2446:
1841:
1396:
156:
1558:
349:
1385:
1836:{\displaystyle {\begin{aligned}\Delta V_{AB}&=V(\mathbf {r} _{B})-V(\mathbf {r} _{A})\\&=-\int _{\mathbf {r} _{0}}^{\mathbf {r} _{B}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}-\left(-\int _{\mathbf {r} _{0}}^{\mathbf {r} _{A}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}\right)\\&=-\int _{\mathbf {r} _{A}}^{\mathbf {r} _{B}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}\end{aligned}}}
2529:
2712:
50:
2098:
When using a lumped element model, it is assumed that the effects of changing magnetic fields produced by the circuit are suitably contained to each element. Under these assumptions, the electric field in the region exterior to each component is conservative, and voltages between nodes in the circuit
2432:
of water moved. Similarly, in an electrical circuit, the work done to move electrons or other charge carriers is equal to "electrical pressure difference" multiplied by the quantity of electrical charges moved. In relation to "flow", the larger the "pressure difference" between two points (potential
1909:
The electric potential can be generalized to electrodynamics, so that differences in electric potential between points are well-defined even in the presence of time-varying fields. However, unlike in electrostatics, the electric field can no longer be expressed only in terms of the electric
2457:
Specifying a voltage measurement requires explicit or implicit specification of the points across which the voltage is measured. When using a voltmeter to measure voltage, one electrical lead of the voltmeter must be connected to the first point, one to the second point.
2325:
2190:
2195:
as long as the path of integration does not pass through the inside of any component. The above is the same formula used in electrostatics. This integral, with the path of integration being along the test leads, is what a voltmeter will actually measure.
2445:
2637:
is connected between two different types of metal, it measures not the electrostatic potential difference, but instead something else that is affected by thermodynamics. The quantity measured by a voltmeter is the negative of the difference of the
2070:
1871:
In this case, the voltage increase from point A to point B is equal to the work done per unit charge, against the electric field, to move the charge from A to B without causing any acceleration. Mathematically, this is expressed as the
2330:
is path-independent, and there is a well-defined voltage across the inductor's terminals. This is the reason that measurements with a voltmeter across an inductor are often reasonably independent of the placement of the test leads.
3520:
325:
2203:
elements. In the case of a physical inductor though, the ideal lumped representation is often accurate. This is because the external fields of inductors are generally negligible, especially if the inductor has a closed
3243:
2421:. If the pump is not working, it produces no pressure difference, and the turbine will not rotate. Likewise, if the automobile's battery is very weak or "dead" (or "flat"), then it will not turn the starter motor.
1917:
In this general case, some authors use the word "voltage" to refer to the line integral of the electric field, rather than to differences in electric potential. In this case, the voltage rise along some path
3568:
This statement makes a few assumptions about the nature of the voltmeter (these are discussed in the cited paper). One of these assumptions is that the current drawn by the voltmeter is negligible.
2214:
2700:(potential difference): the observed potential difference at the terminals of an electrochemical cell when it was open circuit must exactly balance the emf of the cell so that no current flowed.
2105:
1563:
2633:
Inside a conductive material, the energy of an electron is affected not only by the average electric potential but also by the specific thermal and atomic environment that it is in. When a
2469:). The voltage drop is the difference between the two readings. Two points in an electric circuit that are connected by an ideal conductor without resistance and not within a changing
906:
3232:
1998:
1969:
1550:
1521:
1469:
1440:
879:
1940:
1357:
Voltage is defined so that negatively charged objects are pulled towards higher voltages, while positively charged objects are pulled towards lower voltages. Therefore, the
2405:
between two points. If the pump creates a pressure difference between two points, then water flowing from one point to the other will be able to do work, such as driving a
2006:
1866:
2696:
in the 1820s. However, a clear definition of voltage and method of measuring it had not been developed at this time. Volta distinguished electromotive force (emf) from
891:
1317:
1368:
Historically, voltage has been referred to using terms like "tension" and "pressure". Even today, the term "tension" is still used, for example within the phrase "
1910:
potential. Furthermore, the potential is no longer uniquely determined up to a constant, and can take significantly different forms depending on the choice of
1350:
that exists in structures with junctions of dissimilar materials is also work per charge but cannot be measured with a voltmeter in the external circuit (see
3469:
1492:
3030:
3011:
2604:
lines used to distribute electricity from power stations can be several hundred times greater than consumer voltages, typically 110 to 1200 kV (AC).
1142:
911:
258:
2465:
across the device can be understood as the difference between measurements at each terminal of the device with respect to a common reference point (or
1253:
of the system is used as one of the points. A voltage can be associated with either a source of energy or the loss, dissipation, or storage of energy.
921:
2417:. For example, the voltage provided by a sufficiently-charged automobile battery can "push" a large current through the windings of an automobile's
2424:
The hydraulic analogy is a useful way of understanding many electrical concepts. In such a system, the work done to move water is equal to the "
2095:
are used to represent and analyze circuits. These elements are idealized and self-contained circuit elements used to model physical components.
3433:
2084:
1227:). On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-induced
746:
3385:
3358:
3331:
3199:
3138:
3111:
3084:
3057:
2949:
2880:
2853:
2800:
2773:
761:
383:
2559:, is proportional to the voltage across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in a
2544:
3205:
1891:
in those cases. However, at lower frequencies when the electric and magnetic fields are not rapidly changing, this can be neglected (see
3624:
2520:(DC) and AC, but average voltages can be meaningfully added only when they apply to signals that all have the same frequency and phase.
2473:
have a voltage of zero. Any two points with the same potential may be connected by a conductor and no current will flow between them.
641:
2904:
373:
133:
2600:
Common voltages supplied by power companies to consumers are 110 to 120 volts (AC) and 220 to 240 volts (AC). The voltage in
2676:
3409:
2320:{\displaystyle \Delta V_{AB}=-\int _{\mathrm {exterior} }\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}=L{\frac {dI}{dt}}}
556:
2461:
A common use of the term "voltage" is in describing the voltage dropped across an electrical device (such as a resistor). The
3172:
2185:{\displaystyle \Delta V_{AB}=-\int _{\mathbf {r} _{A}}^{\mathbf {r} _{B}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}}
1135:
901:
378:
71:
2580:
916:
621:
3530:
of the electric field in that region is non-zero, and as a result the electric field is not conservative. For more, see
2731:
781:
771:
756:
521:
388:
2199:
If uncontained magnetic fields throughout the circuit are not negligible, then their effects can be modelled by adding
821:
511:
3619:
2601:
2516:(AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added for
1074:
949:
846:
114:
2506:
1336:
741:
2433:
difference or water pressure difference), the greater the flow between them (electric current or water flow). (See "
86:
2611:
to power railway locomotives is between 12 kV and 50 kV (AC) or between 0.75 kV and 3 kV (DC).
