In
electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of ...
and
electronics
The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons using electronic devices. Electronics uses active devices to control electron flow by amplification ...
, electromotive force (also electromotance, abbreviated emf, denoted
or
) is an
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
transfer to an
electric circuit
An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, ...
per unit of
electric charge
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
, measured in
volt
The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). It is named after the Italian physicist Alessandro Volta (1745–1827).
Defi ...
s. Devices called electrical ''
transducers
A transducer is a device that converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.
Transducers are often employed at the boundaries of automation, measurement, and control ...
'' provide an emf
by
converting
Converting companies are companies that specialize in modifying or combining raw materials such as polyesters, adhesives, silicone, adhesive tapes, foams, plastics, felts, rubbers, liners and metals, as well as other materials, to create new pro ...
other forms of
energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
into
electrical energy.
Other electrical equipment also produce an emf, such as
batteries, which convert
chemical energy
Chemical energy is the energy of chemical substances that is released when they undergo a chemical reaction and transform into other substances. Some examples of storage media of chemical energy include batteries, Schmidt-Rohr, K. (2018). "How ...
, and
generator
Generator may refer to:
* Signal generator, electronic devices that generate repeating or non-repeating electronic signals
* Electric generator, a device that converts mechanical energy to electrical energy.
* Generator (circuit theory), an eleme ...
s, which convert
mechanical energy
In physical sciences, mechanical energy is the sum of potential energy and kinetic energy. The principle of conservation of mechanical energy states that if an isolated system is subject only to conservative forces, then the mechanical energy is ...
.
This energy conversion is achieved by
physical forces applying
physical work on
electric charges
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respectiv ...
. However, electromotive force itself is not a physical force, and for the current
ISO
ISO is the most common abbreviation for the International Organization for Standardization.
ISO or Iso may also refer to: Business and finance
* Iso (supermarket), a chain of Danish supermarkets incorporated into the SuperBest chain in 2007
* Iso ...
/
IEC
The International Electrotechnical Commission (IEC; in French: ''Commission électrotechnique internationale'') is an international standards organization that prepares and publishes international standards for all electrical, electronic and r ...
standards consider the term deprecated, favoring the names source voltage or source tension instead (denoted
).
An
electronic–hydraulic analogy may view emf as the
mechanical work
In physics, work is the energy transferred to or from an object via the application of force along a displacement. In its simplest form, for a constant force aligned with the direction of motion, the work equals the product of the force stre ...
done to water by a
pump, which results in a
pressure difference (analogous to voltage).
In
electromagnetic induction
Electromagnetic or magnetic induction is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field.
Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk ...
, emf can be defined around a closed loop of a
conductor as the electromagnetic
work
Work may refer to:
* Work (human activity), intentional activity people perform to support themselves, others, or the community
** Manual labour, physical work done by humans
** House work, housework, or homemaking
** Working animal, an animal t ...
that would be done on an
elementary electric charge
The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fund ...
(such as an
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
) if it travels once around the loop.
For two-
terminal
Terminal may refer to:
Computing Hardware
* Terminal (electronics), a device for joining electrical circuits together
* Terminal (telecommunication), a device communicating over a line
* Computer terminal, a set of primary input and output dev ...
devices modeled as a
Thévenin equivalent circuit, an equivalent emf can be measured as the
open-circuit voltage
Open-circuit voltage (abbreviated as OCV or VOC) is the difference of electrical potential between two terminals of an electronic device when disconnected from any circuit. There is no external load connected. No external electric current f ...
between the two terminals. This emf can drive an
electric current
An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...
if an external
circuit is attached to the terminals, in which case the device becomes the
voltage source
A voltage source is a two-terminal device which can maintain a fixed voltage. An ideal voltage source can maintain the fixed voltage independent of the load resistance or the output current. However, a real-world voltage source cannot supply unl ...
of that circuit.
Although an emf gives rise to a voltage and can be measured as a voltage and may sometimes informally be called a "voltage", they are not the same phenomenon (see ).
Overview
Devices that can provide emf include
electrochemical cell
An electrochemical cell is a device capable of either generating electrical energy from chemical reactions or using electrical energy to cause chemical reactions. The electrochemical cells which generate an electric current are called voltaic o ...
s,
thermoelectric devices,
solar cells
A solar cell, or photovoltaic cell, is an electronic device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon. ,
photodiodes,
electrical generator
In electricity generation, a generator is a device that converts motive power (mechanical energy) or fuel-based power ( chemical energy) into electric power for use in an external circuit. Sources of mechanical energy include steam turbines, g ...
s,
inductors
An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
,
transformer
A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
s and even
Van de Graaff generator
A Van de Graaff generator is an electrostatic generator which uses a moving belt to accumulate electric charge on a hollow metal globe on the top of an insulated column, creating very high electric potentials. It produces very high voltage
...
s.
