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In the physical sciences, potential difference is the difference of a conserved quantity between two points. It can be described as the across variable[?], where flux is the through variable[?]. The product of the flux and the potential difference is the power, which is the rate of change of the conserved quantity, e.g energy.
There are many types of potential difference:
Electrical potential difference In electrical engineering, the potential difference between two points in an electrical circuit is equal to the difference in their electrical potentials. It is defined as the amount of work per charge needed to move electric charge from the second point to the first, or equivalently, the amount of work that unit charge flowing from the first point to the second can perform.
A potential difference between two points gives rise to a "force" called an electromotive force or emf that tends to push electrons or other charge-carriers from one point to the other. Common sources of emf are the battery, the electrical generator and the capacitor.
In the SI system of units, potential difference, electrical potential and electromotive force are measured in volts, leading to the commonly used term voltage and its abbreviation V. Named after Alessandro Volta, one volt is defined to be one joule of energy per coulomb of charge.
If one thinks of an electrical circuit in analogy to water circulating in a network of pipes, driven by pumps in the absence of gravity, then the potential difference corresponds to the pressure difference between two points. If there is a pressure difference between two points, then water flowing from the first point to the second will be able to do work, such as driving a turbine.
Instruments for measuring potential differences include the voltmeter and the potentiometer and the oscilloscope. The voltmeter works by measuring the current through a fixed resistor, which according to Ohm's Law is proportional to the potential difference across it. The cathode-ray oscilloscope works by amplifying the potential difference and using it to deflect an electron beam from a straight path, so that the deflection of the beam is proportional to the potential difference.
Voltage is additive in the following sense: the voltage between A and C is the same as the voltage between A and B plus the voltage between B and C. Two points in an electric circuit which are connected by an (ideal) conductor without resistance will have a potential difference of zero. But other pairs of points may also have a potential difference of zero. If two such points are connected with a conductor, no current will flow through the connection. The various voltages in a circuit can be computed with Kirchhoff's Laws.