查看“︁Testwiki:臺灣教育專案/臺大物理系服務學習二 (108-1)/電壓”︁的源代码

{{Infobox physical quantity
|bgcolour = {default}
|name = Voltage
|image = [[File:AA AAA AAAA A23 battery comparison-1.jpg|frameless]]
|caption = [[Battery (electricity)|Batteries]] are sources of voltage in many [[Electrical network|electric circuits]].
|unit = [[volt]]
|symbols = {{math|''V''}} , {{math|∆''V''}} , {{math|''U''}} , {{math|∆''U''}}
|dimension = '''M''' '''L'''<sup>2</sup> '''T'''<sup>−3</sup> '''I'''<sup>−1</sup>
| derivations = Voltage = [[Energy]] / [[electric charge|charge]]
}}
'''電壓(Voltage)''', '''電位差(electric potential difference)''', '''electric pressure '''或 '''electric tension''' 是兩個點的電位差距。 在靜電場中，兩點的電壓(電位差)被定義為將一個測試電荷從一點移動到另一點所需要施的功。在SI制單位中，電壓的單位為'''伏特''':<math>1Volt=\frac{1Joule}{1Coulomb}</math> 官方SI單位制中，伏特的定義為<math>1Volt=\frac{1Watt}{1Ampere}</math>，和我們先前更加常見的定義等價。伏特被記為{{math|∆''V''}}，但事實上更常被僅僅記為''V''。

Electric potential differences between points can be caused by electric charge, by [[electric current]] through a [[magnetic field]], by time-varying magnetic fields, or some combination of these three.<ref>Demetrius T. Paris and F. Kenneth Hurd, ''Basic Electromagnetic Theory'', McGraw-Hill, New York 1969, {{ISBN|0-07-048470-8}}, pp. 512, 546</ref><ref>P. Hammond, ''Electromagnetism for Engineers'', p. 135, Pergamon Press 1969 {{OCLC|854336}}.</ref> A [[voltmeter]] can be used to measure the voltage (or potential difference) between two points in a system; often a common reference potential such as the [[ground (electricity)|ground]] of the system is used as one of the points. A voltage may represent either a source of energy ([[electromotive force]]) or lost, used, or stored energy ([[voltage drop|potential drop]]).

==Definition==
There are multiple useful ways to define voltage, including the standard definition mentioned at the start of this page. There are also other useful definitions of work per charge (see [[Voltage#Galvani potential vs. electrochemical potential|this section]]).

Roughly speaking, voltage is defined so that negatively charged objects are pulled towards higher voltages, while positively charged objects are pulled towards lower voltages. Therefore, the [[conventional current]] in a wire or [[resistor]] 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 voltage|high tension]]" (HT) which is commonly used in thermionic valve ([[vacuum tube]]) based electronics.

=== Definition as potential of electric field ===
The voltage increase from some point <math display="inline">x_A</math> to some point <math display="inline">x_B</math> is given by

:<math>\begin{align}
\Delta V_{AB} &= V(x_B) - V(x_A) \\
&= - \int_{r_0}^{x_B} \vec{E} \cdot d\vec{l} - \left( - \int_{r_0}^{x_A} \vec{E} \cdot d\vec{l} \right)\\
&= -\int_{x_A}^{x_B} \vec{E} \cdot d\vec{l}
\end{align} </math>

[[File:Opfindelsernes bog3 fig282.png|thumb|The electric field around the rod exerts a force on the charged pith ball, in an [[electroscope]]]]In this case, the voltage increase from point A to point B is equal to the work which would have to be 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 [[line integral]] of the [[electric field]] along that path. 
Under this definition, the voltage difference between two points is not uniquely defined when there are time-varying magnetic fields since the electric force is not a [[conservative force]] in such cases.[[File:Electrostatic definition of voltage.svg|thumb|In a static field, the work is independent of the path]]
If this definition of voltage is used, any circuit where there are time-varying magnetic fields,<ref group="note">If there are time-varying electric fields or accelerating charges, then there will be time-varying magnetic fields. This means in AC circuits, there are always some non-confined magnetic fields. However, except at higher frequencies, these are neglected.</ref> such as circuits containing [[inductor]]s, will not have a well-defined voltage between nodes in the circuit. However, if magnetic fields are suitably contained to each component, then the electric field is conservative in the region exterior<ref group="note">This relies on the fact that each component has a finite volume. If a component had an infinite extent, the region exterior to the components would not be simply connected, and thus integrals through it would still depend on the path taken.</ref> to the components, and voltages are well-defined in that region.<ref name=":0">{{Cite web|url=http://www.feynmanlectures.caltech.edu/II_22.html|title=The Feynman Lectures on Physics Vol. II Ch. 22: AC Circuits|last=R. Feynman|display-authors=etal|website=Caltech|access-date=4 December 2018}}</ref> In this case, the voltage across an inductor, viewed externally, turns out to be

<math>\Delta V=-L\frac{dI}{dt}</math>

despite the fact that, internally, the electric field in the coil is zero<ref name=":0" /> (assuming it is a perfect conductor).