In nature, emf is generated when
magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
fluctuations occur through a surface. For example, the shifting of the
Earth's magnetic field
Earth's magnetic field, also known as the geomagnetic field, is the magnetic field that extends from Earth's interior out into space, where it interacts with the solar wind, a stream of charged particles emanating from the Sun. The magnetic f ...
during a
geomagnetic storm
A geomagnetic storm, also known as a magnetic storm, is a temporary disturbance of the Earth's magnetosphere caused by a solar wind shock wave and/or cloud of magnetic field that interacts with the Earth's magnetic field.
The disturbance that d ...
induces currents in an
electrical grid as the lines of the magnetic field are shifted about and cut across the conductors.
In a battery, the charge separation that gives rise to a potential difference (
voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
) between the terminals is accomplished by
chemical reactions
A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking ...
at the
electrodes
An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit (e.g. a semiconductor, an electrolyte, a vacuum or air). Electrodes are essential parts of batteries that can consist of a variety of materials dep ...
that convert chemical
potential energy
In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
Common types of potential energy include the gravitational potentia ...
into electromagnetic potential energy.
A
voltaic cell
A galvanic cell or voltaic cell, named after the scientists Luigi Galvani and Alessandro Volta, respectively, is an electrochemical cell in which an electric current is generated from spontaneous Oxidation-Reduction reactions. A common apparatus g ...
can be thought of as having a "charge pump" of atomic dimensions at each electrode, that is:
In an electrical generator, a time-varying magnetic field inside the generator creates an
electric field via
electromagnetic induction
Electromagnetic or magnetic induction is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field.
Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk ...
, which creates a potential difference between the generator terminals. Charge separation takes place within the generator because electrons flow away from one terminal toward the other, until, in the open-circuit case, an electric field is developed that makes further charge separation impossible. The emf is countered by the electrical voltage due to charge separation. If a
load is attached, this voltage can drive a current. The general principle governing the emf in such electrical machines is
Faraday's law of induction.
History
In 1801,
Alessandro Volta
Alessandro Giuseppe Antonio Anastasio Volta (, ; 18 February 1745 – 5 March 1827) was an Italian physicist, chemist and lay Catholic who was a pioneer of electricity and power who is credited as the inventor of the electric battery and the ...
introduced the term "force motrice électrique" to describe the active agent of a battery (which he had invented around 1798).
This is called the "electromotive force" in English.
Around 1830,
Michael Faraday
Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic inducti ...
established that chemical reactions at each of two electrode–electrolyte interfaces provide the "seat of emf" for the voltaic cell. That is, these reactions drive the current and are not an endless source of energy as the earlier
obsolete theory thought.
[ In the open-circuit case, charge separation continues until the electrical field from the separated charges is sufficient to arrest the reactions. Years earlier, ]Alessandro Volta
Alessandro Giuseppe Antonio Anastasio Volta (, ; 18 February 1745 – 5 March 1827) was an Italian physicist, chemist and lay Catholic who was a pioneer of electricity and power who is credited as the inventor of the electric battery and the ...
, who had measured a contact potential difference at the metal–metal (electrode–electrode) interface of his cells, held the incorrect opinion that contact alone (without taking into account a chemical reaction) was the origin of the emf.
Notation and units of measurement
Electromotive force is often denoted by or ''ℰ''.
In a device without internal resistance
A practical electrical power source which is a linear electric circuit may, according to Thévenin's theorem, be represented as an ideal voltage source in series with an impedance. This impedance is termed the internal resistance of the source. ...
, if an electric charge
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
passing through that device gains an energy
In physics, energy (from Ancient Greek: ἐνέργεια, ''enérgeia'', “activity”) is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat a ...
via work, the net emf for that device is the energy gained per unit charge
Charge or charged may refer to:
Arts, entertainment, and media Films
* '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* ''Charge!!'', an album by The Aqu ...
: Like other measures of energy per charge, emf uses the SI unit volt
The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). It is named after the Italian physicist Alessandro Volta (1745–1827).
Defi ...
, which is equivalent to a joule
The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applie ...
(SI unit of energy) per coulomb (SI unit of charge).
Electromotive force in electrostatic unit
The franklin (Fr) or statcoulomb (statC) electrostatic unit of charge (esu) is the physical unit for electrical charge used in the cgs-esu and Gaussian units. It is a derived unit given by
: 1 statC = 1 dyn1/2⋅cm = 1 cm3/2⋅g1/2⋅s−1.
