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Volt

The volt (symbol: V) is the derived unit in the (SI) for measuring difference, also known as voltage, as well as . It is named after the Italian physicist (1745–1827), who invented the in 1800, the first device capable of producing a steady through chemical reactions. One volt represents the electric potential difference between two points in a wire carrying a of one when the power dissipated between those points is one watt. Equivalently, it is the amount of , one joule, required to move one of between the points. In terms of SI base units, the volt is expressed as kilogram meter squared per second cubed per , or kg⋅m²⋅s⁻³⋅A⁻¹. This unit was formally adopted as part of the SI in 1960 through CGPM Resolution 12, building on earlier definitions established in 1948. The volt plays a central role in electrical engineering, physics, and everyday technology, quantifying the "push" that drives electric current through circuits and devices ranging from household appliances to advanced electronics. Since the 2019 SI revision, which fixed the values of fundamental constants like the elementary charge and speed of light, the volt's realization has become more precise through quantum standards such as the Josephson effect, enabling highly accurate voltage measurements independent of material artifacts. Common multiples include the kilovolt (kV) for high-voltage transmission lines and the millivolt (mV) for low-level signals in sensors.

Definition and Fundamentals

Formal SI Definition

The volt (symbol: V) is the SI unit of electric potential difference (voltage). It is defined as the electric potential difference between two points of a conducting wire carrying a constant current of 1 ampere when the power dissipated between these points is equal to 1 watt. This definition derives from the fundamental relation for electric power, P = V I, where P is power in watts, V is potential difference in volts, and I is current in amperes, yielding $1 \, \mathrm{V} = 1 \, \mathrm{W} / 1 \, \mathrm{A}. It connects to resistance through Ohm's law, V = I R, where R is resistance in ohms, such that power dissipation P = I^2 R aligns with the unit definition when I = 1 \, \mathrm{A} and P = 1 \, \mathrm{W}. The definition was proposed by the International Committee for Weights and Measures (CIPM) in 1946 and formally adopted by the 9th General Conference on Weights and Measures (CGPM) in 1948 as part of the electrical units in the metre-kilogram-second (MKS) system. It was incorporated into the upon its establishment in 1960 and remains unchanged in the 2019 revision of the , which redefined base units via fixed constants but preserved the relational definitions of derived units like the volt. The volt is a derived unit, expressed in terms of the base units kilogram, , second, and as \mathrm{V} = \mathrm{kg \cdot m^2 \cdot s^{-3} \cdot A^{-1}}.

Relation to Base Units

The dimensional formula for the volt in the (SI) is [V] = kg·m²·s⁻³·A⁻¹, derived from the relationship between difference and work per unit charge, where one volt is defined as the potential difference across a when one joule of is dissipated per of charge transferred. This formula arises because the joule (J) has dimensions kg·m²·s⁻² and the (C) has dimensions A·s, so dividing the former by the latter yields the volt's dimensions. The volt depends on four of the seven SI base units: (kg), (m), time (s), and (A), with no involvement of temperature (K), (mol), or (cd). This composition reflects the volt's role as a derived in , tying mechanical and electrical quantities together through fundamental interactions. The 2019 redefinition of the units fixed the value of the e to exactly 1.602176634 × 10⁻¹⁹ coulombs, which anchors the —and by extension the volt—to a reproducible quantum constant rather than physical artifacts like the international prototype . This change ensures that the volt's realization is exact and independent of material standards, enhancing precision in . For instance, one volt corresponds to one joule per , or in base units, the of 1 kg·m²·s⁻² imparted to a charge of 1 A·s, illustrating the unit's expression as a gradient per unit charge in fundamental terms.

Physical Interpretation

Connection to Energy and Charge

The volt represents the electric potential difference between two points in an , defined as the amount of work required to move a positive charge from one point to the other. Specifically, one volt is equivalent to one joule of expended per of charge transported, expressed as V = \frac{J}{C}. This relationship underscores the volt as a measure of per charge, where the potential difference quantifies the electrostatic work done against the field. In practical terms, this energy-charge linkage is evident in the of charged particles. For instance, a potential difference of one volt imparts one () of to a single , whose charge is approximately $1.6 \times 10^{-19} C, as the electron gains energy equivalent to qV where q is its charge. This unit, the eV, is widely used in and to describe energy scales on the order of electron interactions. For a uniform , the potential difference V relates directly to the field strength E and the distance d between the points, given by V = Ed. This equation illustrates how voltage arises from the spatial variation of the electric field, providing the driving force for charge separation in capacitors or . In electrical circuits, voltage serves as the motive force that drives I through a conductor, with the instantaneous delivered or dissipated expressed as P = VI. This formulation connects voltage to the rate of , where higher voltages enable greater output for a given current, fundamental to the operation of devices from batteries to amplifiers.