574:
1249:
can be used to measure the voltage between two points in a system. Often a common reference potential such as the
60:
3431:"The origin of voltaic electricity: The contact vs. chemical theory before the concept of E. M. F. was developed"
2693:
2639:
2624:
1343:
1220:
1128:
1089:
616:
606:
546:
541:
481:
3027:
3008:
3463:
2646:) divided by the electron charge and commonly referred to as the voltage difference, while the pure unadjusted
2555:, such as moving-coil instruments, work by measuring the current through a fixed resistor, which, according to
93:
67:
31:
1059:
939:
626:
2983:
2817:
2647:
1064:
1034:
466:
456:
451:
3270:
COMPEL - the
International Journal for Computation and Mathematics in Electrical and Electronic Engineering
3544:
3523:
2088:
886:
656:
431:
155:
100:
2590:
2401:. This can be called a "water circuit". The potential difference between two points corresponds to the
2372:
1395:
1232:
984:
671:
661:
611:
601:
348:
160:
1887:, will not have a well-defined voltage between nodes in the circuit, since the electric force is not a
2065:{\displaystyle \Delta V_{AB}=-\int _{\mathcal {P}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}}
1974:
1945:
1526:
1497:
1445:
1416:
2737:
2654:. The terms "voltage" and "electric potential" are ambiguous in that, in practice, they can refer to
2466:
2092:
1358:
1250:
1228:
1109:
1009:
974:
726:
591:
491:
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411:
251:
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1921:
516:
82:
2513:
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1884:
1282:
1216:
1069:
1049:
1044:
851:
836:
721:
691:
586:
1849:
3548:
3531:
3527:
2717:
2594:
2356:
1904:
1888:
1472:
1404:
1224:
1171:
944:
684:
486:
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164:
2843:
3381:
3354:
3348:
3327:
3195:
3189:
3168:
3134:
3107:
3080:
3053:
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2966:
2945:
2921:
2900:
2876:
2849:
2796:
2769:
2651:
2620:
2584:
2567:
beam from a straight path, so that the deflection of the beam is proportional to the voltage.
2384:
2200:
1347:
1299:
1290:
1182:
1004:
3375:
3128:
3101:
3074:
2939:
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17:
3614:
3321:
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2414:
2410:
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2364:
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1384:
1324:
1286:
1278:
1236:
1104:
1019:
979:
969:
856:
811:
794:
711:
646:
416:
340:
2869:
Aslam, Dr S.; Sharma, Dr
Pradosh Kumar; Rahul, Satyakam; Saluja, Dr Hitanshu (2024-01-26).
3437:
3413:
3034:
3015:
2742:
2689:
2685:
2671:
2563:. The cathode-ray oscilloscope works by amplifying the voltage and using it to deflect an
2352:
1208:
1194:
1039:
964:
959:
826:
701:
666:
561:
526:
426:
244:
1883:
Under this definition, any circuit where there are time-varying magnetic fields, such as
1880:
along that path. In electrostatics, this line integral is independent of the path taken.
1079:
3552:
3515:{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}}
2726:
2560:
2517:
2470:
2434:
2402:
1892:
1877:
1410:
1274:
1178:
1175:
999:
994:
816:
706:
631:
581:
531:
504:
461:
436:
406:
399:
1269:, where 1 volt = 1 joule (of work) per 1 coulomb of charge. The old SI definition for
3608:
3556:
3406:
2681:
2608:
2418:
1873:
1186:
1114:
1099:
1084:
1024:
736:
651:
636:
551:
536:
441:
107:
3559:, the potential changes instantaneously when the source charge distribution changes.
2548:
2462:
2450:
2368:
1911:
1477:
1389:
1369:
1094:
989:
954:
896:
831:
716:
596:
471:
220:
3580:
2556:
2528:
2075:
However, in this case the "voltage" between two points depends on the path taken.
1332:
751:
320:{\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-3}{\mathsf {I}}^{-1}}
3296:
1388:
The electric field around the rod exerts a force on the charged pith ball, in an
2643:
2628:
1373:
1014:
866:
696:
358:
49:
2711:
3281:
2707:
2532:
731:
2634:
2552:
2540:
1246:
1212:
1054:
1029:
841:
766:
363:
38:
2564:
2425:
2394:
1362:
1239:
806:
801:
421:
3130:
Electric System
Operations: Evolving to the Modern Grid, Second Edition
2925:
2406:
1266:
1190:
207:
2941:
10 in One Study
Package for CBSE Physics Class 12 with 5 Model Papers
2429:
1235:. Since it is the difference in electric potential, it is a physical
861:
368:
240:
2989:(Report). National Institute of Standards and Technology. p. 88
2823:(Report). National Institute of Standards and Technology. p. 31
1351:
1346:
is the voltage that can be directly measured with a voltmeter. The
2527:
2444:
1394:
1383:
1262:
2576:
2398:
2340:
1199:
212:
3268:
Bossavit, Alain (January 2008). "What do voltmeters measure?".
2792:
Theory of Energy
Harmony: Mechanism of Fundamental Interactions
1293:
were given defined values for the definition of all SI units.
43:
3297:"The Feynman Lectures on Physics Vol. II Ch. 22: AC Circuits"
1331:
is standardized. It is used, for instance, in the context of
3350:
Scientific Unit
Conversion: A Practical Guide to Metrication
2674:
in 1798, and first appeared in a published paper in 1801 in
2038:
1927:
1207:
The voltage between points can be caused by the build-up of
27:
Difference in electric potential between two points in space
1905:
Electric potential § Generalization to electrodynamics
37:"Potential difference" redirects here. For other uses, see
2505:. The various voltages in a circuit can be computed using
2968:
Production Course for Hiring on
Offshore Oil and Gas Rigs
2872:
Integrating
Electrical Systems With Intelligent Computing
2765:
Economics of
Electricity: Markets, Competition and Rules
3295:
Feynman, Richard; Leighton, Robert B.; Sands, Matthew.
3103:
Electric System
Operations: Evolving to the Modern Grid
2363:. The volt is named in honour of the Italian physicist
3353:. Springer Science & Business Media. p. 340.
