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Electromotive force

From Wikipedia, the free encyclopedia
Electrical action produced by a non-electrical source
Not to be confused withElectromagnetic field.
Electromagnetism
Solenoid

Inelectromagnetism andelectronics,electromotive force (alsoelectromotance, abbreviatedemf,[1][2] denotedE{\displaystyle {\mathcal {E}}}) is anenergy transfer to anelectric circuit per unit ofelectric charge, measured involts. Devices called electricaltransducers provide an emf[3] byconverting other forms ofenergy intoelectrical energy.[3] Other types of electrical equipment also produce an emf, such asbatteries, which convertchemical energy, andgenerators, which convertmechanical energy.[4] This energy conversion is achieved byphysical forces applyingphysical work onelectric charges. However, electromotive force itself is not a physical force,[5] andISO/IEC standards have deprecated the term in favor ofsource voltage orsource tension instead (denotedUs{\displaystyle U_{s}}).[6][7]

Anelectronic–hydraulic analogy may view emf as themechanical work done to water by apump, which results in apressure difference (analogous to voltage).[8]

Inelectromagnetic induction, emf can be defined around a closed loop of aconductor as the electromagneticwork that would be done on anelementary electric charge (such as anelectron) if it travels once around the loop.[9]

For two-terminal devices modeled as aThévenin equivalent circuit, an equivalent emf can be measured as theopen-circuit voltage between the two terminals. This emf can drive anelectric current if an externalcircuit is attached to the terminals, in which case the device becomes thevoltage source 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§ Distinction with potential difference).

Overview

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Devices that can provide emf includeelectrochemical cells,thermoelectric devices,solar cells,photodiodes,electrical generators,inductors,transformers and evenVan de Graaff generators.[10][11] In nature, emf is generated whenmagnetic field fluctuations occur through a surface. For example, the shifting of theEarth's magnetic field during ageomagnetic storm induces currents in anelectrical 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) between the terminals is accomplished bychemical reactions at theelectrodes that convert chemicalpotential energy into electromagnetic potential energy.[12][13] Avoltaic cell can be thought of as having a "charge pump" of atomic dimensions at each electrode, that is:

A (chemical) source of emf can be thought of as a kind ofcharge pump that acts to move positive charges from a point of low potential through its interior to a point of high potential. … By chemical, mechanical or other means, the source of emf performs workdW{\textstyle {\mathit {d}}W} on that charge to move it to the high-potential terminal. The emfE{\textstyle {\mathcal {E}}} of the source is defined as the workdW{\textstyle {\mathit {d}}W} done per chargedq{\textstyle dq}.E=dWdq{\textstyle {\mathcal {E}}={\frac {{\mathit {d}}W}{{\mathit {d}}q}}}.[14]

In an electrical generator, a time-varying magnetic field inside the generator creates anelectric field viaelectromagnetic induction, 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 aload is attached, this voltage can drive a current. The general principle governing the emf in such electrical machines isFaraday's law of induction.

History

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In 1801,Alessandro Volta introduced the term "force motrice électrique" to describe the active agent of a battery (which he had invented around 1798).[15]This is called the "electromotive force" in English.

Around 1830,Michael Faraday 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 earlierobsolete theory thought.[16] 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, 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. It is independent of size of the cell but depends on the nature of the electrolyte used.

Notation and units of measurement

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Electromotive force (emf) is typically denoted by the symbolℰ (script E). It represents the energy provided by a source per unit electric charge. The standard unit of emf in the International System of Units (SI) is thevolt (V).

In a device withoutinternal resistance, if an electric chargeq{\displaystyle q} passing through that device gains an energyW{\displaystyle W} via work, the net emf for that device is the energy gained per unit charge:Wq.{\textstyle {\tfrac {W}{q}}.} Like other measures of energy per charge, emf uses theSI unitvolt, which is equivalent to ajoule (SI unit of energy) percoulomb (SI unit of charge).[17]

Electromotive force inelectrostatic units is thestatvolt (in thecentimeter gram second system of units equal in amount to anerg per electrostatic unit of charge).

