
13:
1:
5504:AC Power History and Timeline
4445:
4251:Charles Eugene Lancelot Brown
4201:Edison Electric Light Company
3963:in 1832. Pixii later added a
2794:has been used and the factor
2216:{\displaystyle {\sqrt {0.5}}}
2071:{\displaystyle V_{\text{pp}}}
1645:
725:Relativistic electromagnetism
5242:Skrabec, Quentin R. (2007).
5054:Ricks, G.W.D. (March 1896).
4864:10.1109/AIEEPAS.1961.4500994
4419:Mains electricity by country
4253:in Germany on one side, and
3971:, inventor and developer of
1383:Mains electricity by country
7:
5056:"Electricity Supply Meters"
4414:Leading and lagging current
4356:
4078:
3985:Sebastian Ziani de Ferranti
2811:{\displaystyle {\sqrt {2}}}
1839:is the peak voltage (unit:
1658:, but rather by means of a
1600:. This reduces losses from
1467:Effects at high frequencies
1377:AC power supply frequencies
1310:electric power transmission
1306:High-voltage direct-current
1146:{\displaystyle P_{\rm {w}}}
1091:Electric power distribution
1087:Electric power transmission
10:
5550:
5269:Clark W. Gellings (2020).
4694:History of the Transformer
4654:Hughes, Thomas P. (1993).
4424:AC power plugs and sockets
4247:Mikhail Dolivo-Dobrovolsky
4140:parallel shunt connections
4087:The Hungarian "ZBD" Team (
3998:In 1876, Russian engineer
3946:
2944:
2393:For a sinusoidal voltage:
2183:
2177:
1706:Mathematics of AC voltages
1495:perfect electric conductor
1470:
1380:
1084:
450:LiĂ©nardâWiechert potential
5423:– via Google Books.
5396:– via Google Books.
5363:Hjulström, Filip (1940).
5211:William R. Huber (2022).
5151:10.1109/MIAS.2020.3028630
4691:Uppenborn, F. J. (1889).
4492:. Trow Press. p. 81.
1602:electromagnetic radiation
1491:electromagnetic radiation
1411:for applications such as
1274:Three-phase high-voltage
715:Mathematical descriptions
425:Electromagnetic radiation
415:Electromagnetic induction
355:Magnetic vector potential
350:Magnetic scalar potential
5072:10.1049/jiee-1.1896.0005
4351:Charles LeGeyt Fortescue
3914:Information transmission
3074:(RMS) value, written as
2940:
2186:Root mean square voltage
2174:Root mean square voltage
1421:incandescent light bulbs
5476:Inside the AC Generator
5327:General Electric Review
5219:McFarland & Company
4271:Almarian William Decker
4121:In the autumn of 1884,
1984:{\displaystyle \sin(x)}
1858:{\displaystyle \omega }
1721:Peak-to-peak amplitude,
1529:(also called IR loss).
1489:(a phenomenon known as
1479:electrically conducting
1350:Three-wire single-phase
265:Electrostatic induction
260:Electrostatic discharge
5519:Electrical engineering
4404:Heavy-duty power plugs
4347:symmetrical components
4188:
4118:
4103:
3904:
3866:
3839:
3804:
3774:
3607:
3554:
3500:
3157:
3095:
3064:
3032:
3008:
2929:
2877:
2812:
2788:
2718:trigonometric identity
2709:
2383:
2286:
2266:
2224:
2217:
2164:
2099:
2072:
2045:
2015:
1985:
1945:
1923:
1887:
1859:
1833:
1799:
1731:
1287:
1254:
1203:
1147:
1101:
695:Electromagnetic tensor
137:
5494:Blalock, Thomas J., "
5457:What's the Difference
5117:on September 30, 2007
4912:"BlĂĄthy, OttĂł Titusz"
4774:Smil, Vaclav (2005).
4579:University of Florida
4571:"Stanley Transformer"
4439:AC/DC receiver design
4349:methods discussed by
4197:Westinghouse Electric
4180:
4109:
4086:
4073:electrical substation
4060:Sebastian de Ferranti
3922:, as in the cases of
3905:
3867:
3840:
3805:
3775:
3608:
3555:
3501:
3158:
3096:
3065:
3033:
3009:
2930:
2878:
2813:
2789:
2710:
2384:
2287:
2267:
2218:
2194:
2178:Further information:
2165:
2100:
2073:
2046:
2016:
1986:
1946:
1924:
1888:
1860:
1834:
1800:
1713:
1676:electrical resistance
1663:electromagnetic field
1624:are commonly used at
1586:electromagnetic waves
1487:electromagnetic waves
1381:Further information:
1273:
1255:
1204:
1148:
1098:
688:Covariant formulation
480:Synchrotron radiation
420:Electromagnetic pulse
410:Electromagnetic field
135:
69:"Alternating current"
5166:on December 12, 2020
4810:Jeszenszky, SĂĄndor.
4316:Redlands, California
3876:
3849:
3814:
3787:
3618:
3567:
3537:
3173:
3108:
3078:
3063:{\displaystyle p(t)}
3045:
3022:
2958:
2896:
2891:centered about zero
2835:
2829:centered about zero
2798:
2723:
2398:
2298:
2276:
2265:{\displaystyle v(t)}
2247:
2203:
2109:
2082:
2055:
2025:
1995:
1963:
1935:
1901:
1877:
1849:
1816:
1749:
1366:electrical impedance
1302:found in the world.
