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Voltage

From Wikipedia, the free encyclopedia
Difference in electric potential between two points in space
For other uses, seeVoltage (disambiguation).
"Potential difference" redirects here. For other uses, seePotential.
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Voltage
Batteries are sources of voltage in manyelectric circuits.
Common symbols
V ,∆V ,U ,∆U
SI unitvolt
InSI base unitskg⋅m2⋅s−3⋅A−1
Derivations from
other quantities
Voltage =Energy /charge
DimensionML2T−3I−1{\displaystyle {\mathsf {M}}{\mathsf {L}}^{2}{\mathsf {T}}^{-3}{\mathsf {I}}^{-1}}
Electromagnetism
Solenoid

Voltage, also known as (electrical)potential difference,electric pressure, orelectric tension, is the difference inelectric potential between two points.[1][2] In astaticelectric field, it corresponds to thework needed per unit ofcharge to move a positivetest charge from the first point to the second point. In theInternational System of Units (SI), thederived unit for voltage is thevolt (V).[3][4][5]

The voltage between points can be caused by the build-up ofelectric charge (e.g., acapacitor), and from anelectromotive force (e.g.,electromagnetic induction in agenerator).[6][7] On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-inducedpiezoelectric effect, photovoltaic effect, and thethermoelectric effect. Since it is the difference in electric potential, it is a physicalscalarquantity.[8]

Avoltmeter can be used to measure the voltage between two points in a system.[9] Often a common reference potential such as theground of the system is used as one of the points. In this case, voltage is often mentioned at a point without completely mentioning the other measurement point. A voltage can be associated with either a source of energy or the loss, dissipation, or storage of energy.

Definition

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The SI unit of work per unit charge is thejoule percoulomb, where 1 volt = 1 joule (of work) per 1 coulomb of charge.[citation needed] The old SI definition forvolt usedpower andcurrent; starting in 1990, thequantum Hall andJosephson effect were used,[10] and in 2019physical constants were given defined values for the definition of all SI units.

Voltage is denoted symbolically byΔV{\displaystyle \Delta V}, simplifiedV, especially inEnglish-speaking countries. Internationally, the symbolU is standardized.[11]

Theelectrochemical potential is the voltage that can be directly measured with a voltmeter.[12][13] TheGalvani potential 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§ Galvani potential vs. electrochemical potential).

Voltage is defined so that negatively charged objects are pulled towards higher voltages, while positively charged objects are pulled towards lower voltages.[14][15] Therefore, theconventional current in a wire orresistor always flows from higher voltage to lower voltage.

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 "high tension" (HT) which is commonly used in the contexts of automotive electronics and systems using thermionic valves (vacuum tubes).

Electrostatics

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The electric field around the rod exerts a force on the charged pith ball, in anelectroscope
In a static field, the work is independent of the path
Main article:Electric potential § Electrostatics

Inelectrostatics, the voltage increase from pointrA{\displaystyle \mathbf {r} _{A}} to some pointrB{\displaystyle \mathbf {r} _{B}} is given by the change inelectrostatic potentialV{\textstyle V} fromrA{\displaystyle \mathbf {r} _{A}} torB{\displaystyle \mathbf {r} _{B}}. By definition,[16]: 78  this is:

ΔVAB=V(rB)−V(rA)=−∫r0rBE⋅dℓ−(−∫r0rAE⋅dℓ)=−∫rArBE⋅dℓ{\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}}}

whereE{\displaystyle \mathbf {E} } is the intensity of the electric field.

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.[16]: 90–91  Mathematically, this is expressed as theline integral of theelectric field along that path. In electrostatics, this line integral is independent of the path taken.[16]: 91 

Under this definition, any circuit where there are time-varying magnetic fields, such asAC circuits, will not have a well-defined voltage between nodes in the circuit, since the electric force is not aconservative force in those cases.[note 1] However, at lower frequencies when the electric and magnetic fields are not rapidly changing, this can be neglected (seeelectrostatic approximation).