Formal definitions

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Inside a source of emf (such as a battery) that is open-circuited, a charge separation occurs between the negative terminalN and the positive terminalP.This leads to anelectrostatic fieldEopen circuit{\displaystyle {\boldsymbol {E}}_{\mathrm {open\ circuit} }} that points fromP toN, whereas the emf of the source must be able to drive current fromN toP when connected to a circuit.This ledMax Abraham[18] to introduce the concept of anonelectrostatic fieldE′{\displaystyle {\boldsymbol {E}}'} that exists only inside the source of emf.In the open-circuit case,E′=−Eopen circuit{\displaystyle {\boldsymbol {E}}'=-{\boldsymbol {E}}_{\mathrm {open\ circuit} }}, while when the source is connected to a circuit the electric fieldE{\displaystyle {\boldsymbol {E}}} inside the source changes butE′{\displaystyle {\boldsymbol {E}}'} remains essentially the same.In the open-circuit case, theconservative electrostatic field created by separation of charge exactly cancels the forces producing the emf.[19] Mathematically:

Esource=∫NPE′⋅dℓ=−∫NPEopen circuit⋅dℓ=VP−VN ,{\displaystyle {\mathcal {E}}_{\mathrm {source} }=\int _{N}^{P}{\boldsymbol {E}}'\cdot \mathrm {d} {\boldsymbol {\ell }}=-\int _{N}^{P}{\boldsymbol {E}}_{\mathrm {open\ circuit} }\cdot \mathrm {d} {\boldsymbol {\ell }}=V_{P}-V_{N}\ ,}

whereEopen circuit{\displaystyle {\boldsymbol {E}}_{\mathrm {open\ circuit} }} is the conservative electrostatic field created by the charge separation associated with the emf,dℓ{\displaystyle \mathrm {d} {\boldsymbol {\ell }}} is an element of the path from terminalN to terminalP, '⋅{\displaystyle \cdot }' denotes the vectordot product, andV{\displaystyle V} is the electric scalar potential.[20] This emf is the work done on a unit charge by the source's nonelectrostatic fieldE′{\displaystyle {\boldsymbol {E}}'} when the charge moves fromN toP.

When the source is connected to a load, its emf is justEsource=∫NPE′⋅dℓ ,{\displaystyle {\mathcal {E}}_{\mathrm {source} }=\int _{N}^{P}{\boldsymbol {E}}'\cdot \mathrm {d} {\boldsymbol {\ell }}\ ,}and no longer has a simple relation to the electric fieldE{\displaystyle {\boldsymbol {E}}} inside it.

In the case of a closed path in the presence of a varyingmagnetic field, the integral of theelectric field around the (stationary) closed loopC{\displaystyle C} may be nonzero.Then, the "induced emf" (often called the "induced voltage") in the loop is:[21]

EC=∮CE⋅dℓ=−dΦCdt=−ddt∮CA⋅dℓ ,{\displaystyle {\mathcal {E}}_{C}=\oint _{C}{\boldsymbol {E}}\cdot \mathrm {d} {\boldsymbol {\ell }}=-{\frac {d\Phi _{C}}{dt}}=-{\frac {d}{dt}}\oint _{C}{\boldsymbol {A}}\cdot \mathrm {d} {\boldsymbol {\ell }}\ ,}

whereE{\displaystyle {\boldsymbol {E}}} is the entire electric field, conservative and non-conservative, and the integral is around an arbitrary, but stationary, closed curveC{\displaystyle C} through which there is a time-varyingmagnetic fluxΦC{\displaystyle \Phi _{C}}, andA{\displaystyle {\boldsymbol {A}}} is thevector potential.The electrostatic field does not contribute to the net emf around a circuit because the electrostatic portion of the electric field isconservative (i.e., the work done against the field around a closed path is zero, seeKirchhoff's voltage law, which is valid, as long as the circuit elements remain at rest and radiation is ignored[22]).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 loopC{\displaystyle C} is a conductor that carries currentI{\displaystyle I} in the direction of integration around the loop, and the magnetic flux is due to that current, we have thatΦB=LI{\displaystyle \Phi _{B}=LI}, whereL{\displaystyle L} 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 aninductor, and to consider that its emf is localized to that region.Then, we can consider a different loopC′{\displaystyle C'} 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 loopC′{\displaystyle C'} is essentially the same as that in loopC{\displaystyle C}:EC=EC′=−dΦC′dt=−LdIdt=∮CE⋅dℓ=∫12Econductor⋅dℓ−∫12Ecenter line⋅dℓ .{\displaystyle {\mathcal {E}}_{C}={\mathcal {E}}_{C'}=-{\frac {d\Phi _{C'}}{dt}}=-L{\frac {dI}{dt}}=\oint _{C}{\boldsymbol {E}}\cdot \mathrm {d} {\boldsymbol {\ell }}=\int _{1}^{2}{\boldsymbol {E}}_{\mathrm {conductor} }\cdot \mathrm {d} {\boldsymbol {\ell }}-\int _{1}^{2}{\boldsymbol {E}}_{\mathrm {center\ line} }\cdot \mathrm {d} {\boldsymbol {\ell }}\ .}

