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Voltage, also known as ( electrical) potential difference, electric pressure, or electric tension, is the difference in electric potential between two points.

(2019). 9781107185654, Cambridge University Press. .
(2020). 9785604473924, Stanislav Tregub. .
In a , it corresponds to the work needed per unit of to move a positive test charge from the first point to the second point. In the (SI), the derived unit for voltage is the ( V).
(2020). 9781119364108, John Wiley & Sons. .
(2024). 9788119843916, Academic Guru Publishing House. .

The voltage between points can be caused by the build-up of (e.g., a ), and from an electromotive force (e.g., electromagnetic induction in a generator).Demetrius T. Paris and F. Kenneth Hurd, Basic Electromagnetic Theory, McGraw-Hill, New York 1969, , pp. 512, 546P. Hammond, Electromagnetism for Engineers, p. 135, Pergamon Press 1969 . On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-induced piezoelectric effect, and the thermoelectric effect. Since it is the difference in electric potential, it is a physical scalar .

(2017). 9789386323729, Disha Publications. .

A can be used to measure the voltage between two points in a system. Often a common reference potential such as the ground 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
The SI unit of work per unit charge is the per , where 1 volt = 1 joule (of work) per 1 coulomb of charge. The old SI definition for volt used and ; starting in 1990, the quantum Hall and were used, and in 2019 physical constants were given defined values for the definition of all SI units.

Voltage is denoted symbolically by \Delta V, simplified V, especially in -speaking countries. Internationally, the symbol U is standardized.IEV: voltage

The electrochemical potential is the voltage that can be directly measured with a voltmeter.

(2009). 9780080920023, Academic Press. .
(2010). 9781139484671, Cambridge University Press. .
The Galvani 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 ).

Voltage is defined so that negatively charged objects are pulled towards higher voltages, while positively charged objects are pulled towards lower voltages.

(2025). 9781608075492, Artech House. .
(2020). 9781630816896, Artech House. .
Therefore, the conventional current in a wire or 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 "" (HT) which is commonly used in the contexts of automotive electronics and systems using thermionic valves ().

Electrostatics
In , the voltage increase from point \mathbf{r}_A to some point \mathbf{r}_B is given by the change in electrostatic potential V from \mathbf{r}_A to \mathbf{r}_B. By definition,
(1999). 013805326X, Prentice Hall. 013805326X
 this is:

\begin{align}
\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{align}

where \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. Mathematically, this is expressed as the of the along that path. In electrostatics, this line integral is independent of the path taken.

Under this definition, any circuit where there are time-varying magnetic fields, such as AC circuits, will not have a well-defined voltage between nodes in the circuit, since the electric force is not a conservative force in those cases.This follows from the Maxwell-Faraday equation:

\nabla\times\mathbf{E}=-\frac{\partial\mathbf{B}}{\partial t}

If there are changing magnetic fields in some simply connected region, then the curl of the electric field in that region is non-zero, and as a result the electric field is not conservative. For more, see . However, at lower frequencies when the electric and magnetic fields are not rapidly changing, this can be neglected (see electrostatic approximation).

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. Furthermore, the potential is no longer uniquely determined up to a constant, and can take significantly different forms depending on the choice of .For example, in the Lorenz gauge, the electric potential is a retarded potential, which propagates at the speed of light; whereas in the , the potential changes instantaneously when the source charge distribution changes.

In this general case, some authors

(2025). 9780486497037, Dover Publications. .
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 \mathcal{P} from \mathbf{r}_A to \mathbf{r}_B is given by:
\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
In circuit analysis and electrical 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.

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 are well-defined, where

\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 in . This integral, with the path of integration being along the test leads, is what a voltmeter will actually measure.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.

If uncontained magnetic fields throughout the circuit are not negligible, then their effects can be modelled by adding mutual 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 closed . If external fields are negligible, we find that

\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. This is the reason that measurements with a voltmeter across an inductor are often reasonably independent of the placement of the test leads.

Volt
The volt (symbol: ) is the derived unit for electric potential, voltage, and electromotive force.
(2022). 9780170458856, Cengage AU. .
(2012). 9781447133940, Springer Science & Business Media. .
The volt is named in honour of the Italian physicist (1745–1827), who invented the , possibly the first chemical battery.

Hydraulic analogy
A simple analogy for an is water flowing in a closed circuit of , driven by a mechanical . This can be called a "water circuit". The potential difference between two points corresponds to the 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 . Similarly, work can be done by an driven by the potential difference provided by a . For example, the voltage provided by a sufficiently-charged automobile battery can "push" a large current through the windings of an automobile's . 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 " drop" (compare p.d.) multiplied by the 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
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). The 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). 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 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 (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
Instruments for measuring voltages include the , the potentiometer, and the . , 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 . The cathode-ray oscilloscope works by amplifying the voltage and using it to deflect an beam from a straight path, so that the deflection of the beam is proportional to the voltage.

Typical voltages
A common voltage for flashlight batteries is 1.5 volts (DC). A common voltage for automobile 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 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 kV (AC).

The voltage used in 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
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 is connected between two different types of metal, it measures not the electrostatic potential difference, but instead something else that is affected by thermodynamics.
(2025). 9780471700586, John Wiley & Sons. .
The quantity measured by a voltmeter is the negative of the difference of the electrochemical potential of electrons () 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 in 1798, and first appeared in a published paper in 1801 in Annales de chimie et de physique. Volta meant by this a force that was not an force, specifically, an force.Robert N. Varney, Leon H. Fisher, "Electromotive force: Volta's forgotten concept" , American Journal of Physics, vol. 48, iss. 5, pp. 405–408, May 1980. The term was taken up by 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.C. J. Brockman, "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 Volta distinguished electromotive force (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.

See also

Footnotes

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