2650:(not measurable with a voltmeter) is sometimes called
1480:
1399:
In a static field, the work is independent of the path
1352:§ Galvani potential vs. electrochemical potential
3472:
3233:"Course materials for 6.002 Circuits and Electronics"
2217:
2108:
2009:
1977:
1948:
1924:
1852:
1561:
1529:
1500:
1448:
1419:
1302:
261:
2734:(list of countries with mains voltage and frequency)
2842:Holloway, Michael D.; Holloway, Emma (2020-12-09).
1372:" (HT) which is commonly used in thermionic valve (
1365:always flows from higher voltage to lower voltage.
250:
231:
218:
206:
172:
148:
74:. Unsourced material may be challenged and removed.
3532:Conservative force § Mathematical description
3514:
2319:
2208:. If external fields are negligible, we find that
2184:
2064:
1992:
1963:
1934:
1860:
1835:
1544:
1515:
1486:
1463:
1434:
1311:
319:
2413:driven by the potential difference provided by a
1327:-speaking countries. Internationally, the symbol
1189:from the first point to the second point. In the
3407:"Electromotive force: Volta's forgotten concept"
3320:Hanssen, Steven; Hampson, Jeffery (2022-09-12).
2680:. Volta meant by this a force that was not an
2615:Galvani potential vs. electrochemical potential
2539:Instruments for measuring voltages include the
3522:If there are changing magnetic fields in some
2982:David B. Newell, Eite Tiesinga (August 2019).
2875:. Academic Guru Publishing House. p. 17.
2816:David B. Newell, Eite Tiesinga (August 2019).
2593:is 1.5 volts (DC). A common voltage for
1185:needed per unit of charge to move a positive
1136:
8:
3188:Moon, Parry; Spencer, Domina Eberle (2013).
3076:Understanding Modern Transistors and Diodes
2762:CretĂŹ, Anna; Fontini, Fulvio (2019-05-30).
1261:The SI unit of work per unit charge is the
3079:. Cambridge University Press. p. 93.
3049:Materials Science for Engineering Students
2768:. Cambridge University Press. p. 18.
2585:Mains electricity § Choice of voltage
1143:
1129:
347:
331:
154:
3496:
3490:
3479:
3471:
3420:, vol. 48, iss. 5, pp. 405â408, May 1980.
3401:
3399:
3397:
2297:
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2225:
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2017:
2008:
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1301:
308:
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301:
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285:
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277:
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263:
262:
260:
134:Learn how and when to remove this message
2895:Demetrius T. Paris and F. Kenneth Hurd,
2393:is water flowing in a closed circuit of
1868:is the intensity of the electric field.
1405:Electric potential § Electrostatics
3455:
3374:Bagotskii, Vladimir Sergeevich (2006).
2848:. John Wiley & Sons. p. 1259.
2754:
2670:was first used by Volta in a letter to
2428:drop" (compare p.d.) multiplied by the
2287:
2178:
2058:
1825:
1756:
1694:
892:Electromagnetism and special relativity
339:
3444:, vol. 5, no. 5, pp. 549â555, May 1928
2984:The International System of Units (SI)
2971:. Petrogav International. p. 328.
2818:The International System of Units (SI)
303:
286:
272:
264:
145:
3380:. John Wiley & Sons. p. 22.
3226:
3224:
3222:
3158:
3156:
3154:
3152:
3150:
912:Maxwell equations in curved spacetime
7:
2845:Dictionary of Industrial Terminology
2409:. Similarly, work can be done by an
1376:) based and automotive electronics.
72:adding citations to reliable sources
3347:Cardarelli, Francois (2012-12-06).
3194:. Dover Publications. p. 126.
1296:Voltage is denoted symbolically by
3503:
3493:
3473:
3405:Robert N. Varney, Leon H. Fisher,
3127:Vadari, Subramanian (2020-01-31).
2944:. Disha Publications. p. 64.
2489:is the sum of the voltage between
2282:
2267:
2264:
2261:
2258:
2255:
2252:
2249:
2246:
2218:
2173:
2109:
2053:
2010:
1820:
1751:
1689:
1566:
1413:, the voltage increase from point
1303:
25:
3249:from the original on 9 April 2016
3231:A. Agarwal & J. Lang (2007).
2688:force. The term was taken up by
1160:(electrical) potential difference
3497:
3480:
3377:Fundamentals of electrochemistry
3073:Pulfrey, David L. (2010-01-28).
3046:Fischer, Traugott (2009-03-13).
2795:. Stanislav Tregub. p. 26.
2789:Tregub, Stanislav (2020-08-08).
2710:
2677:Annales de chimie et de physique
2658:of these in different contexts.
2274:
2165:
2152:
2138:
2045:
1993:{\displaystyle \mathbf {r} _{B}}
1980:
1964:{\displaystyle \mathbf {r} _{A}}
1951:
1854:
1812:
1799:
1785:
1743:
1730:
1716:
1681:
1668:
1654:
1621:
1597:
1545:{\displaystyle \mathbf {r} _{B}}
1532:
1516:{\displaystyle \mathbf {r} _{A}}
1503:
1464:{\displaystyle \mathbf {r} _{B}}
1451:
1435:{\displaystyle \mathbf {r} _{A}}
1422:
48:
3208:from the original on 2022-03-19
3167:(3rd ed.). Prentice Hall.
3165:Introduction to Electrodynamics
3052:. Academic Press. p. 434.
163:are sources of voltage in many
59:needs additional citations for
3547:, the electric potential is a
3323:Electrical Trade Principles 6e
3191:Foundations of Electrodynamics
2920:, p. 135, Pergamon Press 1969
2918:Electromagnetism for Engineers
2899:, McGraw-Hill, New York 1969,
2371:, possibly the first chemical
2367:(1745â1827), who invented the
1935:{\displaystyle {\mathcal {P}}}
1631:
1616:
1607:
1592:
1:
3442:Journal of Chemical Education
2938:Experts, Disha (2017-08-29).
2581:Orders of magnitude (voltage)
1191:International System of Units
917:Relativistic electromagnetism
18:Electric potential difference
3163:Griffiths, David J. (1999).
3133:. Artech House. p. 47.
3106:. Artech House. p. 41.
2897:Basic Electromagnetic Theory
2732:Mains electricity by country
1861:{\displaystyle \mathbf {E} }
3418:American Journal of Physics
2602:electric power transmission
2577:Volt § Common voltages
1893:electrostatic approximation
3641:
3625:Electromagnetic quantities
3551:, which propagates at the
2618:
2574:
2382:
2338:
1902:
1552:. By definition, this is:
1471:is given by the change in
1402:
642:LiĂ©nardâWiechert potential
36:
29:
3326:. Cengage AU. p. 3.