For a good conductor,Econductor{\displaystyle {\boldsymbol {E}}_{\mathrm {conductor} }} is negligible, so we have, to a good approximation,LdIdt=∫12Ecenter line⋅dℓ=V1−V2 ,{\displaystyle L{\frac {dI}{dt}}=\int _{1}^{2}{\boldsymbol {E}}_{\mathrm {center\ line} }\cdot \mathrm {d} {\boldsymbol {\ell }}=V_{1}-V_{2}\ ,}whereV{\displaystyle V} is the electric scalar potential along the centerline between points 1 and 2.

Thus, we can associate an effective "voltage drop"L dI/dt{\displaystyle L\ dI/dt} 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,

∑Esource=∑load elementsvoltage drops,{\displaystyle \sum {\mathcal {E}}_{\mathrm {source} }=\sum _{\mathrm {load\ elements} }\mathrm {voltage\ drops} ,}

where now the induced emf is not considered to be a source emf.[23]

This definition can be extended to arbitrary sources of emf and pathsC{\displaystyle C} moving with velocityv{\displaystyle {\boldsymbol {v}}} through the electric fieldE{\displaystyle {\boldsymbol {E}}} and magnetic fieldB{\displaystyle {\boldsymbol {B}}}:[24]

E=∮C[E+v×B]⋅dℓ+1q∮CEffective chemical forces ⋅ dℓ+1q∮CEffective thermal forces ⋅ dℓ ,{\displaystyle {\begin{aligned}{\mathcal {E}}&=\oint _{C}\left[{\boldsymbol {E}}+{\boldsymbol {v}}\times {\boldsymbol {B}}\right]\cdot \mathrm {d} {\boldsymbol {\ell }}\\&\qquad +{\frac {1}{q}}\oint _{C}\mathrm {Effective\ chemical\ forces\ \cdot } \ \mathrm {d} {\boldsymbol {\ell }}\\&\qquad \qquad +{\frac {1}{q}}\oint _{C}\mathrm {Effective\ thermal\ forces\ \cdot } \ \mathrm {d} {\boldsymbol {\ell }}\ ,\end{aligned}}}

which is a conceptual equation mainly, because the determination of the "effective forces" is difficult.The term∮C[E+v×B]⋅dℓ{\displaystyle \oint _{C}\left[{\boldsymbol {E}}+{\boldsymbol {v}}\times {\boldsymbol {B}}\right]\cdot \mathrm {d} {\boldsymbol {\ell }}}is often called a "motional emf".

In (electrochemical) thermodynamics

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When multiplied by an amount of chargedQ{\displaystyle dQ} the emfE{\displaystyle {\mathcal {E}}} yields a thermodynamic work termEdQ{\displaystyle {\mathcal {E}}\,dQ} that is used in the formalism for the change inGibbs energy when charge is passed in a battery:

dG=−SdT+VdP+EdQ ,{\displaystyle dG=-S\,dT+V\,dP+{\mathcal {E}}\,dQ\ ,}

whereG{\displaystyle G} is the Gibbs free energy,S{\displaystyle S} is theentropy,V{\displaystyle V} is the system volume,P{\displaystyle P} is its pressure andT{\displaystyle T} is itsabsolute temperature.