That ...
s is the statvolt
The statvolt is a unit of voltage and electrical potential used in the CGS-ESU and gaussian systems of units. In terms of its relation to the SI units, one statvolt corresponds to exactly , i.e. to 299.792458 volts.
The statvolt is also ...
(in the centimeter gram second system of units
330px, Different lengths as in respect to the Electromagnetic spectrum, measured by the Metre and its deriveds scales. The Microwave are in-between 1 meter to 1 millimeter.
A centimetre (international spelling) or centimeter (American spellin ...
equal in amount to an erg
The erg is a unit of energy equal to 10−7joules (100 nJ). It originated in the Centimetre–gram–second system of units (CGS). It has the symbol ''erg''. The erg is not an SI unit. Its name is derived from (), a Greek word meaning 'work' o ...
per electrostatic unit of charge
Charge or charged may refer to:
Arts, entertainment, and media Films
* '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary
Music
* ''Charge'' (David Ford album)
* ''Charge'' (Machel Montano album)
* ''Charge!!'', an album by The Aqu ...
).
Formal definitions
''Inside'' a source of emf (such as a battery) that is open-circuited, a charge separation occurs between the negative terminal ''N'' and the positive terminal ''P''.
This leads to an electrostatic field
An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field f ...
that points from ''P'' to ''N'', whereas the emf of the source must be able to drive current from ''N'' to ''P'' when connected to a circuit.
This led Max Abraham
Max Abraham (; 26 March 1875 – 16 November 1922) was a German physicist known for his work on electromagnetism and his opposition to the theory of relativity.
Biography
Abraham was born in Danzig, Imperial Germany (now Gdańsk in Poland) t ...
[
] to introduce the concept of a nonelectrostatic field that exists only inside the source of emf.
In the open-circuit case, , while when the source is connected to a circuit the electric field inside the source changes but remains essentially the same.
In the open-circuit case, the conservative
Conservatism is a cultural, social, and political philosophy that seeks to promote and to preserve traditional institutions, practices, and values. The central tenets of conservatism may vary in relation to the culture and civilization i ...
electrostatic field created by separation of charge exactly cancels the forces producing the emf.[
]
Mathematically:
where is the conservative electrostatic field created by the charge separation associated with the emf, is an element of the path from terminal ''N'' to terminal ''P'', '' denotes the vector dot product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an alge ...
, and is the electric scalar potential.[
Only the electric field that results from charge separation caused by the emf is counted. While a solar cell has an electric field that results from a contact potential (see contact potentials and ]solar cells
A solar cell, or photovoltaic cell, is an electronic device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon. ), this electric field component is not included in the integral. Only the electric field that results from charge separation caused by photon energy is included.
This emf is the work done on a unit charge by the source's nonelectrostatic field when the charge moves from ''N'' to ''P''.
When the source is connected to a load, its emf is just
and no longer has a simple relation to the electric field inside it.
In the case of a closed path in the presence of a varying magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
, the integral of the electric field around the (stationary) closed loop may be nonzero.
Then, the "''induced emf''" (often called the "induced voltage") in the loop is:
where is the entire electric field, conservative and non-conservative, and the integral is around an arbitrary, but stationary, closed curve through which there is a time-varying magnetic flux , and is the vector potential
In vector calculus, a vector potential is a vector field whose curl is a given vector field. This is analogous to a ''scalar potential'', which is a scalar field whose gradient is a given vector field.
Formally, given a vector field v, a ''vecto ...
.
The electrostatic field does not contribute to the net emf around a circuit because the electrostatic portion of the electric field is conservative
Conservatism is a cultural, social, and political philosophy that seeks to promote and to preserve traditional institutions, practices, and values. The central tenets of conservatism may vary in relation to the culture and civilization i ...
(i.e., the work done against the field around a closed path is zero, see Kirchhoff's voltage law
Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchho ...
, which is valid, as long as the circuit elements remain at rest and radiation is ignored[
]).
That is, the "induced emf" (like the emf of a battery connected to a load) is not a "voltage" in the sense of a difference in the electric scalar potential.
If the loop is a conductor that carries current in the direction of integration around the loop, and the magnetic flux is due to that current, we have that , where is the self inductance of the loop.
If in addition, the loop includes a coil that extends from point 1 to 2, such that the magnetic flux is largely localized to that region, it is customary to speak of that region as an inductor
An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a c ...
, and to consider that its emf is localized to that region.
Then, we can consider a different loop that consists of the coiled conductor from 1 to 2, and an imaginary line down the center of the coil from 2 back to 1.
The magnetic flux, and emf, in loop is essentially the same as that in loop :
For a good conductor, is negligible, so we have, to a good approximation,
where is the electric scalar potential along the centerline between points 1 and 2.
