# Voltage

Last updated

Voltage
Batteries are sources of voltage in many electric circuits.
Common symbols
V , V , U , U
SI unit volt
Derivations from
other quantities
Voltage = Energy / charge
Dimension ML2T−3I−1

Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points. The difference in electric potential between two points (i.e., voltage) 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 is named volt . [1] 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 official SI definition for volt uses power and current, where 1 volt = 1 watt (of power) per 1 ampere (of current). [1] This definition is equivalent to the more commonly used 'joules per coulomb'. Voltage or electric potential difference is denoted symbolically by V, but more often simply as V, for instance in the context of Ohm's or Kirchhoff's circuit laws.

An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific point inside the field without producing an acceleration. Typically, the reference point is the Earth or a point at infinity, although any point beyond the influence of the electric field charge can be used.

An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them. Mathematically the electric field is a vector field that associates to each point in space the force, called the Coulomb force, that would be experienced per unit of charge by an infinitesimal test charge at that point. The units of the electric field in the SI system are newtons per coulomb (N/C), or volts per meter (V/m). Electric fields are created by electric charges, or by time-varying magnetic fields. Electric fields are important in many areas of physics, and are exploited practically in electrical technology. On an atomic scale, the electric field is responsible for the attractive force between the atomic nucleus and electrons that holds atoms together, and the forces between atoms that cause chemical bonding. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces of nature.

Electrical work is the work done on a charged particle by an electric field. The equation for 'electrical' work is equivalent to that of 'mechanical' work:

## Contents

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. [2] [3] 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).

An electric current is a flow of electric charge. In electric circuits this charge is often carried by electrons moving through a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in an ionized gas (plasma).

A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field varies with location. As such, it is an example of a vector field.

A voltmeter is an instrument used for measuring electrical potential difference between two points in an electric circuit. Analog voltmeters move a pointer across a scale in proportion to the voltage of the circuit; digital voltmeters give a numerical display of voltage by use of an analog to digital converter.

## 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 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.

A resistor is a passive two-terminal electrical component that implements electrical resistance as a circuit element. In electronic circuits, resistors are used to reduce current flow, adjust signal levels, to divide voltages, bias active elements, and terminate transmission lines, among other uses. High-power resistors that can dissipate many watts of electrical power as heat, may be used as part of motor controls, in power distribution systems, or as test loads for generators. Fixed resistors have resistances that only change slightly with temperature, time or operating voltage. Variable resistors can be used to adjust circuit elements, or as sensing devices for heat, light, humidity, force, or chemical activity.

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 term high voltage usually means electrical energy at voltages high enough to inflict harm on living organisms. Equipment and conductors that carry high voltage warrant particular safety requirements and procedures. In certain industries, high voltage means voltage above a particular threshold (see below). High voltage is used in electrical power distribution, in cathode ray tubes, to generate X-rays and particle beams, to demonstrate arcing, for ignition, in photomultiplier tubes, and in high power amplifier vacuum tubes and other industrial, military and scientific applications.

In electronics, a vacuum tube, an electron tube, or valve or, colloquially, a tube, is a device that controls electric current flow in a high vacuum between electrodes to which an electric potential difference has been applied.

### Definition as potential of electric field

The voltage increase from some point ${\textstyle x_{A}}$ to some point ${\textstyle x_{B}}$ is given by

{\displaystyle {\begin{aligned}\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{aligned}}}

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.

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. [4] In this case, the voltage across an inductor, viewed externally, turns out to be

${\displaystyle \Delta V=-L{\frac {dI}{dt}}}$

despite the fact that, internally, the electric field in the coil is zero [4] (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 electrodynamics:

${\displaystyle {\vec {E}}=-\nabla V-{\frac {\partial {\vec {A}}}{\partial t}}}$

where ${\textstyle {\vec {A}}}$ is the magnetic vector potential. The above decomposition is justified by Helmholtz's theorem.

In this case, the voltage increase from ${\textstyle x_{A}}$ to ${\textstyle x_{B}}$ is given by

{\displaystyle {\begin{aligned}\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{aligned}}}

where ${\textstyle {\vec {E}}_{\mathrm {induced} }}$ 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 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. [5] 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

${\displaystyle \int _{\mathrm {exterior} }{\vec {E}}\cdot d{\vec {l}}=-L{\frac {dI}{dt}}}$

is path-independent, and there is a well-defined voltage across the inductor's terminals. [4] 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: 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.

## 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 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 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".)

## 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 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.

## Measuring instruments

Instruments for measuring voltages include the voltmeter, the potentiometer, and the oscilloscope. The voltmeter works 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

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 1.5 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 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. [6] 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.