The combination(E,Q){\displaystyle ({\mathcal {E}},Q)} is an example of aconjugate pair of variables. At constant pressure the above relationship produces aMaxwell relation that links the change in open cell voltage with temperatureT{\displaystyle T} (a measurable quantity) to the change in entropyS{\displaystyle S} when charge is passedisothermally andisobarically. The latter is closely related to the reactionentropy of the electrochemical reaction that lends the battery its power. This Maxwell relation is:[25]

(∂E∂T)Q=−(∂S∂Q)T{\displaystyle \left({\frac {\partial {\mathcal {E}}}{\partial T}}\right)_{Q}=-\left({\frac {\partial S}{\partial Q}}\right)_{T}}

If a mole of ions goes into solution (for example, in a Daniell cell, as discussed below) the charge through the external circuit is:

ΔQ=−n0F0 ,{\displaystyle \Delta Q=-n_{0}F_{0}\ ,}

wheren0{\displaystyle n_{0}} is the number of electrons/ion, andF0{\displaystyle F_{0}} is theFaraday constant 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:[25]

ΔH=−n0F0(E−TdEdT),{\displaystyle \Delta H=-n_{0}F_{0}\left({\mathcal {E}}-T{\frac {d{\mathcal {E}}}{dT}}\right)\,,}

whereΔH{\displaystyle \Delta H} is theenthalpy of reaction. The quantities on the right are all directly measurable. Assuming constant temperature and pressure:

ΔG=−n0F0E{\displaystyle \Delta G=-n_{0}F_{0}{\mathcal {E}}}

which is used in the derivation of theNernst equation.

Distinction with potential difference

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Although anelectrical potential difference (voltage) is sometimes called an emf,[26][27][28][29][30] they are formally distinct concepts:

  • Potential difference is a more general term that includes emf.
  • Emf is the cause of a potential difference.
  • In 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 chemical forces in the battery.
    • For a circuit using an electric generator, the emf is due solely to a time-varying magnetic forces within the generator.
  • Both a 1 volt emf and a 1 volt potential difference correspond to 1 joule per coulomb of charge.

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 calledreversible cells.[31][32]

The electric charge that has been separated creates an electricpotential difference that can (in many cases) be measured with avoltmeter 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.[27]It can, however, be inferred from a measurement of the currentI{\displaystyle I} and potential differenceV{\displaystyle V}, provided that the internal resistanceR{\displaystyle R} already has been measured:E=Vload+IR.{\displaystyle {\mathcal {E}}=V_{\text{load}}+IR\,.}

"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 fromA toB. If a voltmeter always measured the potential difference betweenA andB, then the position of the voltmeter would make no difference. However, it is quite possible for the measurement by a voltmeter between pointsA andB to depend on the position of the voltmeter, if a time-dependent magnetic field is present. For example, consider an infinitely longsolenoid using anAC current 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 pointsA andB. The induced voltage, by Faraday's law isV{\displaystyle V}, so the currentI=V/(100+200).{\displaystyle I=V/(100+200).} Therefore, the voltage across the 100 Ω resistor is100 I{\displaystyle 100\ I} and the voltage across the 200 Ω resistor is200 I{\displaystyle 200\ I}, yet the two resistors are connected on both ends, butVAB{\displaystyle V_{AB}} measured with the voltmeter to the left of the solenoid is not the same asVAB{\displaystyle V_{AB}} measured with the voltmeter to the right of the solenoid.[33][34]

Generation

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Chemical sources

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Main article:Electrochemical cell
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 Bergmannet al.[35] andTransition state.
Galvanic cell using asalt 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 byWalther Nernst[36] to be primarily at the interfaces between theelectrodes and theelectrolyte.[16]

Atoms in molecules or solids are held together bychemical bonding, 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.[37] 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 orredox 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, aDaniell 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):

Zn(s)→Zn(aq)2++2e− {\displaystyle \mathrm {Zn_{(s)}\rightarrow Zn_{(aq)}^{2+}+2e^{-}\ } }

The zinc sulfate is theelectrolyte in that half cell. It is a solution which contains zinc cationsZn2+{\displaystyle \mathrm {Zn} ^{2+}}, and sulfate anionsSO42−{\displaystyle \mathrm {SO} _{4}^{2-}} 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:

Cu(aq)2++2e−→Cu(s) {\displaystyle \mathrm {Cu_{(aq)}^{2+}+2e^{-}\rightarrow Cu_{(s)}\ } }

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.)[38] 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 thesalt 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.[39] 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 wickcations 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 emfE{\displaystyle {\mathcal {E}}} = 1.0934 V, with a temperature coefficient ofdE/dT{\displaystyle d{\mathcal {E}}/dT} = −4.53×10−4 V/K.[25]

Voltaic cells

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Volta developed the voltaic cell about 1792, and presented his work March 20, 1800.[40] Volta correctly identified the role of dissimilar electrodes in producing the voltage, but incorrectly dismissed any role for the electrolyte.[41] 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."[42] 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

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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.