Thus, we can associate an effective "voltage drop" with an inductor (even though our basic understanding of induced emf is based on the vector potential rather than the scalar potential), and consider it as a load element in Kirchhoff's voltage law,
where now the induced emf is not considered to be a source emf.
This definition can be extended to arbitrary sources of emf and paths '''' moving with velocity through the electric field and magnetic field :
which is a conceptual equation mainly, because the determination of the "effective forces" is difficult.
The term
is often called a "motional emf".
In (electrochemical) thermodynamics
When multiplied by an amount of charge the emf yields a thermodynamic work term that is used in the formalism for the change in Gibbs energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pre ...
when charge is passed in a battery:
:
where is the Gibbs free energy, is the entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
, is the system volume, is its pressure and is its absolute temperature
Thermodynamic temperature is a quantity defined in thermodynamics as distinct from kinetic theory or statistical mechanics.
Historically, thermodynamic temperature was defined by Kelvin in terms of a macroscopic relation between thermodynamic wor ...
.
The combination is an example of a conjugate pair of variables. At constant pressure the above relationship produces a Maxwell relation
file:Thermodynamic map.svg, 400px, Flow chart showing the paths between the Maxwell relations. P is pressure, T temperature, V volume, S entropy, \alpha coefficient of thermal expansion, \kappa compressibility, C_V heat capacity at constant volu ...
that links the change in open cell voltage with temperature '''' (a measurable quantity) to the change in entropy '''' when charge is passed isothermally
In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature ''T'' of a system remains constant: Δ''T'' = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and ...
and isobarically. The latter is closely related to the reaction entropy
Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...
of the electrochemical reaction that lends the battery its power. This Maxwell relation is:[
:
If a mole of ions goes into solution (for example, in a Daniell cell, as discussed below) the charge through the external circuit is:
:
where is the number of electrons/ion, and is the ]Faraday constant
In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of ...
and the minus sign indicates discharge of the cell. Assuming constant pressure and volume, the thermodynamic properties of the cell are related strictly to the behavior of its emf by:[
:
where is the ]enthalpy of reaction
The standard enthalpy of reaction (denoted \Delta_ H^\ominus or \Delta H_^\ominus) for a chemical reaction is the difference between total reactant and total product molar enthalpies, calculated for substances in their standard states. This can in ...
. The quantities on the right are all directly measurable. Assuming constant temperature and pressure:
:
which is used in the derivation of the Nernst equation
In electrochemistry, the Nernst equation is a chemical thermodynamical relationship that permits the calculation of the reduction potential of a reaction ( half-cell or full cell reaction) from the standard electrode potential, absolute tempe ...
.
Distinction with potential difference
Although an electrical potential difference (voltage) is sometimes called an emf,[
][
][
][
][
] however they are formally distinct concepts:
* Emf is the cause of a potential difference. Potential difference in turn is a cause of current flow.
* Potential difference itself is not the cause of an emf.
** Consider Kirchhoff's voltage law
Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits. They were first described in 1845 by German physicist Gustav Kirchho ...
, which says the sum of potential differences going through any loop in a circuit is zero. For a circuit of a voltage source and a resistor, the sum of the source's applied voltage plus the ohmic voltage drop through the resistor is zero. But the resistor provides no emf, only the voltage source does:
*** For a circuit using a battery source, the emf is due solely to the chemistry in the battery that causes charge separation, which generates a potential difference.
*** For a circuit using an electric generator, the emf is due solely to a time-varying magnetic field within the generator that causes charge separation, which generates a potential difference.
* Both a 1 volt emf and a 1 volt potential difference correspond to 1 joule per coulomb of charge. However:
** a 1 volt emf means that the source supplies an energy of 1 joule to each coulomb of charge passing through.
** a 1 volt potential difference between two points on a circuit means that each coulomb of charge will need to either:
*** gain 1 joule of energy to move up that potential difference,
*** or give up 1 joule of energy to move down that potential difference.
In the case of an open circuit, the electric charge that has been separated by the mechanism generating the emf creates an electric field opposing the separation mechanism. For example, the chemical reaction in a voltaic cell stops when the opposing electric field at each electrode is strong enough to arrest the reactions. A larger opposing field can reverse the reactions in what are called ''reversible'' cells.[
]
The electric charge that has been separated creates an electric potential difference
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to m ...
that can (in many cases) be measured with a voltmeter
A voltmeter is an instrument used for measuring electric potential difference between two points in an electric circuit. It is connected in parallel. It usually has a high resistance so that it takes negligible current from the circuit.
A ...
between the terminals of the device, when not connected to a load. The magnitude 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 using the external voltage because some voltage is lost inside the source.