1222:
1164:
1128:
1008:. The abbreviations
730:Stressâenergy tensor
655:Reluctance (complex)
400:Displacement current
54:improve this article
5463:American Experience
4940:on December 2, 2010
4819:University of Pavia
4721:"Ferranti Timeline"
4624:1880Natur..21..282D
4434:War of the currents
4223:war of the currents
4193:George Westinghouse
3511:Full-wave rectified
2661:
2557:
2448:
2340:
1951:is the time (unit:
1300:mains power systems
1280:electric generation
964:Alternating current
645:Magnetomotive force
530:Electromotive force
500:Alternating current
435:Jefimenko equations
395:Cyclotron radiation
18:Alternating Current
5481:2014-12-28 at the
5438:Willam A. Meyers,
4371:Electronics portal
4281:mine in Sweden. A
4275:Pomona, California
4189:
4123:KĂĄroly Zipernowsky
4119:
4104:
4089:KĂĄroly Zipernowsky
4005:'electric candles'
3969:Guillaume Duchenne
3900:
3862:
3835:
3800:
3770:
3603:
3550:
3496:
3494:
3153:
3091:
3060:
3028:
3004:
2925:
2873:
2808:
2784:
2705:
2703:
2647:
2543:
2434:
2379:
2326:
2282:
2262:
2225:
2213:
2160:
2095:
2068:
2041:
2011:
1981:
1941:
1919:
1883:
1871:radians per second
1855:
1829:
1795:
1732:
1606:inductive coupling
1288:
1276:transmission lines
1250:
1199:
1143:
1102:
990:kitchen appliances
493:Electrical network
330:Gauss magnetic law
295:Static electricity
255:Electric potential
138:
5420:978-0-88385-570-6
5393:978-0-8018-7397-3
5255:978-0-87586-508-9
5088:, Volume 50. 1923
4793:978-0-19-803774-3
4472:978-0-07-451965-3
4429:Utility frequency
4399:Electrical wiring
4339:Charles Steinmetz
4266:Adams Power Plant
4156:electricity meter
4033:power transformer
3859:
3833:
3823:
3797:
3764:
3755:
3741:
3732:
3727:
3718:
3704:
3679:
3664:
3647:
3628:
3600:
3592:
3588:
3577:
3547:
3458:
3454:
3432:
3389:
3372:
3289:
3283:
3269:
3206:
3167:Power oscillation
3148:
3135:
3118:
3088:
3031:{\displaystyle R}
3002:
2919:
2906:
2868:
2867:
2860:
2845:
2827:triangle waveform
2806:
2782:
2699:
2698:
2691:
2670:
2645:
2627:
2608:
2541:
2523:
2504:
2460:
2432:
2412:
2374:
2324:
2308:
2285:{\displaystyle T}
2211:
2157:
2138:
2119:
2092:
2065:
2038:
2008:
1944:{\displaystyle t}
1886:{\displaystyle f}
1867:angular frequency
1826:
1774:
1626:audio frequencies
1055:guitar amplifiers
986:electrical energy
961:
960:
660:Reluctance (real)
630:Gyratorâcapacitor
575:Resonant cavities
465:Maxwell equations
130:
129:
122:
104:
16:(Redirected from
5541:
5524:Electric current
5425:
5424:
5404:
5398:
5397:
5377:
5371:
5370:
5360:
5354:
5353:
5346:General Electric
5341:
5335:
5334:
5322:
5316:
5315:
5297:
5291:
5290:
5277:River Publishers
5266:
5260:
5259:
5239:
5233:
5232:
5208:
5202:
5201:
5199:
5192:
5182:
5176:
5175:
5173:
5171:
5162:. Archived from
5153:
5144:. IEEE.org: 12.
5133:
5127:
5126:
5124:
5122:
5107:
5098:
5095:
5089:
5083:
5077:
5075:
5051:
5045:
5044:
5042:
5041:
5036:on June 25, 2008
5025:
5019:
5018:
5010:
5004:
4998:
4992:
4989:
4983:
4982:
4980:
4978:
4972:
4965:
4961:"Induction Coil"
4956:
4950:
4949:
4947:
4945:
4930:
4924:
4923:
4921:
4919:
4908:
4902:
4901:
4899:
4897:
4882:
4876:
4875:
4847:
4838:
4837:
4835:
4833:
4827:
4816:
4807:
4801:
4800:
4798:ZBD transformer.