EMFCell chemistryCommon name
AnodeSolvent, electrolyteCathode
1.2 VCadmiumWater, potassium hydroxideNiO(OH)nickel-cadmium
1.2 VMischmetal (hydrogen absorbing)Water, potassium hydroxideNickelnickel–metal hydride
1.5 VZincWater, ammonium or zinc chlorideCarbon, manganese dioxideZinc carbon
2.1 VLeadWater, sulfuric acidLead dioxideLead–acid
3.6 V to 3.7 VGraphiteOrganic solvent, Li saltsLiCoO2Lithium-ion
1.35 VZincWater, sodium or potassium hydroxideHgOMercury cell

Other chemical sources

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Other chemical sources includefuel cells.

Electromagnetic induction

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Main article: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 asmutual 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 toFaraday's law of induction.

An emf is induced in a coil or conductor whenever there is change in theflux linkages. 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 isstatically induced. The electromotive force generated by motion is often referred to asmotional emf. When the change in flux linkage arises from a change in the magnetic field around the stationary conductor, the emf isdynamically induced. The electromotive force generated by a time-varying magnetic field is often referred to astransformer emf.

Contact potentials

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See also:Volta potential andElectrochemical 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 thecontact potential.[43] Dissimilar metals in contact produce what is known also as a contact electromotive force orGalvani potential. The magnitude of this potential difference is often expressed as a difference inFermi levels in the two solids when they are at charge neutrality, where the Fermi level (a name for thechemical potential of an electron system[44][45]) describes the energy necessary to remove an electron from the body to some common point (such as ground).[46] 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, theFermi 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.[47]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 inKirchhoff'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 ofall the contact potentials is zero, and so they may be ignored in Kirchhoff's law.[48][49]

Solar cell

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Main article:Theory of solar cells
Theequivalent circuit of a solar cell, ignoring parasitic resistances.

Operation of asolar cell can be understood fromits equivalent circuit.Photons with energy greater than thebandgap of thesemiconductor create mobileelectron–hole pairs. Charge separation occurs because of a pre-existing electric field associated with thep-n junction. This electric field is created from abuilt-in potential, which arises from thecontact potential between the two different materials in the junction. The charge separation between positiveholes and negativeelectrons across thep–n diode yields aforward voltage, thephoto voltage, between the illuminated diode terminals,[50] which drives current through any attached load.Photo voltage is sometimes referred to as thephoto emf, distinguishing between the effect and the cause.

Solar cell current–voltage relationship

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Two internal current lossesISH+ID{\displaystyle I_{SH}+I_{D}} limit the total currentI{\displaystyle I} available to the external circuit. The light-induced charge separation eventually creates a forward currentISH{\displaystyle I_{SH}} through the cell's internal resistanceRSH{\displaystyle R_{SH}} in the direction opposite the light-induced currentIL{\displaystyle I_{L}}. In addition, the induced voltage tends toforward bias the junction, which at high enough voltages will cause a recombination currentID{\displaystyle I_{D}} 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 smallestISH+ID{\displaystyle I_{SH}+I_{D}} losses and consequently the maximum output current, which for a high-quality solar cell is approximately equal to the light-induced currentIL{\displaystyle I_{L}}.[51] 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:

I=IL−I0(eVm VT−1) .{\displaystyle I=I_{L}-I_{0}\left(e^{\frac {V}{m\ V_{\mathrm {T} }}}-1\right)\ .}

I0{\displaystyle I_{0}} is thereverse saturation current. Two parameters that depend on the solar cell construction and to some degree upon the voltage itself are theideality factorm and thethermal voltageVT=kTq{\displaystyle V_{\mathrm {T} }={\tfrac {kT}{q}}}, which is about 26 millivolts atroom temperature.[51]

Solar cell photo emf

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Solar cell output voltage for two light-induced currentsIL expressed as a ratio to the reverse saturation currentI0[52] and using a fixed ideality factorm of 2.[53] Their emf is the voltage at their y-axis intercept.

Solving the illuminated diode's above simplifiedcurrent–voltage relationship for output voltage yields:

V=m VTln⁡(IL−II0+1) ,{\displaystyle V=m\ V_{\mathrm {T} }\ln \left({\frac {I_{\text{L}}-I}{I_{0}}}+1\right)\ ,}

which is plotted againstI/I0{\displaystyle I/I_{0}} in the figure.