It can, however, be inferred from a measurement of the current and potential difference , provided that the internal resistance already has been measured: ''''
"Potential difference" is not the same as "induced emf" (often called "induced voltage").
The potential difference (difference in the electric scalar potential) between two points A and B is independent of the path we take from ''A'' to ''B''.
If a voltmeter always measured the potential difference between ''A'' and ''B'', then the position of the voltmeter would make no difference.
However, it is quite possible for the measurement by a voltmeter between points ''A'' and ''B'' to depend on the position of the voltmeter, if a time-dependent magnetic field is present.
For example, consider an infinitely long solenoid using an AC current
Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
to generate a varying flux in the interior of the solenoid.
Outside the solenoid we have two resistors connected in a ring around the solenoid.
The resistor on the left is 100 Ω and the one on the right is 200 Ω, they are connected at the top and bottom at points ''A'' and ''B''.
The induced voltage, by Faraday's law is , so the current Therefore the voltage across the 100 Ω resistor is and the voltage across the 200 Ω resistor is , yet the two resistors are connected on both ends, but measured with the voltmeter to the left of the solenoid is not the same as measured with the voltmeter to the right of the solenoid.
[
]
Generation
Chemical sources
The question of how batteries (galvanic cell
A galvanic cell or voltaic cell, named after the scientists Luigi Galvani and Alessandro Volta, respectively, is an electrochemical cell in which an electric current is generated from spontaneous Oxidation-Reduction reactions. A common apparatus ...
s) generate an emf occupied scientists for most of the 19th century. The "seat of the electromotive force" was eventually determined in 1889 by Walther Nernst to be primarily at the interfaces between the electrode
An electrode is an electrical conductor used to make contact with a nonmetallic part of a circuit (e.g. a semiconductor, an electrolyte, a vacuum or air). Electrodes are essential parts of batteries that can consist of a variety of materials d ...
s and the electrolyte.
Atoms in molecules or solids are held together by chemical bond
A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
ing, which stabilizes the molecule or solid (i.e. reduces its energy). When molecules or solids of relatively high energy are brought together, a spontaneous chemical reaction can occur that rearranges the bonding and reduces the (free) energy of the system.[
The brave reader can find an extensive discussion for organic electrochemistry in
] In batteries, coupled half-reactions, often involving metals and their ions, occur in tandem, with a gain of electrons (termed "reduction") by one conductive electrode and loss of electrons (termed "oxidation") by another (reduction-oxidation or redox reactions
Redox (reduction–oxidation, , ) is a type of chemical reaction in which the oxidation states of substrate change. Oxidation is the loss of electrons or an increase in the oxidation state, while reduction is the gain of electrons or a d ...
). The spontaneous overall reaction can only occur if electrons move through an external wire between the electrodes. The electrical energy given off is the free energy lost by the chemical reaction system.
As an example, a Daniell cell
The Daniell cell is a type of electrochemical cell invented in 1836 by John Frederic Daniell, a British chemist and meteorologist, and consists of a copper pot filled with a copper (II) sulfate solution, in which is immersed an unglazed earthenw ...
consists of a zinc anode (an electron collector) that is oxidized as it dissolves into a zinc sulfate solution. The dissolving zinc leaving behind its electrons in the electrode according to the oxidation reaction (''s'' = solid electrode; ''aq'' = aqueous solution):
:
The zinc sulfate is the electrolyte in that half cell. It is a solution which contains zinc cations , and sulfate anions with charges that balance to zero.
In the other half cell, the copper cations in a copper sulfate electrolyte move to the copper cathode to which they attach themselves as they adopt electrons from the copper electrode by the reduction reaction:
:
which leaves a deficit of electrons on the copper cathode. The difference of excess electrons on the anode and deficit of electrons on the cathode creates an electrical potential between the two electrodes. (A detailed discussion of the microscopic process of electron transfer between an electrode and the ions in an electrolyte may be found in Conway.)[
] The electrical energy released by this reaction (213 kJ per 65.4 g of zinc) can be attributed mostly due to the 207 kJ weaker bonding (smaller magnitude of the cohesive energy) of zinc, which has filled 3d- and 4s-orbitals, compared to copper, which has an unfilled orbital available for bonding.
If the cathode and anode are connected by an external conductor, electrons pass through that external circuit (light bulb in figure), while ions pass through the salt bridge
In electrochemistry, a salt bridge or ion bridge is a laboratory device used to connect the oxidation and reduction half-cells of a galvanic cell (voltaic cell), a type of electrochemical cell. It maintains electrical neutrality within the in ...
to maintain charge balance until the anode and cathode reach electrical equilibrium of zero volts as chemical equilibrium is reached in the cell. In the process the zinc anode is dissolved while the copper electrode is plated with copper. The salt bridge has to close the electrical circuit while preventing the copper ions from moving to the zinc electrode and being reduced there without generating an external current. It is not made of salt but of material able to wick cations and anions
An ion () is an atom or molecule with a net electrical charge.
