Noun

Singular voltage

Plural voltages

voltage (plural voltages)

1. (physics) The amount of electrostatic potential between two points in space.

Voltage is commonly used as a short name for electrical potential difference. Its corresponding SI unit is the volt (symbol: V, not italicized). Electric potential is a hypothetically measurable physical dimension, and is denoted by the algebraic variable V (italicized.)

The voltage between two (electron) positions "A" and "B", inside a solid electrical conductor (or inside two electrically-connected, solid electrical conductors), is denoted by (V_A − V_B). This voltage is the electrical driving force that drives a conventional electric current in the direction A to B. Voltage can be directly measured by an "ideal voltmeter". Well-constructed, correctly used, real voltmeters approximate very well to ideal voltmeters. For non-scientists, an analogy involving the flow of water is sometimes helpful in understanding the concept of voltage (see below).

Precise modern and historic definitions of voltage exist, but (due to the development of the electron theory of metal conduction in the period 1897 to 1933, and to developments in theoretical surface science from about 1910 to about 1950, particularly the theory of local work function) some older definitions are not now regarded as strictly correct. This is because they neglect the existence of "chemical" effects and surface effects. A particular lesson from surface science is that, to get consistency and universality, formal definitions must relate to positions or (better) electron states inside conductors.

In conduction processes occurring in metals and most other solids, electric currents consist almost exclusively of the flow of electrons in the direction B to A. This movement of electrons is controlled by differences in a so-called "total local thermodynamic potential" often denoted by the symbol µ ("mu"). This parameter is often called the "local Fermi level" or sometimes the "(local) electrochemical potential of an electron" or the "total (local) chemical potential of an electron". The modern electron-based definition of voltage (V_A − V_B) is in terms of differences in µ:

where e is the elementary positive charge. It is sometimes convenient to put µ_B=0 and V_B=0, and choose position "B" so that it can be a convenient reference zero for V. It is common to choose position "B" to be inside a good electrical conductor solidly connected (by a very-low-electrical-resistance path) to the local "Earth" or "Ground". In the analysis of electrical circuit diagrams, it is common to show the point in the circuit that is being taken as the reference position B, by attaching a "Ground" ("Earth") symbol to this point.

A common misapprehension is to assume that difference in voltage is always equal to difference in electric potential (i.e. electrostatic potential). This is often untrue, because differences in "chemical effects" (e.g., as between conductors made from different materials) also contribute to differences in µ, and hence to differences in voltage. Some textbooks (especially old physics textbooks) give historic definitions of voltage that are not strictly equivalent to the modern definition. However, the difference in value between a "voltage difference" and the related "electric potential difference" is always small (at most a few volts, often less), and in many contexts it is commonplace (and acceptable) to disregard the distinction. Nonetheless, in some contexts, such as the theory of contact potential differences, the distinction is vital.