Distinction from Related Concepts

The volt (V) is the for difference, a often interchangeably called voltage in technical and colloquial usage. While voltage denotes the magnitude of the potential difference between two points in an , the volt specifically quantifies this difference as the work done per unit charge to move a charge between those points, equivalent to one joule per . This distinction ensures precision in measurement, as voltage encompasses the broader concept, but only the volt serves as the standardized unit in the (). A key differentiation exists between the volt and electromotive force (EMF), both expressed in volts but representing distinct aspects of electrical systems. EMF refers to the maximum potential difference a source, such as a battery or generator, can provide when no current flows through an external circuit, essentially the open-circuit voltage generated by the source's internal mechanisms. In contrast, the volt measures the actual potential difference across any two points in a circuit, which may be lower than the EMF due to internal resistance or load effects when current is drawn. This clarifies that while EMF drives the circuit, the volt applies universally to any observed potential drop. The volt quantifies potential rather than absolute , which is a value at a single point relative to an arbitrary reference (often or ). Electric potential itself lacks a fixed and is meaningful only through , so the volt always describes the change in potential () between locations, not an . This underscores that potentials are path-independent in electrostatic fields, but the unit remains the volt for the . Common misconceptions arise with () and () voltages, both denominated in volts yet interpreted differently for effective power delivery. DC voltages are straightforward steady-state values, whereas AC voltages are typically specified as root-mean-square () values, which equal the DC equivalent for the same heating effect in a —approximately 0.707 times the value for sinusoidal waveforms. Peak or instantaneous AC values, while also in volts, do not represent the effective voltage for most practical calculations, leading to errors if not distinguished from RMS.

Analogies for Understanding

Hydraulic Analogy

The likens electrical circuits to systems of flowing through pipes, offering an intuitive framework for grasping the concept of voltage. In this model, voltage represents the difference—measured in pascals for but conceptualized in volts for —that drives the of charges, much like hydrostatic propels through a conduit. A higher voltage provides a greater "push" on electrons, analogous to increased overcoming gravitational or frictional forces to maintain . This emphasizes voltage as the potential difference across a circuit, motivating charge movement without directly representing the charges themselves. Central to the analogy are the mappings between electrical quantities and hydraulic counterparts. , measured in amperes, corresponds to the of , quantifying how much charge passes a point per unit time, similar to gallons per second in a . , in ohms, parallels the frictional resistance or in the , such as narrower or rougher surfaces that impede for a given . , in watts, equates to the hydraulic power delivered, akin to the work rate of ( times ), illustrating how voltage and current together determine energy transfer. These correspondences align with fundamental laws, like ( equals voltage divided by ), mirroring Poiseuille's law for . A practical example is a 12 V in a simple circuit with a , where the acts as a source equivalent to a 12-unit head of , forcing through the like flow through a narrow, friction-filled . The resulting depends on the 's "narrowness," just as pipe restrictions limit throughput under fixed . While effective for direct current (DC) circuits with ohmic components, the hydraulic analogy has limitations, particularly in capturing alternating current (AC) dynamics or non-linear behaviors, where fluid flow does not naturally replicate oscillatory pressures or reactive elements like capacitors and inductors. It remains particularly valuable, however, for building conceptual understanding of voltage's role in steady-state scenarios.