## Related Research Articles

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 of extending the CGS system 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 around a core.

In electrical engineering, the power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit, and is a dimensionless number in the closed interval of −1 to 1. A power factor of less than one indicates the voltage and current are not in phase, reducing the instantaneous product of the two. Real power is the instantaneous product of voltage and current and represents the capacity of the electricity for performing work. Apparent power is the average product of current and voltage. Due to energy stored in the load and returned to the source, or due to a non-linear load that distorts the wave shape of the current drawn from the source, the apparent power may be greater than the real power. A negative power factor occurs when the device generates power, which then flows back towards the source.

Electrical impedance is the measure of the opposition that a circuit presents to a current when a voltage is applied. The term complex impedance may be used interchangeably.

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:

Electromotive force, abbreviated emf, is the electrical intensity or "pressure" developed by a source of electrical energy such as a battery or generator. A device that converts other forms of energy into electrical energy provides an emf as its output.

In electrical and electronic systems, reactance is the opposition of a circuit element to a change in current or voltage, due to that element's inductance or capacitance. The notion of reactance is similar to electrical resistance, but it differs in several respects.

In electromagnetism and electronics, inductance is a proportionality factor, relating timely varying electromagnetic quantities, that solely depends on the geometric setting of the involved electrical conductors and material properties. By induction a change in the electric current flowing in one conductor induces an electromotive force (voltage) in this and in the other conductors. The figure describing the effect of one conductor on itself is more precisely called self-inductance, and the figures describing the effects of one conductor with changing current on nearby conductors are called mutual inductances. The notion of inductance is especially handy for dealing with discrete, concentrated components at low frequencies.

Components of an electrical circuit or electronic circuit can be connected in series, parallel, or series-parallel. The two simplest of these are called series and parallel and occur frequently. Components connected in series are connected along a single conductive path, so the same current flows through all of the components but voltage is dropped (lost) across each of the resistances. In a series circuit, the sum of the voltages consumed by each individual resistance is equal to the source voltage. Components connected in parallel are connected along multiple paths so that the current can split up; the same voltage is applied to each component.

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

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 power is the rate, per unit time, at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second.

A capacitor is a passive two-terminal electronic component that stores electrical energy in an electric field. The effect of a capacitor is known as capacitance. While some capacitance exists between any two electrical conductors in proximity in a circuit, a capacitor is a component designed to add capacitance to a circuit. The capacitor was originally known as a condenser or condensator. The original name is still widely used in many languages, but not commonly in English.

The Volta potential in electrochemistry, is the electrostatic potential difference between two metals that are in contact and are in thermodynamic equilibrium. Specifically, it is the potential difference between a point close to the surface of the first metal, and a point close to the surface of the second metal.

Electrostatic voltmeter can refer to an electrostatic charge meter, known also as surface DC voltmeter, or to a voltmeter to measure large electrical potentials, traditionally called electrostatic voltmeter.

Most of the terms listed in Wikipedia glossaries are already defined and explained within Wikipedia itself. However, glossaries like this one are useful for looking up, comparing and reviewing large numbers of terms together. You can help enhance this page by adding new terms or writing definitions for existing ones.

Electromagnetism is the study of interactions between particles and the electromagnetic field. It includes the study of forces between charged particles, electromagnetic fields and potential, the behavior of conductors and insulators in fields, circuits, magnetism, and electromagnetic waves. An understanding of electromagnetism is important for practical applications like electrical engineering and chemistry. In addition, concepts taught in courses on electromagnetism provide a basis for more advanced material in physics, such as quantum field theory and general relativity. This article focuses on a conceptual understanding of the topics rather than the details of the mathematics involved.

## References

1. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN   92-822-2213-6, archived (PDF) from the original on 2017-08-14, p. 144
2. Demetrius T. Paris and F. Kenneth Hurd, Basic Electromagnetic Theory, McGraw-Hill, New York 1969, ISBN   0-07-048470-8, pp. 512, 546
3. P. Hammond, Electromagnetism for Engineers, p. 135, Pergamon Press 1969 OCLC   854336.
4. R. Feynman; et al. "The Feynman Lectures on Physics Vol. II Ch. 22: AC Circuits". Caltech. Retrieved 4 December 2018.
5. A. Agarwal & J. Lang (2007). "Course materials for 6.002 Circuits and Electronics" (PDF). MIT OpenCourseWare. Retrieved 4 December 2018.
6. Bagotskii, Vladimir Sergeevich (2006). Fundamentals of electrochemistry. p. 22. ISBN   978-0-471-70058-6.

## Footnotes

1. 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.
2. 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.