The solar cell'sphoto emfEphoto{\displaystyle {\mathcal {E}}_{\mathrm {photo} }} has the same value as the open-circuit voltageVoc{\displaystyle V_{oc}}, which is determined by zeroing the output currentI{\displaystyle I}:

Ephoto=Voc=m VTln⁡(ILI0+1) .{\displaystyle {\mathcal {E}}_{\mathrm {photo} }=V_{\text{oc}}=m\ V_{\mathrm {T} }\ln \left({\frac {I_{\text{L}}}{I_{0}}}+1\right)\ .}

It has alogarithmic dependence on the light-induced currentIL{\displaystyle I_{L}} 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.[54] While for high-quality silicon panels it can exceed 0.7 volts in direct sunlight.[55]

When driving a resistive load, the output voltage can be determined usingOhm's law and will lie between the short-circuit value of zero volts and the open-circuit voltageVoc{\displaystyle V_{oc}}.[56] When that resistance is small enough such thatI≈IL{\displaystyle I\approx I_{L}} (the near-vertical part of the two illustrated curves), the solar cell acts more like acurrent generator rather than a voltage generator,[57] 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

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See also

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References

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  1. ^"EMF".American Heritage Dictionary of the English Language, 3rd ed. Houghton Mifflin. 1992.
  2. ^"EMF".Oxford English Dictionary.
  3. ^abTipler, Paul A. (January 1976).Physics. New York, NY: Worth Publishers, Inc. p. 803.ISBN 978-0-87901-041-6.
  4. ^Stewart, Joseph V. (2001).Intermediate electromagnetic theory. Singapore River Edge, NJ: World Scientific. p. 389.ISBN 978-981-02-4470-5.OCLC 47127179.
  5. ^Matthews, Michael R. (2014-07-03).International Handbook of Research in History, Philosophy and Science Teaching. Springer. p. 142.ISBN 978-94-007-7654-8.[Volta] stated that a new type of "force" was acting upon the charges, separating them and keeping them separated, and he called this action the electromotive force, the name that is still applied.
  6. ^"IEC 60050 - International Electrotechnical Vocabulary - Details for IEV number 131-12-22: "source voltage"".www.electropedia.org. Retrieved2022-12-19.
  7. ^"IEC 80000-6:2022".International Organization for Standardization. Retrieved2022-12-19.
  8. ^Langmuir, Irving (1916)."The Relation Between Contact Potentials and Electrochemical Action".Transactions of the American Electrochemical Society.29. The Society: 175.
  9. ^Cook, David M. (2003).The Theory of the Electromagnetic Field. Courier Dover. p. 157.ISBN 978-0-486-42567-2.
  10. ^Lerner, Lawrence M. (1997).Physics for scientists and engineers. Jones & Bartlett Publishers. pp. 724–727.ISBN 978-0-7637-0460-5.
  11. ^Tipler, Paul A.; Mosca, Gene (2007).Physics for Scientists and Engineers (6 ed.). Macmillan. p. 850.ISBN 978-1-4292-0124-7.
  12. ^Halpern, Alvin M.; Erlbach, Erich (1998).Schaum's outline of theory and problems of beginning physics II. McGraw-Hill Professional. p. 138.ISBN 978-0-07-025707-8.
  13. ^Lehrman, Robert L. (1998).Physics the easy way. Barron's Educational Series. p. 274.ISBN 978-0-7641-0236-3.emf separated charge reaction potential.
  14. ^Singh, Kongbam Chandramani (2009)."§3.16 EMF of a source".Basic Physics. Prentice Hall India. p. 152.ISBN 978-81-203-3708-4.
  15. ^Volta, Alessandro (1801)."De l'électricité dite galvanique".Annales de Chimie. Chez Fuchs, Paris.
  16. ^abCajori, Florian (1899).A History of Physics in Its Elementary Branches: Including the Evolution of Physical Laboratories. The Macmillan Company. pp. 218–219.seat of electromotive force.
  17. ^Valkenburgh, Van (1995).Basic Electricity. Cengage Learning. pp. 1–46.ISBN 978-0-7906-1041-2.
  18. ^Abraham, M.; Becker, R. (1932).The Classical Theory of Electricity and Magnetism. Blackie & Son. pp. 116–122.
  19. ^Griffiths, David J (1999).Introduction to Electrodynamics (3rd ed.). Pearson/Addison-Wesley. p. 293.ISBN 978-0-13-805326-0.
  20. ^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 (seecontact potentials andsolar cells), 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.
  21. ^Olenick, Richard P.; Apostol, Tom M.; Goodstein, David L. (1986).Beyond the mechanical universe: from electricity to modern physics. Cambridge University Press. p. 245.ISBN 978-0-521-30430-6.
  22. ^McDonald, Kirk T. (2012)."Voltage Drop, Potential Difference and EMF"(PDF).Physics Examples. Princeton University.
  23. ^Feynman, R.P.; Leighton, R.B.; Sands, M. (1964).The Feynman Lectures on Physics, Vol. II, chap. 22. Addison Wesley.
  24. ^Cook, David M. (2003).The Theory of the Electromagnetic Field. Courier Dover. p. 158.ISBN 978-0-486-42567-2.
