Editing Electromotive force (section)

==Generation==

===Chemical sources===
{{Main|Electrochemical cell}}

[[File:Reaction path.JPG|thumb|380px|A typical reaction path requires the initial reactants to cross an energy barrier, enter an intermediate state and finally emerge in a lower energy configuration. If charge separation is involved, this energy difference can result in an emf. See Bergmann ''et al.''<ref name=Bergmann>{{cite book |title=Constituents of Matter: Atoms, Molecules, Nuclei, and Particles |first=Nikolaus|last=Risch |chapter=Molecules - bonds and reactions |editor=L Bergmann |display-editors=etal |isbn=978-0-8493-1202-1  |year=2002 |publisher=CRC Press |chapter-url=https://books.google.com/books?id=mGj1y1WYflMC}}</ref> and [[Transition state]].]]

[[Image:Galvanic cell labeled.svg|thumb|380px|[[Galvanic cell]] using a [[salt bridge]]]]

The question of how batteries (galvanic cells) 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]]<ref>{{cite journal |last1=Nernst |first1=Walter |title=Die elektromotorische Wirksamkeit der Ionen |journal=[[Z. Phys. Chem.]] |date=1889 |volume=4 |page=129}}</ref> to be primarily at the interfaces between the [[electrode]]s and the [[electrolyte]].<ref name=cajori>{{cite book
 | title = A History of Physics in Its Elementary Branches: Including the Evolution of Physical Laboratories
 | first = Florian|last=Cajori
 | publisher = The Macmillan Company
 | year = 1899
 | pages = [https://archive.org/details/ahistoryphysics03cajogoog/page/n232 218]–219
 | url = https://archive.org/details/ahistoryphysics03cajogoog
 | quote = seat of electromotive force.
 }}</ref>

Atoms in molecules or solids are held together by [[chemical bond]]ing, which stabilizes the molecule or solid (i.e. [[Minimum total potential energy principle|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.<ref name=reconfigure>
The brave reader can find an extensive discussion for organic electrochemistry in {{cite book |title=Organic electrochemistry |edition=4 |year=2000 |publisher=CRC Press |isbn=978-0-8247-0430-8 |editor1=Henning Lund |editor2=Ole Hammerich |chapter-url=https://books.google.com/books?id=tBxxZclgKyMC&pg=PA23 |first=Christian| last=Amatore |chapter=Basic concepts}}
</ref> 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|redox reactions]]). 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]] 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):

:<math>\mathrm{Zn_{(s)} \rightarrow Zn^{2+}_{(aq)} + 2  e ^- \ } </math>

The zinc sulfate is the [[electrolyte]] in that half cell. It is a solution which contains zinc cations <math>\mathrm{Zn}^{2+}</math>, and sulfate anions <math>\mathrm{SO}_4^{2-} </math> 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:

:<math> \mathrm{Cu^{2+}_{(aq)} + 2 e^- \rightarrow Cu_{(s)}\ } </math>

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.)<ref name=Conway>
{{cite book |title=Electrochemical supercapacitors |first=BE|last=Conway |chapter=Energy factors in relation to electrode potential |page=37 |chapter-url=https://books.google.com/books?id=8yvzlr9TqI0C&pg=PA37 |isbn=978-0-306-45736-4 |year=1999 |publisher=Springer}}
</ref> 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]] 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.<ref name= Tilley>{{cite book |title=Understanding Solids |url=https://archive.org/details/understandingsol0000till |url-access=registration |page=[https://archive.org/details/understandingsol0000till/page/267 267] |first=R. J. D.|last=Tilley |isbn=978-0-470-85275-0 |year=2004 |publisher=Wiley}}</ref> 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]] (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 <math>\mathcal{E}</math> = 1.0934 V, with a temperature coefficient of <math>d\mathcal{E}/dT</math>&nbsp;= −4.53×10<sup>−4</sup> V/K.<ref name= Finn>{{cite book |title=Thermal Physics |first=Colin B P|last=Finn |page=163 |url=https://books.google.com/books?id=BTMPThGxXQ0C&pg=PA162 |isbn=978-0-7487-4379-7 |year=1992 |publisher=CRC Press}}</ref>