4781:
4771:
4765:
4759:
4753:
4747:
4741:
4740:
4738:
4736:
4727:. Archived from
4717:
4711:
4705:
4699:
4698:
4688:
4679:
4678:
4676:
4674:
4651:
4645:
4644:
4642:
4640:
4635:
4633:10.1038/021282b0
4601:
4595:
4594:
4592:
4590:
4581:. Archived from
4567:
4558:
4557:
4551:
4543:
4525:
4519:
4518:
4516:
4515:
4506:. Archived from
4500:
4494:
4493:
4483:
4477:
4476:
4456:
4387:
4382:
4381:
4373:
4368:
4367:
4343:Oliver Heaviside
4305:
4294:
4287:
4235:Galileo Ferraris
4210:Great Barrington
4185:US patent 373035
4041:John Dixon Gibbs
4000:Pavel Yablochkov
3993:Galileo Ferraris
3928:cable television
3909:
3907:
3906:
3901:
3871:
3869:
3868:
3863:
3861:
3860:
3857:
3844:
3842:
3841:
3836:
3834:
3829:
3824:
3821:
3809:
3807:
3806:
3801:
3799:
3798:
3795:
3779:
3777:
3776:
3771:
3766:
3765:
3762:
3756:
3753:
3748:
3747:
3742:
3737:
3734:
3733:
3730:
3728:
3725:
3719:
3717:
3716:
3715:
3706:
3705:
3702:
3692:
3691:
3690:
3681:
3680:
3677:
3667:
3665:
3660:
3659:
3658:
3649:
3648:
3645:
3635:
3630:
3629:
3626:
3612:
3610:
3609:
3604:
3602:
3601:
3598:
3590:
3589:
3584:
3579:
3578:
3575:
3559:
3557:
3556:
3551:
3549:
3548:
3545:
3531:root mean square
3505:
3503:
3502:
3497:
3495:
3456:
3455:
3453:
3445:
3444:
3443:
3434:
3433:
3430:
3420:
3400:
3399:
3390:
3385:
3384:
3383:
3374:
3373:
3370:
3360:
3290:
3285:
3284:
3281:
3275:
3270:
3265:
3251:
3208:
3207:
3204:
3162:
3160:
3159:
3154:
3149:
3144:
3143:
3138:
3137:
3136:
3133:
3125:
3120:
3119:
3116:
3100:
3098:
3097:
3092:
3090:
3089:
3086:
3072:root mean square
3069:
3067:
3066:
3061:
3037:
3035:
3034:
3029:
3013:
3011:
3010:
3005:
3003:
2998:
2988:
2987:
2977:
2934:
2932:
2931:
2926:
2921:
2920:
2917:
2908:
2907:
2904:
2882:
2880:
2879:
2874:
2869:
2863:
2862:
2861:
2858:
2852:
2847:
2846:
2843:
2817:
2815:
2814:
2809:
2807:
2802:
2793:
2791:
2790:
2785:
2783:
2778:
2752:
2735:
2734:
2714:
2712:
2711:
2706:
2704:
2700:
2694:
2693:
2692:
2689:
2683:
2675:
2671:
2669:
2660:
2655:
2646:
2644:
2633:
2631:
2629:
2628:
2625:
2613:
2609:
2607:
2556:
2551:
2542:
2540:
2529:
2527:
2525:
2524:
2521:
2509:
2505:
2503:
2496:
2495:
2462:
2461:
2458:
2447:
2442:
2433:
2425:
2423:
2414:
2413:
2410:
2388:
2386:
2385:
2380:
2375:
2373:
2366:
2365:
2339:
2334:
2325:
2317:
2315:
2310:
2309:
2306:
2291:
2289:
2288:
2283:
2271:
2269:
2268:
2263:
2222:
2220:
2219:
2214:
2212:
2207:
2197:root mean square
2169:
2167:
2166:
2161:
2159:
2158:
2155:
2140:
2139:
2136:
2121:
2120:
2117:
2104:
2102:
2101:
2096:
2094:
2093:
2090:
2077:
2075:
2074:
2069:
2067:
2066:
2063:
2050:
2048:
2047:
2042:
2040:
2039:
2036:
2020:
2018:
2017:
2012:
2010:
2009:
2006:
1990:
1988:
1987:
1982:
1950:
1948:
1947:
1942:
1928:
1926:
1925:
1920:
1892:
1890:
1889:
1884:
1864:
1862:
1861:
1856:
1838:
1836:
1835:
1830:
1828:
1827:
1824:
1804:
1802:
1801:
1796:
1776:
1775:
1772:
1724:Effective value,
1667:surface currents
1656:electric current
1259:
1257:
1256:
1251:
1236:
1235:
1234:
1208:
1206:
1205:
1200:
1191:
1190:
1178:
1177:
1176:
1152:
1150:
1149:
1144:
1142:
1141:
1140:
1059:triangular waves
972:electric current
953:
946:
939:
620:Electric machine
603:Magnetic circuit
565:Parallel circuit
555:Network analysis
520:Electric current
455:London equations
300:Triboelectricity
290:Potential energy
159:
149:Electromagnetism
140:
139:
125:
118:
114:
111:
105:
103:
62:
38:
30:
21:
5549:
5548:
5544:
5543:
5542:
5540:
5539:
5538:
5509:
5508:
5483:Wayback Machine
5450:
5445:
5434:
5432:Further reading
5429:
5428:
5421:
5405:
5401:
5394:
5378:
5374:
5361:
5357:
5343:
5342:
5338:
5324:
5323:
5319:
5312:
5298:
5294:
5287:
5267:
5263:
5256:
5240:
5236:
5229:
5209:
5205:
5197:
5190:
5184:
5183:
5179:
5169:
5167:
5134:
5130:
5120:
5118:
5109:
5108:
5101:
5096:
5092:
5086:The Electrician
5084:
5080:
5052:
5048:
5039:
5037:
5026:
5022:
5011:
5007:
4999:
4995:
4990:
4986:
4976:
4974:
4970:
4963:
4957:
4953:
4943:
4941:
4932:
4931:
4927:
4917:
4915:
4910:
4909:
4905:
4895:
4893:
4884:
4883:
4879:
4848:
4841:
4831:
4829:
4825:
4814:
4808:
4804:
4794:
4772:
4768:
4760:
4756:
4748:
4744:
4734:
4732:
4719:
4718:
4714:
4706:
4702:
4689:
4682:
4672:
4670:
4668:
4652:
4648:
4638:
4636:
4602:
4598:
4588:
4586:
4569:
4568:
4561:
4545:
4544:
4540:
4526:
4522:
4513:
4511:
4502:
4501:
4497:
4484:
4480:
4473:
4457:
4453:
4448:
4443:
4383:
4376:
4369:
4362:
4359:
4300:
4289:
4282:
4231:induction motor
4206:William Stanley
4182:
4081:
4024:
4018:
4013:Austria-Hungary
3961:Hippolyte Pixii
3957:Michael Faraday
3949:
3916:
3877:
3874:
3873:
3856:
3852:
3850:
3847:
3846:
3828:
3820:
3815:
3812:
3811:
3794:
3790:
3788:
3785:
3784:
3761:
3757:
3752:
3743:
3736:
3735:
3729:
3724:
3723:
3711:
3707:
3701:
3697:
3693:
3686:
3682:
3676:
3672:
3668:
3666:
3654:
3650:
3644:
3640:
3636:
3634:
3625:
3621:
3619:
3616:
3615:
3597:
3593:
3583:
3574:
3570:
3568:
3565:
3564:
3544:
3540:
3538:
3535:
3534:
3525:supply used in
3519:
3493:
3492:
3446:
3439:
3435:
3429:
3425:
3421:
3419:
3395:
3391:
3379:
3375:
3369:
3365:
3361:
3359:
3325:
3310:
3309:
3280:
3276:
3274:
3252:
3250:
3243:
3228:
3227:
3203:
3199:
3192:
3176:
3174:
3171:
3170:
3139:
3132:
3128:
3127:
3126:
3124:
3115:
3111:
3109:
3106:
3105:
3085:
3081:
3079:
3076:
3075:
3046:
3043:
3042:
3023:
3020:
3019:
2983:
2979:
2978:
2976:
2959:
2956:
2955:
2949:
2943:
2938:
2916:
2912:
2903:
2899:
2897:
2894:
2893:
2889:square waveform
2857:
2853:
2851:
2842:
2838:
2836:
2833:
2832:
2801:
2799:
2796:
2795:
2753:
2751:
2730:
2726:
2724:
2721:
2720:
2702:
2701:
2688:
2684:
2682:
2673:
2672:
2662:
2656:
2651:
2637:
2632:
2630:
2624:
2620:
2611:
2610:
2561:
2552:
2547:
2533:
2528:
2526:
2520:
2516:
2507:
2506:
2491:
2487:
2457:
2453:
2452:
2443:
2438:
2424:
2422:
2415:
2409:
2405:
2401:
2399:
2396:
2395:
2361:
2357:
2341:
2335:
2330:
2316:
2314:
2305:
2301:
2299:
2296:
2295:
2277:
2274:
2273:
2248:
2245:
2244:
2206:
2204:
2201:
2200:
2199:(RMS) value at
2189:
2182:
2176:
2154:
2150:
2135:
2131:
2116:
2112:
2110:
2107:
2106:
2105:, is therefore
2089:
2085:
2083:
2080:
2079:
2062:
2058:
2056:
2053:
2052:
2035:
2031:
2026:
2023:
2022:
2005:
2001:
1996:
1993:
1992:
1964:
1961:
1960:
1936:
1933:
1932:
1902:
1899:
1898:
1878:
1875:
1874:
1850:
1847:
1846:
1823:
1819:
1817:
1814:
1813:
1771:
1767:
1750:
1747:
1746:
1730:
1708:
1692:
1648:
1619:
1594:
1580:, which causes
1576:under periodic
1574:electric charge
1570:
1559:radio frequency
1551:radio frequency
1535:
1483:electric charge
1475:
1469:
1453:
1409:traction motors
1405:
1385:
1379:
1230:
1229:
1225:
1223:
1220:
1219:
1186:
1182:
1172:
1171:
1167:
1165:
1162:
1161:
1136:
1135:
1131:
1129:
1126:
1125:
1116:efficiently at
1093:
1085:Main articles:
1083:
957:
928:
927:
743:
735:
734:
690:
680:
679:
635:Induction motor
605:
595:
594:
510:Current density
495:
485:
484:
475:Poynting vector
385:
383:Electrodynamics
375:
374:
370:Right-hand rule
335:Magnetic dipole
325:BiotâSavart law
315:
305:
304:
240:Electric dipole
235:Electric charge
210:
126:
115:
109:
106:
63:
61:
51:
39:
28:
23:
22:
15:
12:
11:
5:
5547:
5537:
5536:
5531:
5529:Electric power
5526:
5521:
5507:
5506:
5501:
5492:
5487:
5470:
5449:
5448:External links
5446:
5444:
5443:
5435:
5433:
5430:
5427:
5426:
5419:
5399:
5392:
5372:
5355:
5336:
5317:
5310:
5292:
5285:
5279:. p. 62.
5261:
5254:
5234:
5227:
5221:. p. 84.
5203:
5177:
5128:
5099:
5090:
5078:
5066:(120): 57â77.
5046:
5028:Eugenii Katz.
5020:
5005:
4993:
4984:
4951:
4925:
4903:
4877:
4858:(3): 121â125.
4839:
4802:
4792:
4766:
4754:
4752:, p. 208.