3284:– via ResearchGate.
3282:10.1108/03321640810836582
2965:International, Petrogav.
2694:electromagnetic induction
2640:electrochemical potential
2625:Electrochemical potential
2397:, driven by a mechanical
1344:electrochemical potential
1221:electromagnetic induction
1174:between two points. In a
907:Mathematical descriptions
617:Electromagnetic radiation
607:Electromagnetic induction
547:Magnetic vector potential
542:Magnetic scalar potential
153:
3464:Maxwell-Faraday equation
2684:force, specifically, an
2507:Kirchhoff's circuit laws
2497:and the voltage between
2389:A simple analogy for an
2099:are well-defined, where
1337:Kirchhoff's circuit laws
1312:{\displaystyle \Delta V}
1281:; starting in 1990, the
1181:, it corresponds to the
32:Voltage (disambiguation)
2648:electrostatic potential
2597:is 12 volts (DC).
1473:electrostatic potential
1289:were used, and in 2019
457:Electrostatic induction
452:Electrostatic discharge
3516:
3462:This follows from the
2536:
2535:set to measure voltage
2454:
2321:
2186:
2089:electrical engineering
2066:
1994:
1965:
1936:
1862:
1837:
1546:
1517:
1488:
1465:
1436:
1400:
1392:
1313:
887:Electromagnetic tensor
321:
3517:
3100:Vadari, Mani (2013).
2589:A common voltage for
2531:
2524:Measuring instruments
2448:
2322:
2187:
2093:lumped element models
2067:
1995:
1966:
1937:
1863:
1838:
1547:
1518:
1489:
1466:
1437:
1398:
1387:
1314:
1233:thermoelectric effect
1170:is the difference in
880:Covariant formulation
672:Synchrotron radiation
612:Electromagnetic pulse
602:Electromagnetic field
322:
3543:For example, in the
3470:
2738:Open-circuit voltage
2607:The voltage used in
2595:automobile batteries
2591:flashlight batteries
2481:The voltage between
2477:Addition of voltages
2215:
2106:
2007:
1975:
1946:
1922:
1850:
1559:
1527:
1498:
1478:
1446:
1417:
1359:conventional current
1300:
1229:piezoelectric effect
922:Stressâenergy tensor
847:Reluctance (complex)
592:Displacement current
259:
68:improve this article
30:For other uses, see
3581:Electrical voltage
2692:in connection with
2668:electromotive force
2514:alternating current
2512:When talking about
2403:pressure difference
2361:electromotive force
2163:
1810:
1741:
1679:
1217:electromotive force
1197:for voltage is the
837:Magnetomotive force
722:Electromotive force
692:Alternating current
627:Jefimenko equations
587:Cyclotron radiation
3620:Electrical systems
3549:retarded potential
3512:
3436:2022-07-17 at the
3412:2021-04-16 at the
3240:MIT OpenCourseWare
3033:2016-02-03 at the
3014:2021-04-28 at the
3009:electric potential
2718:Electronics portal
2537:
2455:
2357:electric potential
2345:The volt (symbol:
2317:
2182:
2131:
2062:
1990:
1961:
1932:
1889:conservative force
1858:
1833:
1831:
1778:
1709:
1647:
1542:
1513:
1484:
1461:
1432:
1401:
1393:
1309:
1291:physical constants
1172:electric potential
685:Electrical network
522:Gauss magnetic law
487:Static electricity
447:Electric potential
317:
222:SI base units
3555:; whereas in the
3526:region, then the
3510:
3387:978-0-471-70058-6
3360:978-1-4471-3394-0
3333:978-0-17-045885-6
3201:978-0-486-49703-7
3140:978-1-63081-689-6
3113:978-1-60807-549-2
3086:978-1-139-48467-1
3059:978-0-08-092002-3
2951:978-93-86323-72-9
2882:978-81-19843-91-6
2855:978-1-119-36410-8
2802:978-5-6044739-2-4
2775:978-1-107-18565-4
2652:Galvani potential
2621:Galvani potential
2553:Analog voltmeters
2385:Hydraulic analogy
2379:Hydraulic analogy
2315:
2201:mutual inductance
1348:Galvani potential
1164:electric pressure
1153:
1152:
852:Reluctance (real)
822:Gyratorâcapacitor
767:Resonant cavities
657:Maxwell equations
330:
329:
165:electric circuits
144:
143:
136:
118:
16:(Redirected from
3632:
3569:
3566:
3560:
3541:
3535:
3524:simply connected
3521:
3519:
3518:
3513:
3511:
3509:
3501:
3500:
3491:
3483:
3460:
3445:
3429:C. J. Brockman,
3427:
3421:
3403:
3392:
3391:
3371:
3365:
3364:
3344:
3338:
3337:
3317:
3311:
3310:
3308:
3307:
3292:
3286:
3285:
3265:
3259:
3258:
3256:
3254:
3248:
3237:
3228:
3217:
3216:
3214:
3213:
3185:
3179:
3178:
3160:
3145:
3144:
3124:
3118:
3117:
3097:
3091:
3090:
3070:
3064:
3063:
3043:
3037:
3024:
3018:
3005:
2999:
2998:
2996:
2994:
2988:
2979:
2973:
2972:
2962:
2956:
2955:
2935:
2929:
2914:
2908:
2893:
2887:
2886:
2866:
2860:
2859:
2839:
2833:
2832:
2830:
2828:
2822:
2813:
2807:
2806:
2786:
2780:
2779:
2759:
2720:
2715:
2714:
2571:Typical voltages
2411:electric current
2391:electric circuit
2365:Alessandro Volta
2350:
2326:
2324:
2323:
2318:
2316:
2314:
2306:
2298:
2290:
2285:
2277:
2272:
2271:
2270:
2233:
2232:
2191:
2189:
2188:
2183:
2181:
2176:
2168:
2162:
2161:
2160:
2155:
2148:
2147:
2146:
2141:
2124:
2123:
2085:circuit analysis