Mechanical and Thermal Analogies

The mechanical analogy for voltage draws a parallel between electric potential difference and gravitational potential difference in a uniform field. Just as the gravitational potential energy of a mass increases with height in a gravitational field, the electric potential energy of a charge increases as it moves against an electric field; thus, voltage, defined as the potential energy per unit charge, is analogous to the height difference per unit mass, or gh where g is gravitational acceleration and h is height. Specifically, a voltage of 1 V corresponds to an electric potential energy change of 1 J for a charge of 1 C, equivalent in energy scale to the gravitational potential energy gained by lifting a mass that yields 1 J when raised by a certain height under gravity. In this analogy, positive charges "fall" from regions of high electric potential to low potential, converting potential energy into kinetic energy, much like objects rolling downhill in a gravitational field and accelerating due to the height difference. The thermal analogy compares voltage to a that drives flow, particularly through the Seebeck effect in thermoelectrics. In the Seebeck effect, a difference \Delta T across a junction of dissimilar materials generates an (voltage) proportional to \Delta T, where the determines the voltage per unit difference. This voltage arises as charge carriers diffuse from the hot to the cold region, creating a potential difference that opposes further flow, analogous to how a induces transfer until equilibrium. For instance, in a , the generated voltage can power a when the difference is maintained, highlighting the direct link between thermal disequilibrium and electrical potential. These analogies underscore the conservative nature of electrostatic fields, where the work done by the on a charge between two points is path-independent, depending only on the potential difference (voltage) at those points. This path independence mirrors the behavior in gravitational and thermal conservative systems, emphasizing that voltage represents a tied to differences rather than the specific . As noted in the connection between voltage and per charge, such analogies aid in conceptualizing how drives charge motion without dissipation along closed paths.

Measurement and Standards

Historical Measurement Methods

In the late , early measurements of relied on , devices that detected voltage through the repulsion of charged objects. The gold-leaf electrometer, invented by Abraham Bennet in 1787, consisted of two thin gold leaves suspended from a conducting rod within a enclosure; when a voltage was applied, the leaves diverged proportionally to the potential difference due to electrostatic repulsion, allowing qualitative and semi-quantitative assessments. This instrument marked a significant advance over prior pith-ball electroscopes, providing greater sensitivity for measuring potentials in electrostatic experiments, though it required careful calibration and was limited to low-current, high-impedance scenarios. By the mid-19th century, as electrochemical cells emerged, the served as a key reference for absolute voltage measurements. Invented by John Frederic Daniell in 1836, this cell produced a stable of approximately 1.1 volts from the reaction between and electrodes in their respective solutions, separated by a porous barrier to minimize polarization. In the 1860s, during early efforts to define electrical standards, the Daniell cell's output was adopted by bodies like the British Association for the Advancement of Science as a practical benchmark for the volt, enabling more reproducible comparisons in and laboratory work. Into the early , paired with offered precise voltage comparisons via null methods. The slide-wire , originating from Johann Christian Poggendorff's 1841 design and refined in commercial forms by the , used a uniform resistance wire along which a sliding contact balanced an unknown voltage against a known from a , with a sensitive detecting zero current at the balance point. This technique, employed in instruments like those from Leeds & Northrup, achieved accuracies to within millivolts without drawing significant current from the source, making it ideal for measurements in research and industry. These historical methods faced substantial challenges from environmental and material inconsistencies, hindering precision. Temperature variations notably affected cell outputs, with the Daniell cell's voltage decreasing by about 0.0004 volts per degree rise due to shifts in properties and . Material impurities and inconsistencies in wire resistances for potentiometers further introduced errors, while electrometers suffered from humidity-induced charge leakage. No unified existed until the 1881 International Electrical Congress in , which formalized the volt and related units to address these discrepancies.

Modern Josephson Junction Standard

The modern realization of the volt relies on the , predicted by in 1962, which describes a direct current-voltage relationship in a under irradiation. In this effect, a constant DC voltage V appears across the junction at specific steps given by the equation V = \frac{n h f}{2 e}, where n is an integer representing the step number, h is Planck's constant, e is the , and f is the of the applied radiation. This quantum phenomenon enables precise voltage generation tied to measurable frequency, independent of material properties beyond the fundamental constants. Since 1972, national metrology institutes have implemented Josephson voltage standards based on this effect to maintain the volt, starting with systems at the National Bureau of Standards (now NIST) that disseminated the U.S. legal volt using 10 mV arrays. Prior to the 2019 SI revision, the conventional Josephson constant K_{J-90} = 2e/[h](/page/H+) was fixed at 483597.9 GHz/V, such that 1 V corresponded to a frequency of approximately 483.598 GHz times an integer n. Following the redefinition of the SI units, which fixed the values of h and e, the Josephson constant became exactly K_J = 483597.8484\ldots GHz/V, allowing direct realization of the volt from frequency measurements alone, with frequency serving as the sole input parameter traceable to the second. These standards offer exceptional reproducibility, achieving relative uncertainties as low as $10^{-10} or better in inter-laboratory comparisons, far surpassing classical methods due to the intrinsic quantum locking of voltage steps. National metrology laboratories, including NIST and PTB, employ them as primary references for calibrating voltage artifacts and ensuring global consistency in electrical measurements. To generate practical voltages beyond millivolts, series arrays of thousands to hundreds of thousands of Josephson junctions are integrated into superconducting chips, operated at cryogenic temperatures around 4 under microwave excitation. For instance, modern programmable Josephson voltage standards (PJVS) use over 265,000 junctions to produce stable outputs up to 10 V, enabling rapid switching and application in both and metrology. This array configuration ensures Shapiro steps remain sharp and uniform, supporting uncertainties below 1 part in $10^{10} for routine use. As of August 2025, NIST has developed a single integrated device that realizes the SI standards for voltage (via ), resistance (via ), and current (via single-electron transport) within one , improving efficiency and precision in quantum electrical .