4742:
4712:
4700:
4680:
4666:
4646:
4596:
4559:
4538:
4520:
4495:
4478:
4471:
4450:
4449:
4447:
4444:
4442:
4441:
4436:
4431:
4426:
4421:
4416:
4411:
4406:
4401:
4396:
4390:
4389:
4388:
4374:
4358:
4355:
4299:a distance of
4255:Jonas Wenström
4163:direct current
4144:toroidal cores
4080:
4077:
4037:Lucien Gaulard
4023:
4020:
3989:Lucien Gaulard
3977:direct current
3973:electrotherapy
3948:
3945:
3915:
3912:
3899:
3896:
3893:
3890:
3887:
3884:
3881:
3855:
3832:
3827:
3819:
3793:
3781:
3780:
3769:
3760:
3751:
3746:
3740:
3722:
3714:
3710:
3700:
3696:
3689:
3685:
3675:
3671:
3663:
3657:
3653:
3643:
3639:
3633:
3624:
3613:
3596:
3587:
3582:
3573:
3543:
3527:many countries
3518:
3515:
3507:
3506:
3491:
3488:
3485:
3482:
3479:
3476:
3473:
3470:
3467:
3464:
3461:
3452:
3449:
3442:
3438:
3428:
3424:
3418:
3415:
3412:
3409:
3406:
3403:
3398:
3394:
3388:
3382:
3378:
3368:
3364:
3358:
3355:
3352:
3349:
3346:
3343:
3340:
3337:
3334:
3331:
3328:
3326:
3324:
3321:
3318:
3315:
3312:
3311:
3308:
3305:
3302:
3299:
3296:
3293:
3288:
3279:
3273:
3268:
3264:
3261:
3258:
3255:
3249:
3246:
3244:
3242:
3239:
3236:
3233:
3230:
3229:
3226:
3223:
3220:
3217:
3214:
3211:
3202:
3198:
3195:
3193:
3191:
3188:
3185:
3182:
3179:
3178:
3168:
3164:
3163:
3152:
3147:
3142:
3131:
3123:
3114:
3084:
3059:
3056:
3053:
3050:
3027:
3016:
3015:
3001:
2997:
2994:
2991:
2986:
2982:
2975:
2972:
2969:
2966:
2963:
2945:Main article:
2942:
2939:
2937:
2936:
2935:
2924:
2915:
2911:
2902:
2885:
2884:
2883:
2872:
2866:
2856:
2850:
2841:
2823:
2818:is called the
2805:
2781:
2777:
2774:
2771:
2768:
2765:
2762:
2759:
2756:
2750:
2747:
2744:
2741:
2738:
2733:
2729:
2715:
2697:
2687:
2681:
2678:
2676:
2674:
2668:
2665:
2659:
2654:
2650:
2643:
2640:
2636:
2623:
2619:
2616:
2614:
2612:
2606:
2603:
2600:
2597:
2594:
2591:
2588:
2585:
2582:
2579:
2576:
2573:
2570:
2567:
2564:
2560:
2555:
2550:
2546:
2539:
2536:
2532:
2519:
2515:
2512:
2510:
2508:
2502:
2499:
2494:
2490:
2486:
2483:
2480:
2477:
2474:
2471:
2468:
2465:
2456:
2451:
2446:
2441:
2437:
2431:
2428:
2421:
2418:
2416:
2408:
2404:
2403:
2391:
2390:
2389:
2378:
2372:
2369:
2364:
2360:
2356:
2353:
2350:
2347:
2344:
2338:
2333:
2329:
2323:
2320:
2313:
2304:
2281:
2261:
2258:
2255:
2252:
2240:
2231:) is assumed.
2223:(about 0.707).
2210:
2175:
2172:
2153:
2149:
2146:
2143:
2134:
2130:
2127:
2124:
2115:
2088:
2061:
2034:
2030:
2004:
2000:
1980:
1977:
1974:
1971:
1968:
1957:
1956:
1940:
1930:
1918:
1915:
1912:
1909:
1906:
1882:
1854:
1844:
1822:
1807:
1806:
1794:
1791:
1788:
1785:
1782:
1779:
1770:
1766:
1763:
1760:
1757:
1754:
1729:
1728:
1725:
1722:
1719:
1715:
1707:
1704:
1691:
1688:
1647:
1644:
1622:Coaxial cables
1618:
1617:Coaxial cables
1615:
1593:
1590:
1569:
1566:
1555:power supplies
1534:
1531:
1471:Main article:
1468:
1465:
1452:
1451:High frequency
1449:
1404:
1401:
1378:
1375:
1355:electric shock
1261:
1260:
1249:
1245:
1242:
1239:
1233:
1228:
1210:
1209:
1198:
1194:
1189:
1185:
1181:
1175:
1170:
1139:
1134:
1082:
1079:
1002:electric lamps
982:electric power
977:direct current
959:
958:
956:
955:
948:
941:
933:
930:
929:
926:
925:
920:
915:
910:
905:
900:
895:
890:
885:
880:
875:
870:
865:
860:
855:
850:
845:
840:
835:
830:
825:
820:
815:
810:
805:
800:
795:
790:
785:
780:
775:
770:
765:
760:
755:
750:
744:
741:
740:
737:
736:
733:
732:
727:
722:
717:
712:
710:Four-potential
707:
702:
697:
691:
686:
685:
682:
681:
678:
677:
672:
667:
662:
657:
652:
647:
642:
637:
632:
627:
625:Electric motor
622:
617:
612:
606:
601:
600:
597:
596:
593:
592:
587:
582:
580:Series circuit
577:
572:
567:
562:
557:
552:
550:Kirchhoff laws
547:
542:
537:
532:
527:
522:
517:
515:Direct current
512:
507:
502:
496:
491:
490:
487:
486:
483:
482:
477:
472:
470:Maxwell tensor
467:
462:
457:
452:
447:
442:
440:Larmor formula
437:
432:
427:
422:
417:
412:
407:
402:
397:
392:
390:Bremsstrahlung
386:
381:
380:
377:
376:
373:
372:
367:
362:
357:
352:
347:
342:
340:Magnetic field
337:
332:
327:
322:
316:
313:Magnetostatics
311:
310:
307:
306:
303:
302:
297:
292:
287:
282:
277:
272:
267:
262:
257:
252:
247:
245:Electric field
242:
237:
232:
227:
222:
217:
215:Charge density
211:
208:Electrostatics
206:
205:
202:
201:
200:
199:
194:
189:
184:
179:
174:
169:
161:
160:
152:
151:
145:
144:
143:Articles about
128:
127:
42:
40:
33:
26:
9:
6:
4:
3:
2:
5546:
5535:
5532:
5530:
5527:
5525:
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5520:
5517:
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5514:
5505:
5502:
5499:
5498:
5493:
5491:
5488:
5485:
5484:
5480:
5477:
5471:
5468:
5464:
5460:
5458:
5452:
5451:
5441:
5437:
5436:
5422:
5416:
5412:
5411:
5403:
5395:
5389:
5386:. JHU Press.