The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by convent ...
(a dissociated salt) into the solutions. The flow of positively charged cations along the bridge is equivalent to the same number of negative charges flowing in the opposite direction.
If the light bulb is removed (open circuit) the emf between the electrodes is opposed by the electric field due to the charge separation, and the reactions stop.
For this particular cell chemistry, at 298 K (room temperature), the emf = 1.0934 V, with a temperature coefficient of = −4.53×10−4 V/K.
Voltaic cells
Volta developed the voltaic cell about 1792, and presented his work March 20, 1800. Volta correctly identified the role of dissimilar electrodes in producing the voltage, but incorrectly dismissed any role for the electrolyte. Volta ordered the metals in a 'tension series', "that is to say in an order such that any one in the list becomes positive when in contact with any one that succeeds, but negative by contact with any one that precedes it." A typical symbolic convention in 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 implies that, given ten electrodes (for example, zinc and nine other materials), 45 unique combinations of voltaic cells (10 × 9/2) can be created.
Typical values
The electromotive force produced by primary (single-use) and secondary (rechargeable) 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.
Other chemical sources
Other chemical sources include fuel cell
A fuel cell is an electrochemical cell that converts the chemical energy of a fuel (often hydrogen) and an oxidizing agent (often oxygen) into electricity through a pair of redox reactions. Fuel cells are different from most batteries in requ ...
s.
Electromagnetic induction
Electromagnetic induction
Electromagnetic or magnetic induction is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field.
Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk ...
is the production of a circulating electric field by a time-dependent magnetic 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 an electric current), or by changing the electric current in a fixed circuit. The effect on the circuit itself, of changing the electric current, is known as self-induction; the effect on another circuit is known as mutual induction
Inductance is the tendency of an electrical conductor to oppose a change in the electric current flowing through it. The flow of electric current creates a magnetic field around the conductor. The field strength depends on the magnitude of the ...
.
For a given circuit, the electromagnetically induced emf is determined purely by the rate of change of the magnetic flux through the circuit according to Faraday's law of induction.
An emf is induced in a coil or conductor whenever there is change in the flux linkage
In circuit theory, flux linkage is a property of a two-terminal element. It is an extension rather than an equivalent of magnetic flux and is defined as a time integral
:\lambda = \int \mathcal \,dt,
where \mathcal is the voltage across the de ...
s. Depending on the way in which the changes are brought about, there are two types: When the conductor is moved in a stationary magnetic field to procure a change in the flux linkage, the emf is ''statically induced''. The electromotive force generated by motion is often referred to as ''motional emf''. When the change in flux linkage arises from a change in the magnetic field around the stationary conductor, the emf is ''dynamically induced.'' The electromotive force generated by a time-varying magnetic field is often referred to as ''transformer emf''.
Contact potentials
When solids of two different materials are in contact, thermodynamic equilibrium
Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In the ...
requires that one of the solids assume a higher electrical potential than the other. This is called the ''contact potential''. Dissimilar metals in contact produce what is known also as a contact electromotive force or Galvani potential
In electrochemistry, the Galvani potential (also called Galvani potential difference, or inner potential difference, Δφ, delta phi) is the electric potential difference between two points in the bulk of two phases. These phases can be two differ ...
. The magnitude of this potential difference is often expressed as a difference in Fermi levels in the two solids when they are at charge neutrality, where the Fermi level (a name for the chemical potential
In thermodynamics, the chemical potential of a species is the energy that can be absorbed or released due to a change of the particle number of the given species, e.g. in a chemical reaction or phase transition. The chemical potential of a species ...
of an electron system[
]) describes the energy necessary to remove an electron from the body to some common point (such as ground). If there is an energy advantage in taking an electron from one body to the other, such a transfer will occur. The transfer causes a charge separation, with one body gaining electrons and the other losing electrons. This charge transfer causes a potential difference between the bodies, which partly cancels the potential originating from the contact, and eventually equilibrium is reached. At thermodynamic equilibrium, the Fermi levels are equal (the electron removal energy is identical) and there is now a built-in electrostatic potential between the bodies.
The original difference in Fermi levels, before contact, is referred to as the emf.
The contact potential cannot drive steady current through a load attached to its terminals because that current would involve a charge transfer. No mechanism exists to continue such transfer and, hence, maintain a current, once equilibrium is attained.