  25. ^abcFinn, Colin B P (1992).Thermal Physics. CRC Press. p. 163.ISBN 978-0-7487-4379-7.
  26. ^Fogiel, M. (2002).Basic Electricity. Research & Education Association. p. 76.ISBN 978-0-87891-420-3.
  27. ^abHalliday, David; Resnick, Robert; Walker, Jearl (2008).Fundamentals of Physics (6th ed.). Wiley. p. 638.ISBN 978-0-471-75801-3.
  28. ^Freeman, Roger L (2005).Fundamentals of Telecommunications (2nd ed.). Wiley. p. 576.ISBN 978-0-471-71045-5.
  29. ^Croft, Terrell (1917).Practical Electricity. McGraw-Hill. p. 533.
  30. ^Loeb, Leonard B. (2007).Fundamentals of Electricity and Magnetism (Reprint of Wiley 1947 3rd ed.). Read Books. p. 86.ISBN 978-1-4067-0733-5.
  31. ^Warn, J. R. W.; Peters, A. P. H. (1996).Concise Chemical Thermodynamics (2 ed.). CRC Press. p. 123.ISBN 978-0-7487-4445-9.
  32. ^Glasstone, Samuel (2007).Thermodynamics for Chemists (Reprint of D. Van Nostrand Co (1964) ed.). Read Books. p. 301.ISBN 978-1-4067-7322-4.
  33. ^Shadowitz, Albert (1975).The Electromagnetic Field (1st ed.). McGraw-Hill Book Company. pp. 396–398.ISBN 0-07-056368-3.
  34. ^McDonald, Kirk T. (2010)."Lewin's Circuit Paradox"(PDF).Physics Examples. Princeton University.
  35. ^Risch, Nikolaus (2002)."Molecules - bonds and reactions". In L Bergmann; et al. (eds.).Constituents of Matter: Atoms, Molecules, Nuclei, and Particles. CRC Press.ISBN 978-0-8493-1202-1.
  36. ^Nernst, Walter (1889). "Die elektromotorische Wirksamkeit der Ionen".Z. Phys. Chem.4: 129.
  37. ^The brave reader can find an extensive discussion for organic electrochemistry inAmatore, Christian (2000)."Basic concepts". In Henning Lund; Ole Hammerich (eds.).Organic electrochemistry (4 ed.). CRC Press.ISBN 978-0-8247-0430-8.
  38. ^Conway, BE (1999)."Energy factors in relation to electrode potential".Electrochemical supercapacitors. Springer. p. 37.ISBN 978-0-306-45736-4.
  39. ^Tilley, R. J. D. (2004).Understanding Solids. Wiley. p. 267.ISBN 978-0-470-85275-0.
  40. ^Mottelay, Paul Fleury (2008).Bibliographical History of Electricity and Magnetism (Reprint of 1892 ed.). Read Books. p. 247.ISBN 978-1-4437-2844-7.
  41. ^Kragh, Helge (2000)."Confusion and Controversy: Nineteenth-century theories of the voltaic pile"(PDF).Nuova Voltiana:Studies on Volta and His Times. Università degli studi di Pavia. Archived fromthe original(PDF) on 2009-03-20.
  42. ^Cumming, Linnaus (2008).An Introduction to the Theory of Electricity (Reprint of 1885 ed.). BiblioBazaar. p. 118.ISBN 978-0-559-20742-6.
  43. ^Trigg, George L. (1995).Landmark experiments in twentieth century physics (Reprint of Crane, Russak & Co 1975 ed.). Courier Dover. p. 138ff.ISBN 978-0-486-28526-9.
  44. ^Rockett, Angus (2007)."Diffusion and drift of carriers".Materials science of semiconductors. New York, NY: Springer Science. p. 74ff.ISBN 978-0-387-25653-5.
  45. ^Kittel, Charles (2004)."Chemical potential in external fields".Elementary Statistical Physics (Reprint of Wiley 1958 ed.). Courier Dover. p. 67.ISBN 978-0-486-43514-5.
  46. ^Hanson, George W. (2007).Fundamentals of Nanoelectronics. Prentice Hall. p. 100.ISBN 978-0-13-195708-4.
  47. ^Sato, Norio (1998)."Semiconductor photoelectrodes".Electrochemistry at metal and semiconductor electrodes (2nd ed.). Elsevier. p. 110ff.ISBN 978-0-444-82806-4.
  48. ^Quimby, Richard S. (2006).Photonics and lasers. Wiley. p. 176.ISBN 978-0-471-71974-8.
  49. ^Neamen, Donald A. (2002).Semiconductor physics and devices (3rd ed.). McGraw-Hill Professional. p. 240.ISBN 978-0-07-232107-4.
  50. ^Dhir, S. M. (2000) [1999]."§3.1 Solar cells".Electronic Components and Materials: Principles, Manufacture & Maintenance (2007 fifth reprint ed.). India:Tata McGraw-Hill Publishing Company Limited. p. 283.ISBN 0-07-463082-2.
  51. ^abAraújo, Gerardo L. (1994)."§2.5.1 Short-circuit current and open-circuit voltage". In Eduardo Lorenzo (ed.).Solar Electricity: Engineering of photovoltaic systems. Progenza for Universidad Politechnica Madrid. p. 74.ISBN 978-84-86505-55-4.
  52. ^Nelson, Jenny (2003).The physics of solar cells. Imperial College Press. p. 8.ISBN 978-1-86094-349-2.
  53. ^In practice, at low voltagesm → 2, whereas at high voltagesm → 1. See Araújo,op. cit.ISBN 84-86505-55-0.page 72
  54. ^Northrop, Robert B. (2005)."§6.3.2 Photovoltaic Cells".Introduction to Instrumentation and Measurements. CRC Press. p. 176.ISBN 978-0-8493-7898-0.
  55. ^"Open-Circuit Voltage".
  56. ^Nelson, Jenny (2003).The physics of solar cells. Imperial College Press. p. 6.ISBN 978-1-86094-349-2.
  57. ^Nelson, Jenny (2003).The physics of solar cells. Imperial College Press. p. 7.ISBN 978-1-86094-349-2.
  58. ^John S. Rigden, ed. (1996).Macmillan encyclopedia of physics. New York: Macmillan.