2071:
2069:
2068:
2063:
2061:
2056:
2048:
2043:
2042:
2041:
2025:
2024:
1999:
1997:
1996:
1991:
1989:
1988:
1983:
1970:
1968:
1967:
1962:
1960:
1959:
1954:
1941:
1939:
1938:
1933:
1931:
1930:
1867:
1865:
1864:
1859:
1857:
1842:
1840:
1839:
1834:
1832:
1828:
1823:
1815:
1809:
1808:
1807:
1802:
1795:
1794:
1793:
1788:
1768:
1764:
1760:
1759:
1754:
1746:
1740:
1739:
1738:
1733:
1726:
1725:
1724:
1719:
1697:
1692:
1684:
1678:
1677:
1676:
1671:
1664:
1663:
1662:
1657:
1637:
1630:
1629:
1624:
1606:
1605:
1600:
1581:
1580:
1551:
1549:
1548:
1543:
1541:
1540:
1535:
1522:
1520:
1519:
1514:
1512:
1511:
1506:
1493:
1491:
1490:
1485:
1470:
1468:
1467:
1462:
1460:
1459:
1454:
1441:
1439:
1438:
1433:
1431:
1430:
1425:
1323:, especially in
1318:
1316:
1315:
1310:
1287:Josephson effect
1168:electric tension
1158:, also known as
1145:
1138:
1131:
812:Electric machine
795:Magnetic circuit
757:Parallel circuit
747:Network analysis
712:Electric current
647:London equations
492:Triboelectricity
482:Potential energy
351:
341:Electromagnetism
332:
326:
324:
323:
318:
316:
315:
307:
306:
299:
298:
290:
289:
282:
281:
276:
275:
268:
267:
235:other quantities
233:Derivations from
223:
202:
195:
189:
182:
158:
146:
139:
132:
128:
125:
119:
117:
76:
52:
44:
21:
3640:
3639:
3635:
3634:
3633:
3631:
3630:
3629:
3605:
3604:
3577:
3572:
3567:
3563:
3542:
3538:
3502:
3492:
3468:
3467:
3461:
3457:
3453:
3448:
3438:Wayback Machine
3428:
3424:
3414:Wayback Machine
3404:
3395:
3388:
3373:
3372:
3368:
3361:
3346:
3345:
3341:
3334:
3319:
3318:
3314:
3305:
3303:
3294:
3293:
3289:
3267:
3266:
3262:
3252:
3250:
3246:
3235:
3230:
3229:
3220:
3211:
3209:
3202:
3187:
3186:
3182:
3175:
3162:
3161:
3148:
3141:
3126:
3125:
3121:
3114:
3099:
3098:
3094:
3087:
3072:
3071:
3067:
3060:
3045:
3044:
3040:
3035:Wayback Machine
3025:
3021:
3016:Wayback Machine
3006:
3002:
2992:
2990:
2986:
2981:
2980:
2976:
2964:
2963:
2959:
2952:
2937:
2936:
2932:
2915:
2911:
2894:
2890:
2883:
2868:
2867:
2863:
2856:
2841:
2840:
2836:
2826:
2824:
2820:
2815:
2814:
2810:
2803:
2788:
2787:
2783:
2776:
2761:
2760:
2756:
2752:
2747:
2743:Phantom voltage
2716:
2709:
2706:
2690:Michael Faraday
2686:electrochemical
2672:Giovanni Aldini
2664:
2631:
2619:Main articles:
2617:
2587:
2575:Main articles:
2573:
2526:
2479:
2443:
2387:
2381:
2359:, voltage, and
2346:
2343:
2337:
2307:
2299:
2240:
2221:
2213:
2212:
2150:
2136:
2112:
2104:
2103:
2081:
2032:
2013:
2005:
2004:
1978:
1973:
1972:
1949:
1944:
1943:
1920:
1919:
1907:
1901:
1899:Electrodynamics
1848:
1847:
1830:
1829:
1797:
1783:
1766:
1765:
1728:
1714:
1705:
1701:
1666:
1652:
1635:
1634:
1619:
1595:
1582:
1569:
1557:
1556:
1530:
1525:
1524:
1501:
1496:
1495:
1476:
1475:
1449:
1444:
1443:
1420:
1415:
1414:
1407:
1382:
1298:
1297:
1259:
1215:), and from an
1209:electric charge
1149:
1120:
1119:
935:
927:
926:
882:
872:
871:
827:Induction motor
797:
787:
786:
702:Current density
687:
677:
676:
667:Poynting vector
577:
575:Electrodynamics
567:
566:
562:Right-hand rule
527:Magnetic dipole
517:BiotâSavart law
507:
497:
496:
432:Electric dipole
427:Electric charge
402:
300:
283:
269:
257:
256:
236:
234:
221:
197:
191:
184:
178:
175:
168:
140:
129:
123:
120:
77:
75:
65:
53:
42:
35:
28:
23:
22:
15:
12:
11:
5:
3638:
3636:
3628:
3627:
3622:
3617:
3607:
3606:
3603:
3602:
3589:, resistivity
3576:
3575:External links
3573:
3571:
3570:
3561:
3553:speed of light
3536:
3508:
3505:
3499:
3495:
3489:
3486:
3482:
3478:
3475:
3454:
3452:
3449:
3447:
3446:
3422:
3393:
3386:
3366:
3359:
3339:
3332:
3312:
3287:
3260:
3218:
3200:
3180:
3173:
3146:
3139:
3119:
3112:
3092:
3085:
3065:
3058:
3038:
3019:
3000:
2974:
2957:
2950:
2930:
2909:
2907:, pp. 512, 546
2888:
2881:
2861:
2854:
2834:
2808:
2801:
2781:
2774:
2753:
2751:
2748:
2746:
2745:
2740:
2735:
2729:
2727:Electric shock
2723:
2722:
2721:
2705:
2702:
2663:
2660:
2642:of electrons (
2616:
2613:
2609:overhead lines
2572:
2569:
2561:bridge circuit
2525:
2522:
2518:direct current
2478:
2475:
2471:magnetic field
2442:
2439:
2435:electric power
2383:Main article:
2380:
2377:
2339:Main article:
2336:
2333:
2328:
2327:
2313:
2310:
2305:
2302:
2296:
2293:
2289:
2284:
2280:
2276:
2269:
2266:
2263:
2260:
2257:
2254:
2251:
2248:
2243:
2239:
2236:
2231:
2228:
2224:
2220:
2193:
2192:
2180:
2175:
2171:
2167:
2159:
2154:
2145:
2140:
2134:
2130:
2127:
2122:
2119:
2115:
2111:
2080:
2079:Circuit theory
2077:
2073:
2072:
2060:
2055:
2051:
2047:
2040:
2035:
2031:
2028:
2023:
2020:
2016:
2012:
1987:
1982:
1958:
1953:
1929:
1903:Main article:
1900:
1897:
1878:electric field
1856:
1844:
1843:
1827:
1822:
1818:
1814:
1806:
1801:
1792:
1787:
1781:
1777:
1774:
1771:
1769:
1767:
1763:
1758:
1753:
1749:
1745:
1737:
1732:
1723:
1718:
1712:
1708:
1704:
1700:
1696:
1691:
1687:
1683:
1675:
1670:
1661:
1656:
1650:
1646:
1643:
1640:
1638:
1636:
1633:
1628:
1623:
1618:
1615:
1612:
1609:
1604:
1599:
1594:
1591:
1588:
1585:
1583:
1579:
1576:
1572:
1568:
1565:
1564:
1539:
1534:
1510:
1505:
1487:{\textstyle V}
1483:
1458:
1453:
1442:to some point
1429:
1424:
1411:electrostatics
1403:Main article:
1381:
1380:Electrostatics
1378:
1308:
1305:
1258:
1255:
1179:electric field
1151:
1150:
1148:
1147:
1140:
1133:
1125:
1122:
1121:
1118:
1117:
1112:
1107:
1102:
1097:
1092:
1087:
1082:
1077:
1072:
1067:
1062:
1057:
1052:
1047:
1042:
1037:
1032:
1027:
1022:
1017:
1012:
1007:
1002:
997:
992:
987:
982:
977:
972:
967:
962:
957:
952:
947:
942:
936:
933:
932:
929:
928:
925:
924:
919:
914:
909:
904:
902:Four-potential
899:
894:
889:
883:
878:
877:
874:
873:
870:
869:
864:
859:
854:
849:
844:
839:
834:
829:
824:
819:
817:Electric motor
814:
809:
804:
798:
793:
792:
789:
788:
785:
784:
779:
774:
772:Series circuit
769:
764:
759:
754:
749:
744:
742:Kirchhoff laws
739:
734:
729:
724:
719:
714:
709:
707:Direct current
704:
699:
694:
688:
683:
682:
679:
678:
675:
674:
669:
664:
662:Maxwell tensor
659:
654:
649:
644:
639:
634:
632:Larmor formula
629:
624:
619:
614:
609:
604:
599:
594:
589:
584:
582:Bremsstrahlung
578:
573:
572:
569:
568:
565:
564:
559:
554:
549:
544:
539:
534:
532:Magnetic field
529:
524:
519:
514:
508:
505:Magnetostatics
503:
502:
499:
498:
495:
494:
489:
484:
479:
474:
469:
464:
459:
454:
449:
444:
439:
437:Electric field
434:
429:
424:
419:
414:
409:
407:Charge density
403:
400:Electrostatics
398:
397:
394:
393:
392:
391:
386:
381:
376:
371:
366:
361:
353:
352:
344:
343:
337:
336:
335:Articles about
328:
327:
314:
311:
305:
297:
294:
288:
280:
274:
266:
254:
248:
247:
237:
232:
229:
228:
225:
216:
215:
210:
204:
203:
176:
174:Common symbols
173:
170:
169:
159:
151:
150:
142:
141:
56:
54:
47:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
3637:
3626:
3623:
3621:
3618:
3616:
3613:
3612:
3610:
3601:
3600:
3596:
3592:
3588:
3584:
3579:
3578:
3574:
3565:
3562:
3558:
3557:Coulomb gauge
3554:
3550:
3546:
3540:
3537:
3533:
3529:
3525:
3506:
3487:
3484:
3476:
3465:
3459:
3456:
3450:
3443:
3439:
3435:
3432:
3426:
3423:
3419:
3415:
3411:
3408:
3402:
3400:
3398:
3394:
3389:
3383:
3379:
3378:
3370:
3367:
3362:
3356:
3352:
3351:
3343:
3340:
3335:
3329:
3325:
3324:
3316:
3313:
3302:
3298:
3291:
3288:
3283:
3279:
3275:
3271:
3264:
3261:
3245:
3241:
3234:
3227:
3225:
3223:
3219:
3207:
3203:
3197:
3193:
3192:
3184:
3181:
3176:
3170:
3166:
3159:
3157:
3155:
3153:
3151:
3147:
3142:
3136:
3132:
3131:
3123:
3120:
3115:
3109:
3105:
3104:
3096:
3093:
3088:
3082:
3078:
3077:
3069:
3066:
3061:
3055:
3051:
3050:
3042:
3039:
3036:
3032:
3029:
3023:
3020:
3017:
3013:
3010:
3004:
3001:
2985:
2978:
2975:
2970:
2969:
2961:
2958:
2953:
2947:
2943:
2942:
2934:
2931:
2927:
2923:
2919:
2913:
2910:
2906:
2905:0-07-048470-8
2902:
2898:
2892:
2889:
2884:
2878:
2874:
2873:
2865:
2862:
2857:
2851:
2847:
2846:
2838:
2835:
2819:
2812:
2809:
2804:
2798:
2794:
2793:
2785:
2782:
2777:
2771:
2767:
2766:
2758:
2755:
2749:
2744:
2741:
2739:
2736:
2733:
2730:
2728:
2725:
2724:
2719:
2713:
2708:
2703:
2701:
2699:
2695:
2691:
2687:
2683:
2682:electrostatic
2679:
2678:
2673:
2669:
2661:
2659:
2657:
2653:
2649:
2645:
2641:
2636:
2630:
2626:
2622:
2614:
2612:
2610:
2605:
2603:
2598:
2596:
2592:
2586:
2582:
2578:
2570:
2568:
2566:
2562:
2558:
2554:
2550:
2546:
2545:potentiometer
2542:
2534:
2530:
2523:
2521:
2519:
2515:
2510:
2508:
2504:
2500:
2496:
2492:
2488:
2484:
2476:
2474:
2472:
2468:
2464:
2459:
2452:
2447:
2440:
2438:
2436:
2431:
2427:
2422:
2420:
2419:starter motor
2416:
2412:
2408:
2404:
2400:
2396:
2392:
2386:
2378:
2376:
2374:
2370:
2366:
2362:
2358:
2354:
2349:
2342:
2334:
2332:
2311:
2308:
2303:
2300:
2294:
2291:
2278:
2241:
2237:
2234:
2229:
2226:
2222:
2211:
2210:
2209:
2207:
2206:magnetic path
2202:
2197:
2169:
2157:
2143:
2132:
2128:
2125:
2120:
2117:
2113:
2102:
2101:
2100:
2096:
2094:
2090:
2086:
2078:
2076:
2049:
2033:
2029:
2026:
2021:
2018:
2014:
2003:
2002:
2001:
2000:is given by:
1985:
1956:
1915:
1913:
1906:
1898:
1896:
1894:
1890:
1886:
1881:
1879:
1875:
1874:line integral
1869:
1816:
1804:
1790:
1779:
1775:
1772:
1770:
1761:
1747:
1735:
1721:
1710:
1706:
1702:
1698:
1685:
1673:
1659:
1648:
1644:
1641:
1639:
1626:
1613:
1610:
1602:
1589:
1586:
1584:
1577:
1574:
1570:
1555:
1554:
1553:
1537:
1508:
1481:
1474:
1456:
1427:
1412:
1406:
1397:
1391:
1386:
1379:
1377:
1375:
1371:
1366:
1364:
1361:in a wire or
1360:
1355:
1353:
1349:
1345:
1340:
1338:
1334:
1330:
1326:
1322:
1319:, simplified
1306:
1294:
1292:
1288:
1284:
1280:
1276:
1272:
1268:
1264:
1256:
1254:
1252:
1248:
1243:
1241:
1238:
1234:
1230:
1226:
1222:
1218:
1214:
1210:
1205:
1203:
1201:
1196:
1192:
1188:
1184:
1180:
1177:
1173:
1169:
1165:
1161:
1157:
1146:
1141:
1139:
1134:
1132:
1127:
1126:
1124:
1123:
1116:
1113:
1111:
1108:
1106:
1103:
1101:
1098:
1096:
1093:
1091:
1088:
1086:
1083:
1081:
1078:
1076:
1073:
1071:
1068:
1066:
1063:
1061:
1058:
1056:
1053:
1051:
1048:
1046:
1043:
1041:
1038:
1036:
1033:
1031:
1028:
1026:
1023:
1021:
1018:
1016:
1013:
1011:
1008:
1006:
1003:
1001:
998:
996:
993:
991:
988:
986:
983:
981:
978:
976:
973:
971:
968:
966:
963:
961:
958:
956:
953:
951:
948:
946:
943:
941:
938:
937:
931:
930:
923:
920:
918:
915:
913:
910:
908:
905:
903:
900:
898:
895:
893:
890:
888:
885:
884:
881:
876:
875:
868:
865:
863:
860:
858:
855:
853:
850:
848:
845:
843:
840:
838:
835:
833:
830:
828:
825:
823:
820:
818:
815:
813:
810:
808:
805:
803:
800:
799:
796:
791:
790:
783:
780:
778:
775:
773:
770:
768:
765:
763:
760:
758:
755:
753:
750:
748:
745:
743:
740:
738:
737:Joule heating
735:
733:
730:
728:
725:
723:
720:
718:
715:
713:
710:
708:
705:
703:
700:
698:
695:
693:
690:
689:
686:
681:
680:
673:
670:
668:
665:
663:
660:
658:
655:
653:
652:Lorentz force
650:
648:
645:
643:
640:
638:
635:
633:
630:
628:
625:
623:
620:
618:
615:
613:
610:
608:
605:
603:
600:
598:
595:
593:
590:
588:
585:
583:
580:
579:
576:
571:
570:
563:
560:
558:
555:
553:
552:Magnetization
550:
548:
545:
543:
540:
538:
537:Magnetic flux
535:
533:
530:
528:
525:
523:
520:
518:
515:
513:
510:
509:
506:
501:
500:
493:
490:
488:
485:
483:
480:
478:
475:
473:
470:
468:
465:
463:
460:
458:
455:
453:
450:
448:
445:
443:
442:Electric flux
440:
438:
435:
433:
430:
428:
425:
423:
420:
418:
415:
413:
410:
408:
405:
404:
401:
396:
395:
390:
387:
385:
382:
380:
379:Computational
377:
375:
372:
370:
367:
365:
362:
360:
357:
356:
355:
354:
350:
346:
345:
342:
338:
334:
333:
312:
309:
295:
292:
278:
255:
253:
249:
246:
242:
238:
230:
226:
224:
217:
214:
211:
209:
205:
201:
194:
188:
181:
177:
171:
166:
162:
157:
152:
147:
138:
135:
127:
124:February 2018
116:
113:
109:
106:
102:
99:
95:
92:
88:
85: â
84:
80:
79:Find sources:
73:
69:
63:
62:
57:This article
55:
51:
46:
45:
40:
33:
19:
3598:
3594:
3593:, impedance
3590:
3586:
3582:
3564:
3545:Lorenz gauge
3539:
3458:
3441:
3425:
3417:
3376:
3369:
3349:
3342:
3322:
3315:
3304:. Retrieved
3300:
3290:
3273:
3269:
3263:
3251:. Retrieved
3239:
3210:. Retrieved
3190:
3183:
3164:
3129:
3122:
3102:
3095:
3075:
3068:
3048:
3041:
3022:
3003:
2991:. Retrieved
2977:
2967:
2960:
2940:
2933:
2917:
2916:P. Hammond,
2912:
2896:
2891:
2871:
2864:
2844:
2837:
2825:. Retrieved
2811:
2791:
2784:
2764:
2757:
2697:
2675:
2667:
2665:
2655:
2632:
2606:
2599:
2588:
2549:oscilloscope
2538:
2511:
2502:
2498:
2494:
2490:
2486:
2482:
2480:
2463:voltage drop
2460:
2456:
2451:high voltage
2441:Applications
2423:
2388:
2369:voltaic pile
2353:derived unit
2347:
2344:
2329:
2198:
2194:
2097:
2082:
2074:
1916:
1908:
1882:
1870:
1845:
1408:
1390:electroscope
1370:high tension
1367:
1356:
1341:
1328:
1320:
1295:
1283:quantum Hall
1270:
1260:
1244:
1206:
1198:
1195:derived unit
1167:
1163:
1159:
1155:
1154:
897:Four-current
832:Linear motor
776:
717:Electrolysis
597:Eddy current
557:Permeability
477:Polarization
472:Permittivity
208:SI unit
199:
192:
186:
179:
130:
121:
111:
104:
97:
90:
78:
66:Please help
61:verification
58:
2644:Fermi level
2629:Fermi level
2453:power lines
2449:Working on
1885:AC circuits
1374:vacuum tube
1187:test charge
867:Transformer
697:Capacitance
622:Faraday law
417:Coulomb law
359:Electricity
3609:Categories
3597:, wattage
3585:, current
3306:2021-10-09
3253:4 December
3212:2021-11-19
3174:013805326X
2750:References
2547:, and the
2533:Multimeter
1257:Definition
1231:, and the
1193:(SI), the
934:Scientists
782:Waveguides
762:Resistance
732:Inductance
512:AmpĂšre law
239:Voltage =
94:newspapers
3504:∂
3494:∂
3488:−
3477:×
3474:∇
3451:Footnotes
2993:2 January
2827:2 January
2666:The term
2635:voltmeter
2557:Ohm's law
2541:voltmeter
2351:) is the
2288:ℓ
2279:⋅
2242:∫
2238:−
2219:Δ
2179:ℓ
2170:⋅
2133:∫
2129:−
2110:Δ
2059:ℓ
2050:⋅
2034:∫
2030:−
2011:Δ
1826:ℓ
1817:⋅
1780:∫
1776:−
1757:ℓ
1748:⋅
1711:∫
1707:−
1699:−
1695:ℓ
1686:⋅
1649:∫
1645:−
1611:−
1567:Δ
1304:Δ
1247:voltmeter
1225:generator
1213:capacitor
1211:(e.g., a
1090:Steinmetz
1020:Kirchhoff
1005:Jefimenko
1000:Hopkinson
985:Helmholtz
980:Heaviside
842:Permeance
727:Impedance
467:Insulator
462:Gauss law
412:Conductor
389:Phenomena
384:Textbooks
364:Magnetism
310:−
293:−
252:Dimension
161:Batteries
83:"Voltage"
39:Potential
3434:Archived
3410:Archived
3276:: 9â16.