5385:
5384:
5376:
5368:
5367:
5359:
5351:
5347:
5340:
5332:
5328:
5321:
5313:
5311:9780472101924
5307:
5303:
5296:
5288:
5286:9781000355314
5282:
5278:
5274:
5273:
5265:
5257:
5251:
5247:
5246:
5238:
5230:
5228:9781476686929
5224:
5220:
5216:
5215:
5207:
5196:
5189:
5188:
5181:
5165:
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5157:
5152:
5147:
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5139:
5132:
5116:
5112:
5106:
5104:
5094:
5087:
5082:
5073:
5069:
5065:
5061:
5057:
5050:
5035:
5031:
5024:
5016:
5009:
5003:, p. 96.
5002:
5001:Hughes (1993)
4997:
4988:
4969:
4962:
4955:
4939:
4935:
4929:
4913:
4907:
4892:on 2012-03-22
4891:
4887:
4881:
4873:
4869:
4865:
4861:
4857:
4853:
4846:
4844:
4824:
4820:
4813:
4806:
4799:
4795:
4789:
4785:
4780:
4779:
4770:
4764:, p. 95.
4763:
4762:Hughes (1993)
4758:
4751:
4750:Hughes (1993)
4746:
4731:on 2015-10-03
4730:
4726:
4722:
4716:
4710:, p. 98.
4709:
4708:Hughes (1993)
4704:
4696:
4695:
4687:
4685:
4669:
4667:0-8018-2873-2
4663:
4659:
4658:
4650:
4634:
4629:
4625:
4621:
4617:
4613:
4612:
4607:
4600:
4585:on 2009-01-19
4584:
4580:
4576:
4572:
4566:
4564:
4555:
4549:
4541:
4539:9780853240631
4535:
4531:
4524:
4510:on 2008-09-07
4509:
4505:
4499:
4491:
4490:
4482:
4474:
4468:
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4463:
4455:
4451:
4440:
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4427:
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4417:
4415:
4412:
4410:
4407:
4405:
4402:
4400:
4397:
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4392:
4391:
4386:
4385:Energy portal
4380:
4375:
4372:
4366:
4361:
4354:
4352:
4348:
4344:
4340:
4335:
4333:
4329:
4325:
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4313:
4309:
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4298:
4293:
4286:
4280:
4276:
4272:
4267:
4263:
4258:
4256:
4252:
4248:
4244:
4240:
4236:
4232:
4228:
4224:
4220:
4219:Thomas Edison
4215:
4211:
4207:
4202:
4198:
4194:
4186:
4179:
4175:
4173:
4168:
4167:power station
4164:
4159:
4157:
4153:
4147:
4145:
4141:
4136:
4132:
4128:
4124:
4117:
4113:
4108:
4102:
4098:
4094:
4090:
4085:
4076:
4074:
4070:
4065:
4061:
4056:
4054:
4050:
4046:
4042:
4038:
4035:developed by
4034:
4029:
4019:
4016:
4014:
4010:
4006:
4001:
3996:
3994:
3990:
3986:
3982:
3978:
3974:
3970:
3966:
3962:
3958:
3954:
3944:
3942:
3937:
3933:
3929:
3925:
3921:
3911:
3897:
3894:
3891:
3888:
3885:
3882:
3879:
3853:
3830:
3825:
3817:
3810:is therefore
3791:
3767:
3758:
3749:
3744:
3738:
3720:
3712:
3698:
3687:
3673:
3661:
3655:
3641:
3631:
3622:
3614:
3594:
3585:
3580:
3571:
3563:
3562:
3561:
3541:
3532:
3528:
3524:
3514:
3512:
3483:
3480:
3477:
3471:
3468:
3465:
3462:
3450:
3447:
3440:
3426:
3416:
3410:
3407:
3401:
3396:
3392:
3386:
3380:
3366:
3356:
3350:
3344:
3338:
3332:
3329:
3327:
3319:
3313:
3303:
3300:
3294:
3291:
3286:
3277:
3271:
3266:
3259:
3253:
3247:
3245:
3237:
3231:
3221:
3218:
3212:
3209:
3200:
3196:
3194:
3186:
3180:
3169:
3166:
3165:
3150:
3145:
3140:
3129:
3121:
3112:
3104:
3103:
3102:
3082:
3073:
3054:
3048:
3039:
3025:
2999:
2992:
2984:
2980:
2973:
2967:
2961:
2954:
2953:
2952:
2948:
2922:
2913:
2909:
2900:
2892:
2890:
2886:
2870:
2864:
2854:
2848:
2839:
2831:
2830:
2828:
2824:
2821:
2803:
2779:
2772:
2769:
2763:
2760:
2757:
2754:
2748:
2742:
2736:
2731:
2727:
2719:
2695:
2685:
2679:
2677:
2666:
2663:
2657:
2652:
2648:
2641:
2638:
2634:
2621:
2617:
2615:
2604:
2601:
2592:
2589:
2586:
2583:
2580:
2577:
2571:
2568:
2565:
2562:
2553:
2548:
2544:
2537:
2534:
2530:
2517:
2513:
2511:
2500:
2497:
2492:
2481:
2478:
2475:
2472:
2466:
2463:
2454:
2444:
2439:
2435:
2429:
2426:
2419:
2417:
2406:
2394:
2392:
2376:
2370:
2367:
2362:
2351:
2345:
2336:
2331:
2327:
2321:
2318:
2311:
2302:
2294:
2293:
2279:
2256:
2250:
2242:
2241:
2239:
2237:
2232:
2230:
2208:
2198:
2193:
2187:
2181:
2180:RMS amplitude