====Voltaic cells====
Volta developed the voltaic cell about 1792, and presented his work March 20, 1800.<ref name=Mottelay>{{cite book |title=Bibliographical History of Electricity and Magnetism |first=Paul Fleury|last=Mottelay |page=247 |url=https://books.google.com/books?id=9vzti90Q8i0C&pg=RA1-PA247 |isbn=978-1-4437-2844-7 |publisher=Read Books |year=2008 |edition=Reprint of 1892}}</ref> Volta correctly identified the role of dissimilar electrodes in producing the voltage, but incorrectly dismissed any role for the electrolyte.<ref name=Kragh>{{cite journal
 |journal     = Nuova Voltiana:Studies on Volta and His Times
 |publisher   = Università degli studi di Pavia
 |year        = 2000
 |url         = http://ppp.unipv.it/Collana/Pages/Libri/Saggi/NuovaVoltiana_PDF/sei.pdf
 |title       = Confusion and Controversy: Nineteenth-century theories of the voltaic pile
 |first = Helge|last=Kragh
 |url-status     = dead
 |archive-url  = https://web.archive.org/web/20090320064922/http://ppp.unipv.it/Collana/Pages/Libri/Saggi/NuovaVoltiana_PDF/sei.pdf
 |archive-date = 2009-03-20
}}</ref> 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."<ref name=Cumming>{{cite book |title=An Introduction to the Theory of Electricity |first=Linnaus|last=Cumming |url=https://books.google.com/books?id=Nrb8723u4WEC&pg=PA118 |page=118 |isbn=978-0-559-20742-6 |publisher=BiblioBazaar |year=2008 |edition=Reprint of 1885}}</ref> A typical symbolic convention in a schematic of this circuit ( –<big>|</big>'''<small>|</small>'''– ) 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.

{| class=wikitable

! rowspan="2" | EMF
! colspan="3" | Cell chemistry
! rowspan="2" | Common name
|-
! Anode
! Solvent, electrolyte
! Cathode 
|-
| 1.2&nbsp;V || Cadmium || Water, potassium hydroxide || NiO(OH) || [[Nickel–cadmium battery|nickel-cadmium]]
|-
| 1.2&nbsp;V || [[Mischmetal]] (hydrogen absorbing) || Water, potassium hydroxide || Nickel|| [[Nickel–metal hydride battery|nickel–metal hydride]]
|-
| 1.5&nbsp;V || Zinc || Water, ammonium or zinc chloride || Carbon, manganese dioxide|| [[zinc–carbon battery|Zinc carbon]]
|-
| 2.1&nbsp;V || Lead || Water, sulfuric acid || Lead dioxide || [[Lead–acid battery|Lead–acid]]
|-
| 3.6&nbsp;V to 3.7&nbsp;V || Graphite || Organic solvent, Li salts || LiCoO<sub>2</sub> || [[lithium-ion battery|Lithium-ion]]
|-
| 1.35&nbsp;V || Zinc || Water, sodium or potassium hydroxide || HgO || [[Mercury cell]]
|-
|}

==== Other chemical sources ====
Other chemical sources include [[fuel cell]]s.

===Electromagnetic induction===
{{Main|Faraday's law of induction}}

Electromagnetic induction 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]].