Electrodynamics

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Main article:Electric potential § Generalization to electrodynamics

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 potential.[16]: 417  Furthermore, the potential is no longer uniquely determined up to a constant, and can take significantly different forms depending on the choice ofgauge.[note 2][16]: 419–422 

In this general case, some authors[17] 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 pathP{\displaystyle {\mathcal {P}}} fromrA{\displaystyle \mathbf {r} _{A}} torB{\displaystyle \mathbf {r} _{B}} is given by:

ΔVAB=−∫PE⋅dℓ{\displaystyle \Delta V_{AB}=-\int _{\mathcal {P}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}}

However, in this case the "voltage" between two points depends on the path taken.

Circuit theory

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Incircuit analysis andelectrical engineering,lumped element models are used to represent and analyze circuits. These elements are idealized and self-contained circuit elements used to model physical components.[18]

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.[18] Under these assumptions, the electric field in the region exterior to each component is conservative, and voltages between nodes in the circuit are well-defined, where[18]

ΔVAB=−∫rArBE⋅dℓ{\displaystyle \Delta V_{AB}=-\int _{\mathbf {r} _{A}}^{\mathbf {r} _{B}}\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}}

as long as the path of integration does not pass through the inside of any component. The above is the same formula used inelectrostatics. This integral, with the path of integration being along the test leads, is what a voltmeter will actually measure.[19][note 3]

If uncontained magnetic fields throughout the circuit are not negligible, then their effects can be modelled by addingmutual inductance 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 closedmagnetic path. If external fields are negligible, we find that

ΔVAB=−∫exteriorE⋅dℓ=LdIdt{\displaystyle \Delta V_{AB}=-\int _{\mathrm {exterior} }\mathbf {E} \cdot \mathrm {d} {\boldsymbol {\ell }}=L{\frac {dI}{dt}}}

is path-independent, and there is a well-defined voltage across the inductor's terminals.[20] This is the reason that measurements with a voltmeter across an inductor are often reasonably independent of the placement of the test leads.

Volt

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Main article:Volt

The volt (symbol:V) is thederived unit forelectric potential, voltage, andelectromotive force.[21][22] The volt is named in honour of the Italian physicistAlessandro Volta (1745–1827), who invented thevoltaic pile, possibly the first chemicalbattery.

Hydraulic analogy

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Main article:Hydraulic analogy

A simple analogy for anelectric circuit is water flowing in a closed circuit ofpipework, driven by a mechanicalpump.[citation needed] This can be called a "water circuit". The potential difference between two points corresponds to thepressure difference 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 aturbine. Similarly, work can be done by anelectric current driven by the potential difference provided by abattery. For example, the voltage provided by a sufficiently-charged automobile battery can "push" a large current through the windings of an automobile'sstarter motor. 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.

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 "pressure drop" (compare p.d.) multiplied by thevolume 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 difference or water pressure difference), the greater the flow between them (electric current or water flow). (See "electric power".)

Applications

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Working onhigh-voltage power lines

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.

A common use of the term "voltage" is in describing the voltage dropped across an electrical device (such as a resistor). Thevoltage drop across the device can be understood as the difference between measurements at each terminal of the device with respect to a common reference point (orground). 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 changingmagnetic field 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.

Addition of voltages

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The voltage betweenA andC is the sum of the voltage betweenA andB and the voltage betweenB andC. The various voltages in a circuit can be computed usingKirchhoff's circuit laws.

When talking aboutalternating current (AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added fordirect current (DC) and AC, but average voltages can be meaningfully added only when they apply to signals that all have the same frequency and phase.

