In most circuits current is driven by a so-called "source of emf", which usually is a voltaic cell (or battery, which consists of voltaic cells in series and/or in parallel) or the power company. For a voltaic cell the source of emf is the chemical reactions that occur at each of the electrode-electrolyte interfaces, so that a voltaic cell can be thought of as two "surface pumps" of atomic dimension. The reactions at the electrode-electrolyte interfaces provide the "seat" of emf for the voltaic cell. For the power company, the source of emf is electromagnetic induction, which is more extended than an atomic size, but nevertheless is confined to the power generation building, usually many miles from the user.
Sources of electromotive force include electric generators (both alternating current and continuous current types), batteries, and thermocouples (in a heat gradient). Electromotive force is often denoted by or ℰ (script capital E).
Electromotive force is measured in volts (in the International System of Units equal in amount to a joule per coulomb of electric charge). Electromotive force in electrostatic units is the statvolt (in the centimeter gram second system of units equal in amount to an erg per electrostatic unit of charge).
This formal definition is not very helpful for a voltaic cell; there f due to the chemical reactions is either very large but not calculable (at the electrode-electrolyte interfaces), or zero (everywhere else). However, this definition is quite helpful for emfs generated by a time-dependent magnetic field (Faraday's Law of electromagnetic induction). Note that the electrostatic potential does not contribute to the net emf around a circuit (although it does contribute over parts of a circuit). Like the electric potential at a point and the voltage between two points, the emf around a loop is measured in volts.
The emf is sensitive to non-electrostatic forces, since the force f can include magnetic, chemical, mechanical, and gravitational components. In practice, the power sources for the non-electrostatic forces in a voltaic cell are the chemicals that react at the electrode-electrolyte interfaces; for the power company they are the moving rotors that produce a non-electrostatic field by Faraday's Law of electromagnetic induction; and for a thermoelectric device they are the heaters and coolers that maintain a temperature difference across the device. The EMF of a source (electromagnetic, chemical, thermal or otherwise) may be defined as the work done by an external agent, per unit charge, with sign reversed, in bringing a test charge once around a circuit that contains the source and no other source. Such a source is often described as a "seat" of EMF.
Another term for emf is electromotance.
When multiplied by an amount of charge de the emf ℰ yields a thermodynamic work term ℰde that is used in the formulism for the change in Gibbs free energy when charge is passed in a battery:
The combination ℰ.e is an example of a conjugate pair of variables. At constant pressure the above relationship produces a Maxwell relation that links the change in open cell voltage with temperature (a measurable quantity) to the change in entropy when charge is passed isothermally and isobarically. The latter is closely related to the reaction entropy ΔrS of the electrochemical reaction that lends the battery its power.
According to Maxwell, even a potential difference can have the same effect as an emf. Nevertheless, normal usage does not consider a voltage difference as a source of emf.
If a source of emf is not connected to an external resistor, then an electric current cannot flow through that resistor (Ohm's Law). In this case, between the terminals of the source there must exist a true electric field that produces a voltage difference that exactly cancels the emf of the source.
The source of this true electric field is the electric charge that has been separated by the mechanism generating the emf . For example, the chemical reaction in a voltaic cell stops when the electric field across each electrode is strong enough to stop the reactions at each electrode.
This electric field between the terminals of the battery creates an electric potential difference that can be measured with a voltmeter. The polarity of this measured potential difference is always opposite to that of the generated emf. The value of the emf for the battery (or other source) is the value of this 'open circuit' voltage. When the battery is charging or discharging, the emf itself cannot be measured directly. It can, however, be inferred from a measurement of the current I and voltage difference V, provided that the internal resistance has already been measured: I=( -V)/r.
One of Volta's great contributions to science was to recognize that a voltaic cell has two sources of emf, the chemical reactions at each electrode. He showed that they provide distinct emfs and that oppose one another, so that two identical electrodes give no net emf, but that two different electrodes give a net emf of , which we assume is positive. A schematic of this circuit would have a long electrode 1 and a short electrode 2, to indicate that electrode 1 dominates. Volta's law about opposing electrode emfs means that, given ten electrodes (e.g. zinc and nine other materials), which can be used to produce 45 types of voltaic cells (10*9/2), only nine relative measurements (e.g. copper and each of the nine others) are needed to get all 45 possible emfs that these ten electrodes can produce.
Besides voltaic cells, other devices that produce chemical emfs from electrochemical reactions are fuel cells. Radiant and thermal energy (e.g., a solar cell or a thermocouple) can also produce emfs. Some other sources of emf include thermocouples, thermopiles, and photodiodes.
Dissimilar metals in contact also produce what is known as a contact electromotive force or contact potential (eg., the volta effect). However, this is a truly electrostatic effect, and does not affect the overall emf of a circuit.
The principle of electromagnetic induction, noted above, states that a time-dependent magnetic field can produce a circulating electric field. A time-dependent magnetic field can be produced either by motion of a magnet relative to a circuit, by motion of a circuit relative to another circuit (at least one of these must be carrying a current), or by changing the current in a fixed circuit. The effect on the circuit itself, of changing the current, is known as self-induction; the effect on another circuit is known as mutual induction. The electromotive force generated by motion is often referred to as '''motional electromotive force
For a given circuit, the electromagnetically induced electric field is determined purely by the geometry and the rate of change of the magnetic flux through the circuit, by Faraday's law of induction. However, the accompanying electrostatic field does depend on the details of the circuit, since the emf across a resistor will have contributions from both the electromagnetic and electrostatic fields, and their detailed form will depend on the value and shape of the resistor.
If an electric circuit has self-inductance L, and carries current i, then by Faraday's Law
Given this emf and the resistance of the circuit, the instantaneous current can be computed with Ohm's Law, for example, or more generally by solving the differential equations that arise out of Kirchhoff's laws.
The electromotive force produced by primary and secondary cells is usually of the order of a few volts. The figures quoted below are nominal, because emf varies according to the size of the load and the state of exhaustion of the cell.
|1.2 V||Nickel Metal-Hydride|
|3.6 V to 3.7 V||Lithium-Ion|
Ohm's Law (PDF in German)