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Voltage | |
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Common symbols | V , ∆V , U , ∆U |

SI unit | volt |

In SI base units | kg⋅m^{2}⋅s^{−3}⋅A^{−1} |

Derivations from other quantities | Voltage = Energy / charge |

Dimension | ML^{2}T^{−3}I^{−1} |

Articles about |

Electromagnetism |
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**Voltage**, **electric potential difference**, **electromotive force (emf), electric pressure **or **electric tension** is the difference in electric potential between two points, which (in a static electric field) is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage (potential difference) is named * volt *.^{ [1] }^{:166} In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule (of work) per 1 coulomb (of charge). The old SI definition for *volt* used power and current; starting in 1990, the quantum Hall and Josephson effect were used, and recently (2019) fundamental physical constants have been introduced for the definition of all SI units and derived units.^{ [1] }^{:177f, 197f} Voltage or electric potential difference is denoted symbolically by ∆*V*, simplified *V*,^{ [2] } or *U*,^{ [3] } for instance in the context of Ohm's or Kirchhoff's circuit laws.

- Definition
- Definition as potential of electric field
- Definition via decomposition of electric field
- Treatment in circuit theory
- Volt
- Hydraulic analogy
- Applications
- Addition of voltages
- Measuring instruments
- Typical voltages
- Galvani potential vs. electrochemical potential
- History
- See also
- References
- Footnotes
- External links

Electric potential differences between points can be caused physically by electric charge build up or imbalance (eg. well known "static" and electronic capacitor) also by electric current through a magnetic field, and by time-varying magnetic fields (eg. dynamo or generator), or some combination of these three.^{ [4] }^{ [5] } Additionally on a macroscopic scale potential difference can be caused by electrochemical processes (cells and batteries) and pressure induced piezoelectric effect and heat induced emf across metal junctions. These latter processes at microscopic level have the physical origins previously mentioned. 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 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 (potential drop).

There are multiple useful ways to define voltage, including the standard definition mentioned earlier. There are also other useful definitions of work per charge (see this section).

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 tension" (HT) which is commonly used in thermionic valve (vacuum tube) based electronics.

The voltage increase from point to some point is given by

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 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.

If this definition of voltage is used, any circuit where there are time-varying magnetic fields,^{ [note 1] } such as circuits containing inductors, 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^{ [note 2] } to the components, and voltages are well-defined in that region.^{ [6] } In this case, the voltage across an inductor, viewed externally, turns out to be

despite the fact that, internally, the electric field in the coil is zero^{ [6] } (assuming it is a perfect conductor).

Using the above definition, the electric potential is not defined whenever magnetic fields change with time. In physics, it is 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 electrodynamics:

where is the magnetic vector potential. The above decomposition is justified by Helmholtz's theorem.

In this case, the voltage increase from to is given by

where is the rotational electric field due to time-varying magnetic fields. In this case, the voltage between points is always uniquely defined.

In 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.^{ [7] } If the assumption of negligible leaked fields is too inaccurate, their effects can be modelled by 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 toroid. If leaked fields are negligible, we find that

is path-independent, and there is a well-defined voltage across the inductor's terminals.^{ [6] } This is the reason that measurements with a voltmeter across an inductor are often reasonably independent of the placement of the test leads.

The volt (symbol: **V**) is the 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.

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 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 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 drop" (compare p.d.) 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 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".)

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). 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.

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.

Instruments for measuring voltages include the voltmeter, the potentiometer, and the oscilloscope. Analog voltmeters, 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.

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) and 220 to 240 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 kV (AC).

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

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.^{ [8] } 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.

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 *.^{ [9] }^{:408} Volta meant by this a force that was not an electrostatic force, specifically, an electrochemical force.^{ [9] }^{: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.^{ [10] }^{:554} 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.^{ [9] }^{:405}

- Electric shock
- Mains electricity by country (list of countries with mains voltage and frequency)
- Open-circuit voltage
- Phantom voltage

The **centimetre–gram–second system of units** is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways in which the CGS system was extended to cover electromagnetism.

An **inductor**, also called a **coil**, **choke**, or **reactor**, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a coil.

The **volt** is the derived unit for electric potential, electric potential difference (voltage), and electromotive force. It is named after the Italian physicist Alessandro Volta (1745–1827).

A **voltmeter** is an instrument used for measuring electric potential difference between two points in an electric circuit. It is connected in parallel. It usually has a high resistance so that it takes negligible current from the circuit.

**Ohm's law** states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

The **electric potential** is the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in an electric field with negligible acceleration of the test charge to avoid producing kinetic energy or radiation by test charge. Typically, the reference point is the Earth or a point at infinity, although any point can be used. More precisely it is the energy per unit charge for a small test charge that does not disturb significantly the field and the charge distribution producing the field under consideration.

