Electric Potential Difference

The voltage between two points is a short name for the electrical force that would drive an electric current between those points. Specifically, voltage is equal to energy per unit charge. In the case of static electric fields, the voltage between two points is equal to the electrical potential difference between those points. In the more general case with electric and magnetic fields that vary with time, the terms are no longer synonymous.

Electric potential is the energy required to move a unit electric charge to a particular place in a static electric field.

Voltage can be measured by a voltmeter; real voltmeters approximate ideal voltmeters. The unit of measurement is the volt.

Definition

The voltage between two ends of a path is the total energy required to move a small electric charge along that path, divided by the magnitude of the charge. Mathematically this is expressed as the line integral of the electric field and the time rate of change of magnetic field along that path. In the general case, both a static (unchanging) electric field and a dynamic (time-varying) electromagnetic field must be included in determining the voltage between two points.

Simple applications

Common usage (that "voltage" usually means "voltage difference") is now resumed. Obviously, when using the term "voltage" in the shorthand sense, one must be clear about the two points between which the voltage is specified or measured. When using a voltmeter to measure voltage difference, one electrical lead of the voltmeter must be connected to the first point, one to the second point.

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.