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]]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===
{{See also|Volta potential|Electrochemical potential}}
When solids of two different materials are in contact, [[thermodynamic equilibrium]] requires that one of the solids assume a higher electrical potential than the other. This is called the ''contact potential''.<ref name=Trigg>{{cite book |title=Landmark experiments in twentieth century physics |first=George L.|last=Trigg |page=138 ''ff'' |url=https://books.google.com/books?id=YOQ9fi5yQ4sC&pg=PA138 |isbn=978-0-486-28526-9 |year=1995 |publisher=Courier Dover |edition=Reprint of Crane, Russak & Co 1975}}</ref> Dissimilar metals in contact produce what is known also as a contact electromotive force or [[Galvani potential]]. The magnitude of this potential difference is often expressed as a difference in [[Fermi level]]s in the two solids when they are at charge neutrality, where the Fermi level (a name for the [[chemical potential]] of an electron system<ref name=Rockett>{{cite book |title=Materials science of semiconductors |first=Angus|last=Rockett |chapter=Diffusion and drift of carriers |page=74 ''ff'' |chapter-url=https://books.google.com/books?id=n5zMiMfw6ZUC&pg=PA74 |isbn=978-0-387-25653-5 |year=2007 |publisher=Springer Science |location=New York, NY}}</ref><ref name=Kittel>{{cite book |title=Elementary Statistical Physics |first=Charles|last=Kittel |chapter-url=https://books.google.com/books?id=5sd9SAoRjgQC&pg=PA67 |chapter= Chemical potential in external fields |page=67 |isbn=978-0-486-43514-5 |publisher=Courier Dover |year=2004 |edition=Reprint of Wiley 1958}}
</ref>) describes the energy necessary to remove an electron from the body to some common point (such as ground).<ref name=Hanson>{{cite book |title=Fundamentals of Nanoelectronics |first=George W.|last=Hanson |page=100 |url=https://books.google.com/books?id=L7AUi7ltCksC&pg=PA100 |isbn=978-0-13-195708-4 |year=2007 |publisher=Prentice Hall}}</ref> 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 level]]s 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.<ref name=Sato>{{cite book |title=Electrochemistry at metal and semiconductor electrodes |first=Norio|last=Sato |page=110 ''ff'' |chapter-url=https://books.google.com/books?id=olQzaXNgM74C&pg=PA110 |isbn=978-0-444-82806-4 |year=1998 |publisher=Elsevier |edition=2nd |chapter= Semiconductor photoelectrodes}}</ref>
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 circuit laws|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.<ref name=Quimby>{{cite book |title=Photonics and lasers |first=Richard S.|last=Quimby |page=176 |url=https://books.google.com/books?id=82f-gIvtC7wC&pg=PA176 |isbn=978-0-471-71974-8 |publisher=Wiley |year=2006}}</ref><ref name=Neamen>{{cite book |title=Semiconductor physics and devices |first=Donald A.|last=Neamen |url=https://archive.org/details/semiconductorphy00neam |url-access=registration |page=[https://archive.org/details/semiconductorphy00neam/page/240 240] |year=2002 |isbn=978-0-07-232107-4 |publisher=McGraw-Hill Professional |edition=3rd}}</ref>

===Solar cell===
{{Main|Theory of solar cells}}

[[Image:Solar cell equivalent circuit.svg|thumb|250px |The [[Theory of solar cells#Equivalent circuit of a solar cell|equivalent circuit of a solar cell]], ignoring parasitic resistances.]]

Operation of a [[solar cell]] can be understood from [[Theory of solar cells#Equivalent circuit of a solar cell|its equivalent circuit]]. [[Photon]]s with energy greater than the [[bandgap]] of the [[semiconductor]] create mobile [[electron–hole pair]]s. Charge separation occurs because of a pre-existing electric field associated with the [[p-n junction]]. This electric field is created from a [[p–n junction#Equilibrium (zero bias)|built-in potential]], which arises from the [[Volta potential|contact potential]] between the two different materials in the junction. The charge separation between positive [[Electron hole|hole]]s and negative [[electron]]s across the [[p–n diode]] yields a ''[[forward voltage]]'', the ''photo voltage'', between the illuminated diode terminals,<ref name="Dhir">{{cite book |first=S. M. |last=Dhir |title=Electronic Components and Materials: Principles, Manufacture & Maintenance |date=2000 |orig-year=1999 |publisher=[[Tata McGraw-Hill Publishing Company Limited]] |location=India |edition=2007 fifth reprint |isbn=0-07-463082-2 |page=283 |chapter=§3.1 Solar cells |url=https://books.google.com/books?id=sGbwj4J76tEC |chapter-url=https://books.google.com/books?id=sGbwj4J76tEC&pg=PA283}}</ref> 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 <math>I_{SH} + I_D</math> limit the total current <math>I</math> available to the external circuit. The light-induced charge separation eventually creates a forward current <math> I_{SH}</math> through the cell's internal resistance <math>R_{SH}</math> in the direction opposite the light-induced current <math>I_L</math>. In addition, the induced voltage tends to [[p-n junction#Forward bias|forward bias]] the junction, which at high enough voltages will cause a recombination current <math> I_{D}</math> 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 <math>I_{SH} + I_D</math> losses and consequently the maximum output current, which for a high-quality solar cell is approximately equal to the light-induced current <math> I_{L}</math>.<ref name="Lorenzo">{{cite book
 |title=Solar Electricity: Engineering of photovoltaic systems
 |editor=Eduardo Lorenzo
 |first= Gerardo L.|last=Araújo
 |chapter-url=https://books.google.com/books?id=lYc53xZyxZQC&pg=PA74
 |chapter=§2.5.1 Short-circuit current and open-circuit voltage
 |isbn=978-84-86505-55-4
 |year=1994
 |page=74
 |publisher=Progenza for Universidad Politechnica Madrid
 }}</ref> 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:

:<math>I = I_L -I_0 \left( e^{\frac{V}{m\ V_\mathrm{T}}} - 1 \right) \ . </math>

<math>I_0</math> is the [[reverse saturation current]]. 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]] <math>V_\mathrm{T} = \tfrac{k T}{q} </math>, which is about 26 millivolts at [[room temperature]].<ref name= Lorenzo/>

==== Solar cell photo emf ====

[[File:Solar cell characterisitcs.JPG|thumb|250px |Solar cell output voltage for two light-induced currents ''I''<sub>L</sub> expressed as a ratio to the reverse saturation current ''I''<sub>0</sub><ref>{{cite book |first=Jenny|last=Nelson |url=https://books.google.com/books?id=s5NN34HLWO8C&pg=PA8 |title=The physics of solar cells |publisher=Imperial College Press |year=2003 |isbn=978-1-86094-349-2 |page=8}}</ref> and using a fixed ideality factor ''m'' of 2.<ref name="params">In practice, at low voltages ''m''&nbsp;→ 2, whereas at high voltages ''m''&nbsp;→ 1. See Araújo, ''op. cit.'' {{ISBN|84-86505-55-0}}. [https://books.google.com/books?id=lYc53xZyxZQC&pg=PA72 page 72]</ref> Their emf is the voltage at their y-axis intercept.]]

Solving the illuminated diode's above simplified [[Current-voltage relationship|current–voltage relationship]] for output voltage yields:

:<math>V = m\ V_\mathrm{T} \ln \left( \frac{I_\text{L} - I}{I_0}+1 \right) \ , </math>
which is plotted against <math>I / I_0 </math> in the figure.

The solar cell's ''photo emf'' <math>\mathcal{E}_\mathrm{photo}</math> has the same value as the open-circuit voltage <math>V_{oc}</math>, which is determined by zeroing the output current <math>I</math>:

:<math>\mathcal{E}_\mathrm{photo} = V_\text{oc} = m\ V_\mathrm{T} \ln \left( \frac{I_\text{L}}{I_0}+1 \right) \ . </math>

It has a [[logarithm]]ic dependence on the light-induced current <math>I_L</math> 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.<ref name="Northrop">{{cite book
 | title=Introduction to Instrumentation and Measurements
 | first=Robert B.|last=Northrop
 | page=176
 | chapter=§6.3.2 Photovoltaic Cells
 | chapter-url= https://books.google.com/books?id=mcpcfpQfxB4C&pg=PA176
 | isbn=978-0-8493-7898-0 |year=2005 |publisher=CRC Press
 }}</ref> While for high-quality silicon panels it can exceed 0.7 volts in direct sunlight.<ref>{{cite web| url = https://www.pveducation.org/pvcdrom/solar-cell-operation/open-circuit-voltage#:~:text=Silicon%20solar%20cells%20on%20high,circuit%20voltages%20around%20690%20mV. | title = Open-Circuit Voltage}}</ref>

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 <math>V_{oc}</math>.<ref>{{cite book |first=Jenny|last=Nelson |url=https://books.google.com/books?id=s5NN34HLWO8C&pg=PA8 |title=The physics of solar cells |publisher=Imperial College Press |year=2003 |isbn=978-1-86094-349-2 |page=6}}</ref> When that resistance is small enough such that <math>I \approx I_L</math> (the near-vertical part of the two illustrated curves), the solar cell acts more like a ''current generator'' rather than a voltage generator,<ref name="Nelson_page7">
{{cite book |first=Jenny|last=Nelson |url=https://books.google.com/books?id=s5NN34HLWO8C&pg=PA8 |title=The physics of solar cells |publisher=Imperial College Press |year=2003 |isbn=978-1-86094-349-2 |page=7}}</ref> 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]] 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]] into voltage [[signal]]s:
**a [[microphone]] generates an emf from a moving [[Diaphragm (acoustics)|diaphragm]].
**a [[Pickup (music technology)#Magnetic pickups|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]].
*Devices that use temperature to produce emfs include [[thermocouple]]s and [[thermopiles]].<ref>{{cite book|editor=John S. Rigden|title=Macmillan encyclopedia of physics|location=New York|publisher=Macmillan|year=1996}}</ref>
*Any electrical [[Transducer#Applications|transducer]] which converts a physical energy into electrical energy.