3244:Archived
3206:Archived
3031:Archived
3012:Archived
2704:See also
2565:electron
2426:pressure
2395:pipework
1363:resistor
1240:quantity
1115:Wiechert
1070:Poynting
960:Einstein
807:DC motor
802:AC motor
637:Lenz law
422:Electret
227:kgâ
mâ
sâ
A
3615:Voltage
3301:Caltech
3028:voltage
2698:tension
2662:History
2415:battery
2407:turbine
2373:battery
1876:of the
1325:English
1279:current
1267:coulomb
1219:(e.g.,
1156:Voltage
1100:Thomson
1075:Ritchie
1065:Poisson
1050:Neumann
1045:Maxwell
1040:Lorentz
1035:Liénard
965:Faraday
950:Coulomb
777:Voltage
752:Ohm law
374:History
149:Voltage
108:scholar
3384:
3357:
3330:
3198:
3171:
3137:
3110:
3083:
3056:
2948:
2926:854336
2924:
2903:
2879:
2852:
2799:
2772:
2656:either
2627:, and
2583:, and
2543:, the
2467:ground
2430:volume
1846:where
1251:ground
1237:scalar
1176:static
1085:Singer
1080:Savart
1060:Ărsted
1025:Larmor
1015:Kelvin
970:Fizeau
940:AmpĂšre
862:Stator
369:Optics
245:charge
241:Energy
110:
103:
96:
89:
81:
3247:(PDF)
3236:(PDF)
3026:IEV:
3007:IEV:
2987:(PDF)
2821:(PDF)
1942:from
1912:gauge
1494:from
1333:Ohm's
1275:power
1273:used
1263:joule
1223:in a
1166:, or
1110:Weber
1105:Volta
1095:Tesla
1010:Joule
995:Hertz
990:Henry
975:Gauss
857:Rotor
115:JSTOR
101:books
3528:curl
3382:ISBN
3355:ISBN
3328:ISBN
3255:2018
3196:ISBN
3169:ISBN
3135:ISBN
3108:ISBN
3081:ISBN
3054:ISBN
2995:2024
2946:ISBN
2922:OCLC
2901:ISBN
2877:ISBN
2850:ISBN
2829:2024
2797:ISBN
2770:ISBN
2501:and
2493:and
2485:and
2437:".)
2399:pump
2355:for
2341:Volt
2335:Volt
2087:and
1342:The
1285:and
1277:and
1271:volt
1265:per
1200:volt
1183:work
1030:Lenz
955:Davy
945:Biot
213:volt
87:news
3278:doi
2083:In
1971:to
1895:).
1523:to
1409:In
1354:).
1335:or
1204:.
1202:(V)
1055:Ohm
219:In
70:by
3611::
3466::
3440:,
3416:,
3396:^
3299:.
3274:27
3272:.
3242:.
3238:.
3221:^
3204:.
3149:^
2623:,
2579:,
2551:.
2509:.
2375:.
2091:,
1914:.
1339:.
1245:A
1242:.
1162:,
243:/
196:,
190:,
183:,
3599:P
3595:Z
3591:R
3587:I
3583:V
3534:.
3507:t
3498:B
3485:=
3481:E
3390:.
3363:.
3336:.
3309:.
3280::
3257:.
3215:.
3177:.
3143:.
3116:.
3089:.
3062:.
2997:.
2954:.
2928:.
2885:.
2858:.
2831:.
2805:.
2778:.
2503:C
2499:B
2495:B
2491:A
2487:C
2483:A
2348:V
2312:t
2309:d
2304:I
2301:d
2295:L
2292:=
2283:d
2275:E
2268:r
2265:o
2262:i
2259:r
2256:e
2253:t
2250:x
2247:e
2235:=
2230:B
2227:A
2223:V
2174:d
2166:E
2158:B
2153:r
2144:A
2139:r
2126:=
2121:B
2118:A
2114:V
2054:d
2046:E
2039:P
2027:=
2022:B
2019:A
2015:V
1986:B
1981:r
1957:A
1952:r
1928:P
1855:E
1821:d
1813:E
1805:B
1800:r
1791:A
1786:r
1773:=
1762:)
1752:d
1744:E
1736:A
1731:r
1722:0
1717:r
1703:(
1690:d
1682:E
1674:B
1669:r
1660:0
1655:r
1642:=
1632:)
1627:A
1622:r
1617:(
1614:V
1608:)
1603:B
1598:r
1593:(
1590:V
1587:=
1578:B
1575:A
1571:V
1538:B
1533:r
1509:A
1504:r
1482:V
1457:B
1452:r
1428:A
1423:r
1329:U
1321:V
1307:V
1144:e
1137:t
1130:v
313:1
304:I
296:3
287:T
279:2
273:L
265:M
200:U
198:â
193:U
187:V
185:â
180:V
167:.
137:)
131:(
126:)
122:(
112:·
105:·
98:·
91:·
64:.
41:.
34:.
20:)
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