Common Applications and Values

Everyday and Household Voltages

In households around the world, () mains power provides the primary electrical supply for appliances and lighting. In the United States and , the nominal () voltage is 120 at 60 Hz, with standard tolerances allowing variations from 114 V to 126 V under normal operating conditions, though brief fluctuations up to ±10% can occur due to grid dynamics. In much of and other regions following (IEC) standards, the nominal voltage is 230 V at 50 Hz, with tolerances typically limited to -6% to +10%, ensuring compatibility with connected devices. These voltages originate from large-scale generators in power plants and are stepped down through transformers for safe distribution to homes. Direct current (DC) voltages are prevalent in portable and low-power household applications, often derived from batteries or rectified AC sources. A typical delivers a nominal 1.5 V, suitable for powering small devices like remote controls and clocks. Automotive lead-acid batteries, used for starting engines and auxiliary systems, operate at a standard 12 V when fully charged. Universal Serial Bus (USB) ports, common on computers, chargers, and wall adapters, supply a regulated 5 V, enabling the operation of peripherals such as external drives and charging cables. Many incorporate even lower voltages for efficient operation. Smartphones and similar devices charge via USB protocols that adjust from 5 V for standard rates up to 20 V for fast charging, optimizing power delivery while minimizing heat. Light-emitting diodes (LEDs), widely used in indicators, displays, and lighting strips, require forward voltages of 1.8 V to 3.3 V depending on the diode's color and material, such as lower values for red LEDs and higher for white or blue ones. From a safety perspective, everyday voltages are designed to minimize risks, but thresholds exist for potential electric shock. Voltages above 50 RMS for or 120 for are classified as hazardous under IEC guidelines, as they can drive sufficient through the body to cause , though the actual danger also hinges on factors like , skin resistance, and exposure pathway. Protective measures, such as grounding and fuses in household systems, further mitigate these risks.

Voltages in Scientific and Industrial Contexts

In high-voltage , voltages typically range from 110 to 765 to enable efficient long-distance electricity delivery while minimizing resistive losses described by the I²R term in dissipation. These elevated potentials reduce the required for a given level, as P equals voltage V times I, thereby lowering losses in conductors over hundreds of kilometers. Such systems form the backbone of national grids, with examples including 500 lines for bulk transfer. Scientific applications often demand extreme voltages to accelerate charged particles for probing fundamental physics. In the (LHC) at , superconducting radiofrequency cavities provide accelerating voltages up to 2 MV per cavity, totaling about 16 MV per beam to achieve proton energies of 6.5 TeV. Van de Graaff generators, electrostatic accelerators pivotal in research, can generate terminal voltages reaching 25 MV, enabling ion acceleration for experiments on atomic nuclei and material properties. Linear accelerators in facilities like SLAC extend this to gigavolt scales, with total accelerating potentials around 50 GV over kilometer-long structures to produce high-energy electron beams for studies. These voltages, often applied in pulsed modes, facilitate collisions that reveal subatomic structures but require precise insulation to prevent breakdowns. At the opposite end of the scale, precision scientific contexts utilize ultra-low voltages for sensitive measurements and control. In , superconducting qubits are manipulated using gate voltages on the order of a few (μV) to tune Josephson junctions without introducing that could decohere quantum states. In biomedical research, (EEG) records electrical activity at scalp voltages of 10–100 μV, capturing neural oscillations for diagnosing neurological disorders. These minute signals demand high-impedance amplifiers to preserve fidelity, highlighting voltage's role in non-invasive physiological monitoring. Industrial processes leverage specific voltage ranges tailored to equipment demands, often prioritizing current alongside potential. Electric vehicles employ (DC) battery packs at 400–800 V, predominantly 800 V as of 2025, to drive high-power motors efficiently, enabling rapid acceleration and in models like those from and . operations maintain arcs at 20–50 V, where ensures operator safety while high currents (up to 1000 A) generate the necessary for metal fusion in . These applications underscore voltage optimization for thermal and mechanical performance in .