**Electromagnetic** or **magnetic induction** is the production of an electromotive force across an electrical conductor in a changing magnetic field.

In physics, specifically electromagnetism, the **magnetic flux** through a surface is the surface integral of the normal component of the magnetic field **B** over that surface. It is usually denoted Φ or Φ_{B}. The SI unit of magnetic flux is the weber, and the CGS unit is the maxwell. Magnetic flux is usually measured with a fluxmeter, which contains measuring coils and electronics, that evaluates the change of voltage in the measuring coils to calculate the measurement of magnetic flux.

In electromagnetism and electronics, **electromotive force** is the electrical action produced by a non-electrical source. Devices provide an emf by converting other forms of energy into electrical energy, such as batteries or generators. Sometimes an analogy to water pressure is used to describe electromotive force..

In electric and electronic systems, **reactance** is the opposition of a circuit element to the flow of current due to that element's inductance or capacitance. Greater reactance leads to smaller currents for the same voltage applied. Reactance is similar to electric resistance in this respect, but differs in that reactance does not lead to dissipation of electrical energy as heat. Instead, energy is stored in the reactance, and a quarter-cycle later returned to the circuit, whereas a resistance continuously loses energy.

**Inductance** is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the current, and follows any changes in current. From Faraday's law of induction, any change in magnetic field through a circuit induces an electromotive force (EMF) (voltage) in the conductors, a process known as electromagnetic induction. This induced voltage created by the changing current has the effect of opposing the change in current. This is stated by Lenz's law, and the voltage is called *back EMF*.

Two-terminal components and electrical networks can be connected in series or parallel. The resulting electrical network will have two terminals, and itself can participate in a series or parallel topology. Whether a two-terminal "object" is an electrical component or an electrical network is a matter of perspective. This article will use "component" to refer to a two-terminal "object" that participate in the series/parallel networks.

**Electrostatics** is a branch of physics that studies electric charges at rest.

**Classical electromagnetism** or **classical electrodynamics** is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model. The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are better described by quantum electrodynamics.

The **thermoelectric effect** is the direct conversion of temperature differences to electric voltage and vice versa via a thermocouple. A thermoelectric device creates a voltage when there is a different temperature on each side. Conversely, when a voltage is applied to it, heat is transferred from one side to the other, creating a temperature difference. At the atomic scale, an applied temperature gradient causes charge carriers in the material to diffuse from the hot side to the cold side.

**Faraday's law of induction** is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (EMF)—a phenomenon known as electromagnetic induction. It is the fundamental operating principle of transformers, inductors, and many types of electrical motors, generators and solenoids.

A **magnetic circuit** is made up of one or more closed loop paths containing a magnetic flux. The flux is usually generated by permanent magnets or electromagnets and confined to the path by magnetic cores consisting of ferromagnetic materials like iron, although there may be air gaps or other materials in the path. Magnetic circuits are employed to efficiently channel magnetic fields in many devices such as electric motors, generators, transformers, relays, lifting electromagnets, SQUIDs, galvanometers, and magnetic recording heads.

**Electric field work** is the work performed by an electric field on a charged particle in its vicinity.

In circuit theory, **flux linkage** is a property of a two-terminal element. It is an extension rather than an equivalent of magnetic flux and is defined as a time integral

The **gyrator–capacitor model** - sometimes also the capacitor-permeance model - is a lumped-element model for magnetic circuits, that can be used in place of the more common resistance–reluctance model. The model makes permeance elements analogous to electrical capacitance rather than electrical resistance. Windings are represented as gyrators, interfacing between the electrical circuit and the magnetic model.

- 1 2 International Bureau of Weights and Measures (2019-05-20),
*SI Brochure: The International System of Units (SI)*(PDF) (9th ed.), ISBN 978-92-822-2272-0 - ↑ IEV: electric potential
- ↑ IEV: voltage
- ↑ Demetrius T. Paris and F. Kenneth Hurd,
*Basic Electromagnetic Theory*, McGraw-Hill, New York 1969, ISBN 0-07-048470-8, pp. 512, 546 - ↑ P. Hammond,
*Electromagnetism for Engineers*, p. 135, Pergamon Press 1969 OCLC 854336. - 1 2 3 R. Feynman; et al. "The Feynman Lectures on Physics Vol. II Ch. 22: AC Circuits".
*Caltech*. Retrieved 4 December 2018. - ↑ A. Agarwal & J. Lang (2007). "Course materials for 6.002 Circuits and Electronics" (PDF).
*MIT OpenCourseWare*. Retrieved 4 December 2018. - ↑ Bagotskii, Vladimir Sergeevich (2006).
*Fundamentals of electrochemistry*. p. 22. ISBN 978-0-471-70058-6. - 1 2 3 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. - ↑ 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

- ↑ 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.
- ↑ 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.

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