Measuring instruments

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Multimeter set to measure voltage

Instruments for measuring voltages include thevoltmeter, thepotentiometer, and theoscilloscope.Analog voltmeters, such as moving-coil instruments, work by measuring the current through a fixed resistor, which, according toOhm's law, is proportional to the voltage across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in abridge circuit. The cathode-ray oscilloscope works by amplifying the voltage and using it to deflect anelectron beam from a straight path, so that the deflection of the beam is proportional to the voltage.

Typical voltages

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Main articles:Volt § Common voltages,Orders of magnitude (voltage), andMains electricity § Choice of voltage

A common voltage forflashlight batteries is 1.5 volts (DC).A common voltage forautomobile batteries is 12 volts (DC).

Common voltages supplied by power companies to consumers are 110 to 120 volts (AC) in North America and 220 to 240 volts (AC) in most of Europe. The voltage inelectric power transmission lines used to distribute electricity from power stations can be several hundred times greater than consumer voltages, typically 110 to 1200 kV (AC).

The voltage used inoverhead lines to power railway locomotives is between 12 kV and 50 kV (AC) or between 0.75 kV and 3 kV (DC).

Galvani potential vs. electrochemical potential

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Main articles:Galvani potential,Electrochemical potential, andFermi level

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 avoltmeter is connected between two different types of metal, it measures not the electrostatic potential difference, but instead something else that is affected by thermodynamics.[23]The quantity measured by a voltmeter is the negative of the difference of theelectrochemical potential of electrons (Fermi level) divided by the electron charge and commonly referred to as the voltage difference, while the pure unadjustedelectrostatic potential (not measurable with a voltmeter) is sometimes calledGalvani potential.The terms "voltage" and "electric potential" are ambiguous in that, in practice, they can refer toeither of these in different contexts.

History

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The termelectromotive force was first used by Volta in a letter toGiovanni Aldini in 1798, and first appeared in a published paper in 1801 inAnnales de chimie et de physique.[24]: 408  Volta meant by this a force that was not anelectrostatic force, specifically, anelectrochemical force.[24]: 405  The term was taken up byMichael Faraday in connection withelectromagnetic induction in the 1820s. However, a clear definition of voltage and method of measuring it had not been developed at this time.[25]: 554  Volta distinguished electromotive force (emf) fromtension (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.[24]: 405 