=== Definition via decomposition of electric field ===
Using the above definition, the electric potential is not defined whenever magnetic fields change with time. In physics, it's sometimes useful to generalize the electric potential by only considering the conservative part of the electric field. This is done by the following decomposition used in [[Classical electromagnetism|electrodynamics]]:

<math>\vec{E}=-\nabla V-\frac{\partial\vec{A}}{\partial t}</math>

where <math display="inline">\vec{A}</math> is the [[Magnetic potential|magnetic vector potential]]. The above decomposition is justified by [[Helmholtz decomposition|Helmholtz's theorem]].

In this case, the voltage increase from <math display="inline">x_A</math> to <math display="inline">x_B</math> is given by

<math>\begin{align}
\Delta V_{AB}&=-\int_{x_A}^{x_B}\vec{E}_\mathrm{conservative}\cdot d\vec{l}\\
&=-\int_{x_A}^{x_B}\left(\vec{E}+\frac{\partial\vec{A}}{\partial t}\right)\cdot d\vec{l}\\
&=-\int_{x_A}^{x_B}(\vec{E}-\vec{E}_\mathrm{induced})\cdot d\vec{l}
\end{align}</math>

where <math display="inline">\vec{E}_\mathrm{induced}</math> is the rotational electric field due to time-varying magnetic fields. In this case, the voltage between points is always uniquely defined.

=== Treatment in circuit theory ===
In [[Network analysis (electrical circuits)|circuit analysis]] and [[electrical engineering]], the voltage across an inductor is not considered to be zero or undefined, as the standard definition would suggest. This is because electrical engineers use a [[lumped element model]] to represent and analyze circuits.

When using a lumped element model, it is assumed that there are no magnetic fields in the region surrounding the circuit and that the effects of these are contained in 'lumped elements', which are idealized and self-contained circuit elements used to model physical components.<ref>{{Cite web|url=https://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/video-lectures/6002_l1.pdf|title=Course materials for 6.002 Circuits and Electronics|last=A. Agarwal & J. Lang|date=2007|website=MIT OpenCourseWare|access-date=4 December 2018}}</ref> If the assumption of negligible leaked fields is too inaccurate, their effects can be modelled by [[Parasitic element (electrical networks)|parasitic components]].

In the case of a physical inductor though, the ideal lumped representation is often accurate. This is because the leaked fields of the inductor are generally negligible, especially if the inductor is a [[Toroidal inductors and transformers|toroid]]. If leaked fields are negligible, we find that

<math>\int_\mathrm{exterior}\vec{E}\cdot d\vec{l}=-L\frac{dI}{dt}</math>

is path-independent, and there is a well-defined voltage across the inductor's terminals.<ref name=":0" /> This is the reason that measurements with a voltmeter across an inductor are often reasonably independent of the placement of the test leads.

==Volt==
{{main|Volt}}
The volt (symbol: {{math|'''V'''}}) is the [[SI derived unit|derived unit]] for [[electric potential]], electric potential difference, and [[electromotive force]]. The volt is named in honour of the Italian physicist [[Alessandro Volta]]  (1745–1827), who invented the [[voltaic pile]], possibly the first chemical [[battery (electricity)|battery]].

==Hydraulic analogy==
{{Main|Hydraulic analogy}}

A simple analogy for an [[electric circuit]] is water flowing in a closed circuit of [[pipework]], driven by a mechanical [[pump]].  This can be called a "water circuit".  Potential difference between two points corresponds to the [[fluid pressure|pressure 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 a [[turbine]]. Similarly, work can be done by an [[electric current]] driven by the potential difference provided by a [[electric battery|battery]]. For example, the voltage provided by a sufficiently-charged automobile battery can "push" a large current through the windings of an automobile's [[starter motor]]. If the pump isn't 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]] multiplied by the [[volume]] of water moved. Similarly, in an electrical circuit, the work done to move electrons or other charge-carriers is equal to "electrical pressure" 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#Definition|electric power]]".)

== Applications ==
[[File:US Navy 110315-N-0278E-002 High-voltage electricians from Naval Facilities Engineering Command (NAVFAC) Hawaii reconfigure electrical circuitry and.jpg|thumb|upright|Working on [[high 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 potential difference, 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). The [[voltage 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 (or [[ground (electricity)|ground]]). 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 [[magnetic 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===
The voltage between ''A'' and ''C'' is the sum of the voltage between ''A'' and ''B'' and the voltage between ''B'' and ''C''. The various voltages in a circuit can be computed using [[Kirchhoff's circuit laws]].