One might inquire why the contact potential does not appear in Kirchhoff's law of voltages as one contribution to the sum of potential drops. The customary answer is that any circuit involves not only a particular diode or junction, but also all the contact potentials due to wiring and so forth around the entire circuit. The sum of ''all'' the contact potentials is zero, and so they may be ignored in Kirchhoff's law.
Solar cell
Operation of a solar cell
A solar cell, or photovoltaic cell, is an electronic device that converts the energy of light directly into electricity by the photovoltaic effect, which is a physical and chemical phenomenon. can be understood from its equivalent circuit. Photons
A photon () is an elementary particle that is a quantum of the electromagnetic field, including electromagnetic radiation such as light and radio waves, and the force carrier for the electromagnetic force. Photons are massless, so they alway ...
with energy greater than the bandgap
In solid-state physics, a band gap, also called an energy gap, is an energy range in a solid where no electronic states can exist. In graphs of the electronic band structure of solids, the band gap generally refers to the energy difference (i ...
of the semiconductor
A semiconductor is a material which has an electrical resistivity and conductivity, electrical conductivity value falling between that of a electrical conductor, conductor, such as copper, and an insulator (electricity), insulator, such as glas ...
create mobile electron–hole pair
In the solid-state physics of semiconductors, carrier generation and carrier recombination are processes by which mobile charge carriers (electrons and electron holes) are created and eliminated. Carrier generation and recombination processes are ...
s. Charge separation occurs because of a pre-existing electric field associated with the p-n junction. This electric field is created from a built-in potential, which arises from the contact potential between the two different materials in the junction. The charge separation between positive hole
A hole is an opening in or through a particular medium, usually a solid body. Holes occur through natural and artificial processes, and may be useful for various purposes, or may represent a problem needing to be addressed in many fields of en ...
s and negative electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have no kn ...
s across the p–n diode
This article provides a more detailed explanation of p–n diode behavior than is found in the articles p–n junction or diode.
A p–n diode is a type of semiconductor diode based upon the p–n junction. The diode conducts current in only on ...
yields a ''forward voltage
Forward is a relative direction, the opposite of backward.
Forward may also refer to:
People
*Forward (surname)
Sports
* Forward (association football)
* Forward (basketball), including:
** Point forward
** Power forward (basketball)
** Smal ...
'', the ''photo voltage'', between the illuminated diode terminals, which drives current through any attached load. ''Photo voltage'' is sometimes referred to as the ''photo emf'', distinguishing between the effect and the cause.
Solar cell current–voltage relationship
Two internal current losses limit the total current available to the external circuit. The light-induced charge separation eventually creates a forward current through the cell's internal resistance in the direction opposite the light-induced current . In addition, the induced voltage tends to forward bias
Forward is a relative direction, the opposite of backward.
Forward may also refer to:
People
*Forward (surname)
Sports
* Forward (association football)
* Forward (basketball), including:
** Point forward
** Power forward (basketball)
** Smal ...
the junction, which at high enough voltages will cause a recombination current in the diode opposite the light-induced current.
When the output is short-circuited, the output voltage is zeroed, and so the voltage across the diode is smallest. Thus, short-circuiting results in the smallest losses and consequently the maximum output current, which for a high-quality solar cell is approximately equal to the light-induced current . Approximately this same current is obtained for forward voltages up to the point where the diode conduction becomes significant.
The current delivered by the illuminated diode to the external circuit can be simplified (based on certain assumptions) to:
:
is the reverse saturation current The saturation current (or scale current), more accurately the reverse saturation current, is the part of the reverse current in a semiconductor diode caused by diffusion of minority carriers from the neutral regions to the depletion region. This ...
. Two parameters that depend on the solar cell construction and to some degree upon the voltage itself are the ideality factor ''m'' and the thermal voltage
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a ideal gas, gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas ...
, which is about 26 millivolts at room temperature.[
]
Solar cell photo emf
Solving the illuminated diode's above simplified current–voltage relationship for output voltage yields:
:
which is plotted against in the figure.
The solar cell's ''photo emf'' has the same value as the open-circuit voltage , which is determined by zeroing the output current :
:
It has a logarithmic dependence on the light-induced current and is where the junction's forward bias voltage is just enough that the forward current completely balances the light-induced current. For silicon junctions, it is typically not much more than 0.5 volts. While for high-quality silicon panels it can exceed 0.7 volts in direct sunlight.
When driving a resistive load, the output voltage can be determined using Ohm's law and will lie between the short-circuit value of zero volts and the open-circuit voltage . When that resistance is small enough such that (the near-vertical part of the two illustrated curves), the solar cell acts more like a ''current generator'' rather than a voltage generator,[
] since the current drawn is nearly fixed over a range of output voltages. This contrasts with batteries, which act more like voltage generators.
