[3][4][5] The voltage 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 a generator).

[citation needed] The old SI definition for volt used power and current; starting in 1990, the quantum Hall and Josephson effect were used,[10] and in 2019 physical constants were given defined values for the definition of all SI units.

[17]: 90–91  Mathematically, this is expressed as the line integral of the electric field along that path.

[note 1] However, at lower frequencies when the electric and magnetic fields are not rapidly changing, this can be neglected (see electrostatic approximation).

[17]: 417  Furthermore, the potential is no longer uniquely determined up to a constant, and can take significantly different forms depending on the choice of gauge.

[19] 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[19] as long as the path of integration does not pass through the inside of any component.

[20][note 3] 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.

If external fields are negligible, we find that is path-independent, and there is a well-defined voltage across the inductor's terminals.

The volt (symbol: V) is the derived unit for electric potential, voltage, and electromotive force.

[22][23] The volt is named in honour of the Italian physicist Alessandro Volta (1745–1827), who invented the voltaic pile, possibly the first chemical battery.

Similarly, work can be done by an electric current driven by the potential difference provided by a battery.

If the pump is not 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.

In such a system, the work done to move water is equal to the "pressure drop" (compare p.d.)

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.

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

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).

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.

[24] 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.

However, a clear definition of voltage and method of measuring it had not been developed at this time.

[26]: 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.