2171:
2151:
2147:
2144:
2132:
2128:
2122:
2113:
2086:
2059:
2032:
2028:
2002:
1998:
1975:
1969:
1966:
1954:
1938:
1931:
1916:
1913:
1910:
1907:
1904:
1896:
1880:
1872:
1868:
1852:
1845:
1842:
1820:
1812:
1811:
1810:
1789:
1786:
1780:
1777:
1768:
1764:
1758:
1752:
1745:
1744:
1743:
1741:
1737:
1726:
1723:
1720:
1717:
1716:
1712:
1703:
1701:
1697:
1687:
1685:
1681:
1677:
1673:
1668:
1664:
1661:
1657:
1652:
1643:
1640:
1636:
1631:
1627:
1623:
1614:
1611:
1607:
1603:
1599:
1592:Twisted pairs
1589:
1587:
1583:
1579:
1575:
1565:
1563:
1560:
1556:
1552:
1548:
1545:
1541:
1530:
1528:
1527:ohmic heating
1524:
1520:
1516:
1512:
1508:
1503:
1501:
1496:
1492:
1488:
1484:
1480:
1474:
1464:
1462:
1458:
1448:
1446:
1442:
1438:
1434:
1430:
1424:
1422:
1418:
1414:
1410:
1403:Low frequency
1400:
1398:
1394:
1390:
1384:
1374:
1371:
1367:
1363:
1358:
1356:
1351:
1346:
1340:
1338:
1334:
1333:neutral point
1329:
1325:
1321:
1317:
1313:
1311:
1307:
1303:
1301:
1297:
1293:
1285:
1281:
1277:
1272:
1268:
1266:
1247:
1243:
1240:
1237:
1226:
1218:
1217:
1216:
1213:
1196:
1192:
1187:
1183:
1179:
1168:
1160:
1159:
1158:
1156:
1132:
1123:
1119:
1115:
1111:
1107:
1097:
1092:
1088:
1078:
1076:
1072:
1068:
1064:
1060:
1056:
1052:
1051:
1046:
1042:
1037:
1035:
1034:
1029:
1028:
1023:
1019:
1015:
1011:
1007:
1003:
999:
995:
991:
987:
983:
979:
978:
973:
969:
965:
954:
949:
947:
942:
940:
935:
934:
932:
931:
924:
921:
919:
916:
914:
911:
909:
906:
904:
901:
899:
896:
894:
891:
889:
886:
884:
881:
879:
876:
874:
871:
869:
866:
864:
861:
859:
856:
854:
851:
849:
846:
844:
841:
839:
836:
834:
831:
829:
826:
824:
821:
819:
816:
814:
811:
809:
806:
804:
801:
799:
796:
794:
791:
789:
786:
784:
781:
779:
776:
774:
771:
769:
766:
764:
761:
759:
756:
754:
751:
749:
746:
745:
739:
738:
731:
728:
726:
723:
721:
718:
716:
713:
711:
708:
706:
703:
701:
698:
696:
693:
692:
689:
684:
683:
676:
673:
671:
668:
666:
663:
661:
658:
656:
653:
651:
648:
646:
643:
641:
638:
636:
633:
631:
628:
626:
623:
621:
618:
616:
613:
611:
608:
607:
604:
599:
598:
591:
588:
586:
583:
581:
578:
576:
573:
571:
568:
566:
563:
561:
558:
556:
553:
551:
548:
546:
545:Joule heating
543:
541:
538:
536:
533:
531:
528:
526:
523:
521:
518:
516:
513:
511:
508:
506:
503:
501:
498:
497:
494:
489:
488:
481:
478:
476:
473:
471:
468:
466:
463:
461:
460:Lorentz force
458:
456:
453:
451:
448:
446:
443:
441:
438:
436:
433:
431:
428:
426:
423:
421:
418:
416:
413:
411:
408:
406:
403:
401:
398:
396:
393:
391:
388:
387:
384:
379:
378:
371:
368:
366:
363:
361:
360:Magnetization
358:
356:
353:
351:
348:
346:
345:Magnetic flux
343:
341:
338:
336:
333:
331:
328:
326:
323:
321:
318:
317:
314:
309:
308:
301:
298:
296:
293:
291:
288:
286:
283:
281:
278:
276:
273:
271:
268:
266:
263:
261:
258:
256:
253:
251:
250:Electric flux
248:
246:
243:
241:
238:
236:
233:
231:
228:
226:
223:
221:
218:
216:
213:
212:
209:
204:
203:
198:
195:
193:
190:
188:
187:Computational
185:
183:
180:
178:
175:
173:
170:
168:
165:
164:
163:
162:
158:
154:
153:
150:
147:
146:
142:
141:
134:
124:
121:
113:
102:
99:
95:
92:
88:
85:
81:
78:
74:
71: â
70:
66:
65:Find sources:
59:
55:
49:
48:
43:This article
41:
37:
32:
31:
19:
5495:
5473:
5454:
5439:
5409:
5402:
5382:
5375:
5365:
5358:
5349:
5345:
5339:
5330:
5326:
5320:
5301:
5295:
5271:
5264:
5244:
5237:
5213:
5206:
5186:
5180:
5168:. Retrieved
5164:the original
5141:
5131:
5119:. Retrieved
5115:the original
5093:
5085:
5081:
5063:
5059:
5049:
5038:. Retrieved
5034:the original
5023:
5014:
5008:
4996:
4987:
4975:. Retrieved
4954:
4942:. Retrieved
4938:the original
4928:
4916:. Retrieved
4906:
4894:. Retrieved
4890:the original
4880:
4855:
4851:
4830:. Retrieved
4805:
4797:
4777:
4769:
4757:
4745:
4735:February 22,
4733:. Retrieved
4729:the original
4724:
4715:
4703:
4693:
4671:. Retrieved
4656:
4649:
4637:. Retrieved
4618:(534): 283.