When talking about [[alternating current]] (AC) there is a difference between instantaneous voltage and average voltage. Instantaneous voltages can be added for [[direct 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==

[[File:9VBatteryWithMeter.jpg|thumb|[[Multimeter]] set to measure voltage]]
Instruments for measuring voltages include the [[voltmeter]], the [[Potentiometer (measuring instrument)|potentiometer]], and the [[oscilloscope]]. [[Voltmeter|Analog voltmeter]]s, such as moving-coil instruments, work by measuring the current through a fixed resistor, which, according to [[Ohm's Law]], is proportional to the voltage across the resistor. The potentiometer works by balancing the unknown voltage against a known voltage in a [[bridge circuit]]. The cathode-ray oscilloscope works by amplifying the voltage and using it to deflect an [[electron]] beam from a straight path, so that the deflection of the beam is proportional to the voltage.

==Typical voltages==
{{main|Volt#Common voltages|Orders of magnitude (voltage)|Mains electricity#Choice of voltage}}
A common voltage for [[Battery (electricity)|flashlight batteries]] is 1.5&nbsp;volts (DC).
A common voltage for [[Automotive battery|automobile batteries]] is 12&nbsp;volts (DC).

Common voltages supplied by power companies to consumers are 110 to 120 volts (AC) and 220 to 240&nbsp;volts (AC). The voltage in [[electric power transmission]] lines used to distribute electricity from power stations can be several hundred times greater than consumer voltages, typically 110 to 1200&nbsp;kV (AC).

The voltage used in [[overhead line]]s to power railway locomotives is between 12&nbsp;kV and 50&nbsp;kV (AC) or between 1.5&nbsp;kV and 3&nbsp;kV (DC).

==Galvani potential vs. electrochemical potential==
{{main|Galvani potential|Electrochemical potential|Fermi 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 a [[voltmeter]] is connected between two different types of metal, it measures not the electrostatic potential difference, but instead something else that is affected by thermodynamics.<ref>{{cite book|url=https://books.google.com/books?id=09QI-assq1cC&pg=PA22 |title=Fundamentals of electrochemistry|first= Vladimir Sergeevich|last= Bagotskii|page=22|isbn=978-0-471-70058-6|year=2006}}</ref>
The quantity measured by a voltmeter is the negative of the difference of the [[electrochemical potential]] of electrons ([[Fermi level]]) divided by the electron charge and commonly referred to as the voltage difference, while the pure unadjusted [[electrostatic potential]] (not measurable with a voltmeter) is sometimes called [[Galvani potential]].
The terms "voltage" and "electric potential" are ambiguous in that, in practice, they can refer to ''either'' of these in different contexts.

== History ==
The term ''electromotive force'' was first used by Volta in a letter to [[Giovanni Aldini]] in 1798, and first appeared in a published paper in 1801 in ''[[Annales de chimie et de physique]]''.<ref name=Varney/>{{rp|408}}  Volta meant by this a force that was not an [[electrostatic]] force, specifically, an [[electrochemical]] force.<ref name=Varney>Robert N. Varney, Leon H. Fisher, [https://aapt.scitation.org/doi/abs/10.1119/1.12115 "Electromotive force: Volta's forgotten concept"], ''American Journal of Physics'', vol. 48, iss. 5, pp. 405–408, May 1980.</ref>{{rp|405}}  The term was taken up by [[Michael Faraday]] in connection with [[electromagnetic induction]] in the 1820s.  However, a clear definition of voltage and method of measuring it had not been developed at this time.<ref>C. J. Brockman, [https://pubs.acs.org/doi/abs/10.1021/ed005p549?journalCode=jceda8 "The origin of voltaic electricity: The contact vs. chemical theory before the concept of E. M. F. was developed"], ''Journal of Chemical Education'', vol. 5, no. 5, pp. 549–555, May 1928</ref>{{rp|554}} Volta distinguished emf from ''tension'' (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.<ref name=Varney/>{{rp|405}}

==See also==
{{Portal|Electronics}}
{{div col start}}
* [[Alternating current]] (AC)
* [[Direct current]] (DC)
* [[Electric potential]]
* [[Electric shock]]
* [[Electrical measurements]]
* [[Electrochemical potential]]
* [[Fermi level]]
* [[High voltage]]
* [[Mains electricity]] (an article about domestic power supply voltages)
* [[Mains electricity by country]] (list of countries with mains voltage and frequency)
* [[Ohm's law]]
* [[Ohm]]
* [[Open-circuit voltage]]
* [[Phantom voltage]]
{{div col end}}

==References==
<references />

== Footnotes ==
<references group="note" />

==External links==
{{Wiktionary}}
* [http://www.sengpielaudio.com/calculator-ohm.htm Electrical voltage ''V'', current ''I'', resistivity ''R'', impedance ''Z'', wattage ''P'']
* [http://www.ndt-ed.org/EducationResources/HighSchool/Electricity/voltage.htm Elementary explanation of voltage at NDT Resource Center]

{{Authority control}}

[[Category:Electromagnetism]]
[[Category:Voltage| ]]
[[Category:Electrical systems]]
[[Category:Physical quantities]]