History and Development

Origins and Naming

The unit of electric potential known as the volt is named after (1745–1827), an and renowned for his pioneering work in . In 1800, Volta invented the , the first electrochemical capable of producing a steady through chemical reactions between alternating discs of and separated by brine-soaked cardboard. This breakthrough demonstrated that could be generated continuously from chemical sources, laying foundational concepts for understanding and potential difference. Early efforts to quantify electrical potential predated Volta's contributions. In the , de Cavallo developed an improved —a device using gold leaves to detect and measure electrical charges—that scaled readings in "degrees of " to assess the intensity of static electrical tension. While de Cavallo's instrument advanced the measurement of transient electrical effects, it was Volta's that provided a reliable source of sustained current, enabling more precise standardization of potential concepts in subsequent experiments. The formal adoption of "volt" as the name for the unit of occurred in 1881 at the International Electrical Congress in , where international delegates honored Volta's legacy by selecting the term to denote the difference of potential that drives one of current against one of resistance. This decision marked a key step in unifying electrical amid growing global standardization efforts. Initially, the volt's practical definition relied on the electromotive force of the Clark cell—a mercury-zinc electrochemical reference cell yielding approximately 1.4328 volts at 15 °C—as a reproducible standard for calibration.

Evolution as an SI Unit

In the mid-20th century, the volt underwent formal through international agreements. At the 9th General Conference on Weights and Measures (CGPM) in 1948, the volt was implicitly defined via the newly ratified international and international , where the international was set as the current producing a specific force between conductors, and the international was maintained by an artifact resistance of 1 ; this system relied on physical prototypes for across nations. By the 1960s, a shift occurred toward absolute units independent of artifacts. The 11th CGPM in 1960 established the (SI), designating the as a base unit defined by the force between two parallel conductors carrying constant current, thereby deriving the volt absolutely from the meter, , and second without prototype dependence. From the 1970s to the 1990s, quantum effects revolutionized the precise realization of the volt, reducing uncertainties from parts per million to parts per billion. The AC , discovered in 1962, was internationally adopted in 1972 as a practical voltage standard, linking voltage to frequency via the relation V = \frac{n f h}{2e}, where n is an integer, f is microwave frequency, h is Planck's constant, and e is the ; this enabled stable, reproducible voltages using superconducting junctions. Similarly, the , observed in 1980, provided a resistance standard that complemented Josephson-based voltage measurements for full electrical . In 1988, the International Committee for Weights and Measures (CIPM) adopted conventional values for the Josephson constant K_{J-90} = 483597.9 GHz/V and the von Klitzing constant R_{K-90} = 25812.807 Ω, effective from 1 January 1990, fixing the volt's representation relative to legacy prototypes while aligning quantum realizations globally; this adjustment shifted national standards by small amounts, such as 9.3 ppm for the U.S. volt. The 2019 revision of the SI marked a pivotal advancement, defining the volt exactly through fundamental constants without reliance on artifacts or conventional values. At the 26th CGPM in 2018, effective 20 May 2019, the ampere was redefined by fixing the elementary charge e = 1.602176634 \times 10^{-19} C, with the second unchanged; the volt, as the unit of electric potential difference, derives from the watt (kg m² s⁻³) divided by the ampere, ultimately anchored to fixed values of the , , and . This change maintained the numerical value of the volt but enhanced universality and stability, as realizations now stem directly from invariant physical constants rather than measurable phenomena or prototypes. The Bureau International des Poids et Mesures (BIPM) plays a central role in harmonizing volt realizations worldwide, conducting key comparisons of Josephson voltage standards among national institutes to ensure consistency at the parts-per-billion level. Through ongoing calibrations and resolutions, such as those under the Consultative Committee for Electricity and Magnetism, the BIPM maintains the volt's integrity, supporting global trade, scientific collaboration, and technological interoperability.