4615:
4609:
4599:
4587:. Retrieved
4583:the original
4529:
4523:
4512:. Retrieved
4508:the original
4498:
4488:
4481:
4461:
4454:
4336:
4259:
4239:Nikola Tesla
4195:founded the
4190:
4160:
4152:eddy current
4148:
4120:
4057:
4045:Westinghouse
4028:transformers
4025:
4022:Transformers
4017:
4009:Ganz factory
3997:
3950:
3941:over the air
3917:
3782:
3520:
3508:
3040:
3017:
2950:
2820:crest factor
2233:
2229:DC component
2226:
1958:
1808:
1735:
1733:
1700:fiber optics
1696:ohmic losses
1693:
1690:Fiber optics
1659:
1649:
1620:
1598:twisted pair
1595:
1578:acceleration
1571:
1562:transformers
1536:
1510:
1506:
1504:
1476:
1454:
1425:
1406:
1386:
1359:
1345:single phase
1341:
1324:out of phase
1314:
1304:
1289:
1262:
1214:
1211:
1118:high voltage
1103:
1063:square waves
1048:
1038:
1031:
1025:
1021:
1017:
1013:
1009:
975:
967:
963:
962:
705:Four-current
640:Linear motor
525:Electrolysis
499:
405:Eddy current
365:Permeability
285:Polarization
280:Permittivity
116:
107:
97:
90:
83:
76:
64:
52:Please help
47:verification
44:
4308:three-phase
4279:GrÀngesberg
4243:three-phase
4127:OttĂł BlĂĄthy
4101:transformer
4093:OttĂł BlĂĄthy
4058:In the UK,
3920:information
1680:dissipation
1665:. Although
1515:skin depths
1500:skin effect
1473:Skin effect
1445:Switzerland
1316:Three-phase
1292:power plant
1114:power lines
1110:transformer
1018:alternating
1006:wall socket
994:televisions
675:Transformer
505:Capacitance
430:Faraday law
225:Coulomb law
167:Electricity
5513:Categories
5170:January 1,
5040:2009-08-04
4514:2012-03-23
4446:References
4353:in 1918.
4324:generators
4297:horsepower
4135:Ganz Works
4131:Miksa DĂ©ri
4097:Miksa DĂ©ri
3981:Ganz Works
3965:commutator
3953:alternator
3951:The first
3101:, because
2716:where the
2272:of period
1684:conductors
1672:wavelength
1651:Waveguides
1646:Waveguides
1639:waveguides
1630:dielectric
1523:resistance
1519:conductors
1485:) creates
1362:third wire
1155:resistance
1122:resistance
1075:modulation
1039:The usual
742:Scientists
590:Waveguides
570:Resistance
540:Inductance
320:AmpĂšre law
110:March 2023
80:newspapers
5160:230605234
4548:cite book
4290:9.5
4174:in 1886.
3924:telephone
3895:×
3889:×
3883:×
3826:×
3481:ω
3472:
3466:−
3408:ω
3402:
3301:ω
3295:
3219:ω
3213:
2764:
2758:−
2737:
2649:∫
2593:ϕ
2581:ω
2572:
2566:−
2545:∫
2482:ϕ
2473:ω
2467:
2436:∫
2328:∫
2129:−
2123:−
2029:−
1970:
1914:π
1905:ω
1853:ω
1787:ω
1781:
1635:microwave
1582:radiation
1547:inductors
1540:Litz wire
1457:mainframe
1417:arc lamps
1337:harmonics
1296:generator
1045:sine wave
898:Steinmetz
828:Kirchhoff
813:Jefimenko
808:Hopkinson
793:Helmholtz
788:Heaviside
650:Permeance
535:Impedance
275:Insulator
270:Gauss law
220:Conductor
197:Phenomena
192:Textbooks
172:Magnetism
5534:AC power
5479:Archived
5195:Archived
5030:"Blathy"
4968:Archived
4872:51632693
4823:Archived
4394:AC power
4357:See also
4301:15
4283:45
4245:form by
4227:AC motor
4112:Nagycenk
4079:Pioneers
3936:baseband
2947:AC power
1740:function
1610:balanced
1413:railways
1328:polarity
1041:waveform
970:) is an
923:Wiechert
878:Poynting
768:Einstein
615:DC motor
610:AC motor
445:Lenz law
230:Electret
5474:AC/DC:
5455:AC/DC:
5413:. MAA.
5352:. 1915.
5333:. 1915.
5121:Apr 16,
4977:July 8,
4944:Jan 29,
4918:Feb 29,
4620:Bibcode
4332:Ć ibenik
4214:Siemens
4116:Hungary
3947:History
3822: V
3763:average
3731:average
3546:average
3117:average
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