Other sources that generate emf
*A transformer
A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
coupling two circuits may be considered a source of emf for one of the circuits, just as if it were caused by an electrical generator; this is the origin of the term "transformer emf".
*For converting sound waves
In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid.
In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by the ...
into voltage signals
In signal processing, a signal is a function that conveys information about a phenomenon. Any quantity that can vary over space or time can be used as a signal to share messages between observers. The ''IEEE Transactions on Signal Processing'' ...
:
**a microphone
A microphone, colloquially called a mic or mike (), is a transducer that converts sound into an electrical signal. Microphones are used in many applications such as telephones, hearing aids, public address systems for concert halls and public ...
generates an emf from a moving diaphragm.
**a magnetic pickup generates an emf from a varying magnetic field produced by an instrument.
**a piezoelectric sensor generates an emf from strain on a piezoelectric crystal
Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word ''p ...
.
*Devices that use temperature to produce emfs include thermocouple
A thermocouple, also known as a "thermoelectrical thermometer", is an electrical device consisting of two dissimilar electrical conductors forming an electrical junction. A thermocouple produces a temperature-dependent voltage as a result of th ...
s and thermopiles.
*Any electrical transducer
A transducer is a device that converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.
Transducers are often employed at the boundaries of automation, measurement, and cont ...
which converts a physical energy into electrical energy.
See also
*Counter-electromotive force
Counter-electromotive force (counter EMF, CEMF, back EMF),Graf, "counterelectromotive force", Dictionary of Electronics is the electromotive force (EMF) manifesting as a voltage that opposes the change in current which induced it. CEMF is the EMF c ...
* Electric battery
*Electrochemical cell
An electrochemical cell is a device capable of either generating electrical energy from chemical reactions or using electrical energy to cause chemical reactions. The electrochemical cells which generate an electric current are called voltaic o ...
*Electrolytic cell
An electrolytic cell is an electrochemical cell that utilizes an external source of electrical energy to force a chemical reaction that would not otherwise occur. The external energy source is a voltage applied between the cell′s two electrod ...
*Galvanic cell
A galvanic cell or voltaic cell, named after the scientists Luigi Galvani and Alessandro Volta, respectively, is an electrochemical cell in which an electric current is generated from spontaneous Oxidation-Reduction reactions. A common apparatus ...
*Voltaic pile
upright=1.2, Schematic diagram of a copper–zinc voltaic pile. The copper and zinc discs were separated by cardboard or felt spacers soaked in salt water (the electrolyte). Volta's original piles contained an additional zinc disk at the bottom, ...
References
Further reading
* George F. Barker,
On the measurement of electromotive force
. Proceedings of the American Philosophical Society Held at Philadelphia for Promoting Useful Knowledge, American Philosophical Society. January 19, 1883.
* Andrew Gray, "Absolute Measurements in Electricity and Magnetism"
Electromotive force
Macmillan and co., 1884.
* Charles Albert Perkins, "Outlines of Electricity and Magnetism"
Measurement of Electromotive Force
Henry Holt and co., 1896.
* John Livingston Rutgers Morgan, "The Elements of Physical Chemistry"
Electromotive force
J. Wiley, 1899.
* "Abhandlungen zur Thermodynamik, von H. Helmholtz. Hrsg. von Max Planck". (Tr. "Papers to thermodynamics, on H. Helmholtz. Hrsg. by Max Planck".) Leipzig, W. Engelmann, Of Ostwald classical author of the accurate sciences series. New consequence. No. 124, 1902.
* Theodore William Richards and Gustavus Edward Behr, jr., "The electromotive force of iron under varying conditions, and the effect of occluded hydrogen". Carnegie Institution of Washington publication series, 1906.
* Henry S. Carhart, "Thermo-electromotive force in electric cells, the thermo-electromotive force between a metal and a solution of one of its salts". New York, D. Van Nostrand company, 1920.
* Hazel Rossotti, "Chemical applications of potentiometry". London, Princeton, N.J., Van Nostrand, 1969.
* Nabendu S. Choudhury, 1973
"Electromotive force measurements on cells involving beta-alumina solid electrolyte"
NASA technical note, D-7322.
*
*
* G. W. Burns, et al., "Temperature-electromotive force reference functions and tables for the letter-designated thermocouple types based on the ITS-90". Gaithersburg, MD : U.S. Dept. of Commerce, National Institute of Standards and Technology, Washington, Supt. of Docs., U.S. G.P.O., 1993.
*
*
{{DEFAULTSORT:Electromotive Force
Electromagnetism
Electrodynamics
Voltage