See also

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References

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  1. ^Cretì, Anna; Fontini, Fulvio (2019-05-30).Economics of Electricity: Markets, Competition and Rules. Cambridge University Press. p. 18.ISBN 978-1-107-18565-4.
  2. ^Tregub, Stanislav (2020-08-08).Theory of Energy Harmony: Mechanism of Fundamental Interactions. Stanislav Tregub. p. 26.ISBN 978-5-6044739-2-4.
  3. ^David B. Newell, Eite Tiesinga (August 2019).The International System of Units (SI)(PDF) (Report). National Institute of Standards and Technology. p. 31. Retrieved2 January 2024.
  4. ^Holloway, Michael D.; Holloway, Emma (2020-12-09).Dictionary of Industrial Terminology. John Wiley & Sons. p. 1259.ISBN 978-1-119-36410-8.
  5. ^Aslam, Dr S.; Sharma, Dr Pradosh Kumar; Rahul, Satyakam; Saluja, Dr Hitanshu (2024-01-26).Integrating Electrical Systems With Intelligent Computing. Academic Guru Publishing House. p. 17.ISBN 978-81-19843-91-6.
  6. ^Demetrius T. Paris and F. Kenneth Hurd,Basic Electromagnetic Theory, McGraw-Hill, New York 1969,ISBN 0-07-048470-8, pp. 512, 546
  7. ^P. Hammond,Electromagnetism for Engineers, p. 135, Pergamon Press 1969OCLC 854336.
  8. ^Experts, Disha (2017-08-29).10 in One Study Package for CBSE Physics Class 12 with 5 Model Papers. Disha Publications. p. 64.ISBN 978-93-86323-72-9.
  9. ^International, Petrogav.Production Course for Hiring on Offshore Oil and Gas Rigs. Petrogav International. p. 328.
  10. ^David B. Newell, Eite Tiesinga (August 2019).The International System of Units (SI)(PDF) (Report). National Institute of Standards and Technology. p. 88. Retrieved2 January 2024.
  11. ^IEV:voltageArchived 2016-02-03 at theWayback Machine
  12. ^Fischer, Traugott (2009-03-13).Materials Science for Engineering Students. Academic Press. p. 434.ISBN 978-0-08-092002-3.
  13. ^Pulfrey, David L. (2010-01-28).Understanding Modern Transistors and Diodes. Cambridge University Press. p. 93.ISBN 978-1-139-48467-1.
  14. ^Vadari, Mani (2013).Electric System Operations: Evolving to the Modern Grid. Artech House. p. 41.ISBN 978-1-60807-549-2.
  15. ^Vadari, Subramanian (2020-01-31).Electric System Operations: Evolving to the Modern Grid, Second Edition. Artech House. p. 47.ISBN 978-1-63081-689-6.
  16. ^abcdeGriffiths, David J. (1999).Introduction to Electrodynamics (3rd ed.). Prentice Hall.ISBN 013805326X.
  17. ^Moon, Parry; Spencer, Domina Eberle (2013).Foundations of Electrodynamics. Dover Publications. p. 126.ISBN 978-0-486-49703-7.Archived from the original on 2022-03-19. Retrieved2021-11-19.
  18. ^abcA. Agarwal & J. Lang (2007)."Course materials for 6.002 Circuits and Electronics"(PDF).MIT OpenCourseWare.Archived(PDF) from the original on 9 April 2016. Retrieved4 December 2018.
  19. ^Bossavit, Alain (January 2008). "What do voltmeters measure?".COMPEL - the International Journal for Computation and Mathematics in Electrical and Electronic Engineering.27:9–16.doi:10.1108/03321640810836582 – via ResearchGate.
  20. ^Feynman, Richard; Leighton, Robert B.; Sands, Matthew."The Feynman Lectures on Physics Vol. II Ch. 22: AC Circuits".Caltech. Retrieved2021-10-09.
  21. ^Hanssen, Steven; Hampson, Jeffery (2022-09-12).Electrical Trade Principles 6e. Cengage AU. p. 3.ISBN 978-0-17-045885-6.
  22. ^Cardarelli, Francois (2012-12-06).Scientific Unit Conversion: A Practical Guide to Metrication. Springer Science & Business Media. p. 340.ISBN 978-1-4471-3394-0.
  23. ^Bagotskii, Vladimir Sergeevich (2006).Fundamentals of electrochemistry. John Wiley & Sons. p. 22.ISBN 978-0-471-70058-6.
  24. ^abcRobert N. Varney, Leon H. Fisher,"Electromotive force: Volta's forgotten concept"Archived 2021-04-16 at theWayback Machine,American Journal of Physics, vol. 48, iss. 5, pp. 405–408, May 1980.
  25. ^C. J. Brockman,"The origin of voltaic electricity: The contact vs. chemical theory before the concept of E. M. F. was developed"Archived 2022-07-17 at theWayback Machine,Journal of Chemical Education, vol. 5, no. 5, pp. 549–555, May 1928

Footnotes

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  1. ^This follows from theMaxwell-Faraday equation:∇×E=−∂B∂t{\displaystyle \nabla \times \mathbf {E} =-{\frac {\partial \mathbf {B} }{\partial t}}}If there are changing magnetic fields in somesimply connected region, then thecurl of the electric field in that region is non-zero, and as a result the electric field is not conservative. For more, seeConservative force § Mathematical description.
  2. ^For example, in theLorenz gauge, the electric potential is aretarded potential, which propagates at thespeed of light; whereas in theCoulomb gauge, the potential changes instantaneously when the source charge distribution changes.
  3. ^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.

External links

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Look upvoltage in Wiktionary, the free dictionary.
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