Further reading

[edit]
  • 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.LCCN 07-3935
  • 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.LCCN 20-20413
  • Hazel Rossotti, "Chemical applications of potentiometry". London, Princeton, N.J., Van Nostrand, 1969.ISBN 0-442-07048-9LCCN 69-11985
  • Nabendu S. Choudhury, 1973."Electromotive force measurements on cells involving beta-alumina solid electrolyte". NASA technical note, D-7322.
  • John O'M. Bockris; Amulya K. N. Reddy (1973)."Electrodics".Modern Electrochemistry: An Introduction to an Interdisciplinary Area (2 ed.). Springer.ISBN 978-0-306-25002-6.
  • Roberts, Dana (1983). "How batteries work: A gravitational analog".Am. J. Phys.51 (9): 829.Bibcode:1983AmJPh..51..829R.doi:10.1119/1.13128.
  • 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.
  • Norio Sato (1998)."Semiconductor photoelectrodes".Electrochemistry at metal and semiconductor electrodes (2nd ed.). Elsevier. p. 326ff.ISBN 978-0-444-82806-4.
  • Hai, Pham Nam; Ohya, Shinobu; Tanaka, Masaaki; Barnes, Stewart E.; Maekawa, Sadamichi (2009-03-08). "Electromotive force and huge magnetoresistance in magnetic tunnel junctions".Nature.458 (7237):489–92.Bibcode:2009Natur.458..489H.doi:10.1038/nature07879.PMID 19270681.S2CID 4320209.
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