Potential Difference

Voltage, electric potential difference, 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

''. In SI units, work per unit charge is expressed as

joule

s 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. Voltage or electric potential difference is denoted symbolically by $\Delta V$, simplified ''V'', or ''U'', for instance in the context of

Ohm's

or Kirchhoff's circuit laws.

Electric potential differences between points can be caused by the build up of electric charge (e.g., a

capacitor

), and from an electromotive force (e.g.,

electromagnetic induction

in generator,

inductors

, and

transformers

). On a macroscopic scale, a potential difference can be caused by electrochemical processes (e.g., cells and batteries), the pressure-induced

piezoelectric effect

, and heat-induced electromotive force across metal-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 can represent either a source of energy or the loss, dissipation, or storage of energy.

Definition

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 ).

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.

Definition in electrostatics

In electrostatics, the voltage increase from point $\mathbf_A$ to some point $\mathbf_B$ is given by the change in electrostatic potential from $\mathbf_A$ to $\mathbf_B$. By definition, this is:

:$\begin \Delta V_ &= V(\mathbf_B) - V(\mathbf_A) \\ &= -\int_^ \mathbf \cdot \mathrm\boldsymbol - \left(-\int_^ \mathbf \cdot \mathrm\boldsymbol \right)\\ &= -\int_^ \mathbf \cdot \mathrm\boldsymbol \end$

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. 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:

$\nabla\times\mathbf=-\frac$

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, then this can be neglected (see electrostatic approximation).

Generalization to 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 meaning and value of potential differences will depend on the choice of gauge.

In this general case, some authors 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 $\mathcal$ from $\mathbf_A$ to $\mathbf_B$ is given by:
:$\Delta V_ = -\int_\mathcal \mathbf \cdot \mathrm\boldsymbol$
However, in this case the "voltage" between two points depends on the path taken.

Treatment in 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

:$\Delta V_ = -\int_^ \mathbf \cdot \mathrm\boldsymbol$

as long as the path of integration does not pass through the inside of any component. The above is the same formula used in electrostatics. 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 magnetic path. If external fields are negligible, we find that

:$\Delta V_ = -\int_\mathrm\mathbf\cdot \mathrm\boldsymbol=L\frac$

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

, 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". The 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

".)

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.

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 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

.

Analog voltmeter

s, 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.

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 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

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.
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.

History

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''. Volta meant by this a force that was not an electrostatic force, specifically, an electrochemical 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

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.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

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

References

Footnotes

External links

Electrical voltage ''V'', current ''I'', resistivity ''R'', impedance ''Z'', wattage ''P''

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