# Electromotive force

The electromotive force (EMF) (Engl. Electromotive Force (EMF) ), also called electromotive force called, is the historical name for the source voltage of an electric power source . It is understood as the ability of a system to generate voltage. The term was mainly used in relation to galvanic cells or for the induction voltage in electrical machines such as electric motors and generators . Despite its name, the term does not describe a force in the physical sense, but an electrical voltage . The term electromotive force does not appear in the list of physical quantities or in overview standards such as; in the EMF is listed as "rejected" and "obsolete" designation for source voltage.

## history

The fundamental connection between chemically performed work in galvanic elements and current energy, EMF and force was made through the work of Hermann von Helmholtz and Josiah Willard Gibbs . Max Le Blanc used the normal solutions to standardize the electromotive force of galvanic elements. Le Blanc also found that platinum-coated platinum electrodes are reversible electrodes and can be used for the precise measurement of normal potentials; he proposed the platinum electrode surrounded by hydrogen gas as the standard electrode. Walter Nernst proposed a theory for determining the EMF at different electrolyte concentrations and temperatures.

## Examples

### Galvanic cell

Galvanic cell

The Daniell element is a historical example of an electrochemical cell . It consists of a zinc rod that is immersed in the aqueous solution of a zinc salt and a copper rod that is immersed in the aqueous solution of a copper salt. Both half-cells are combined to form a galvanic cell with the help of an electric key, which contains the solution of an electrolyte - KCl ( potassium chloride ) or NH 4 NO 3 ( ammonium nitrate ) - or with a diaphragm .

If the two metals are connected by a metallic conductor, an electric current flows through the system. The wire heats up. Zinc dissolves on the zinc electrode, copper ions from the solution are deposited on the copper electrode. To determine the EMF, the wire is divided and a voltmeter is connected between the wire ends.

In the Daniell element, the zinc is oxidized at the anode.

${\ displaystyle \ mathrm {Zn \ longrightarrow Zn ^ {2 +} + 2 \ e ^ {-}}}$

Copper is reduced at the cathode.

${\ displaystyle \ mathrm {Cu ^ {2 +} + 2 \ e ^ {-} \ longrightarrow Cu}}$

The half-cell potentials are calculated for each half-cell using the Nernst equation .

${\ displaystyle E = E_ {0} + {\ frac {RT} {z \ cdot F}} \ cdot \ ln \ left (a (\ mathrm {Me} ^ {z +}) \ right)}$
 ${\ displaystyle E}$ Potential difference or electrical voltage against a reference electrode ; [ ] = V ${\ displaystyle E \,}$ ${\ displaystyle E_ {0}}$ Standard potential (look it up under voltage series ); [ ] = V ${\ displaystyle E_ {0}}$ ${\ displaystyle T}$ Temperature ; [ ] = K ${\ displaystyle T}$ ${\ displaystyle a (\ mathrm {Me} ^ {z +})}$ Activity of the metal ions in the solution ${\ displaystyle F}$ Faraday's constant , = 96485.33 C / mol ${\ displaystyle F}$ ${\ displaystyle R}$ Universal or molar gas constant , = 8.314460 J / mol K ${\ displaystyle R}$ ${\ displaystyle z}$ Number of electrons transferred during equipotential bonding per atom or ion

To calculate the EMF for the overall reaction, the difference between the two half-cell potentials is simulated

${\ displaystyle \ Delta E = E _ {\ mathrm {cathode}} -E _ {\ mathrm {anode}}}$

For the Daniell element, one obtains metal ion concentrations of 1 mol / l

${\ displaystyle \ Delta E = E _ {\ mathrm {cathode}} -E _ {\ mathrm {anode}} = E _ {\ mathrm {copper}} -E _ {\ mathrm {zinc}} = 1 {,} 10 \ \ mathrm {V}}$

because under standard conditions (temperature 25 ° C, concentration 1 mol / l , pressure 1013 mbar) the half-cell potential corresponds to the standard potential .

Each half-cell is to be considered separately. A half-cell made of sheet zinc in zinc solution can also be used to produce hydrogen electrochemically. The zinc sheet is connected with a wire and brought into contact with a platinum electrode. Now you immerse the platinum electrode in hydrochloric acid. Hydrogen gas is formed.

The Clark element (zinc / zinc paste / mercury sulfate / mercury) or the Weston element was used in earlier times for calibration or for the correct setting of exactly 1,000 V.

#### Applications

The molar free enthalpy of a redox reaction can be calculated from the EMF .

${\ displaystyle \ Delta G _ {\ mathrm {m}} = - z \ cdot F \ cdot \ Delta E}$

Once the EMF has been determined under standard conditions, the standard free reaction enthalpy can be calculated.

Furthermore, the pH value can be determined with a reference hydrogen electrode by measuring the EMF of probes developed for this purpose when they are immersed in the liquid to be measured. See, for example, pH electrode . The EMF changes by 59.16 mV for every pH change of 1, i.e. H. per power of ten of the hydrogen ion concentration if the measurement temperature of 25 ° C is maintained (Nernst slope). Other electrode systems avoid the difficult handling of the hydrogen electrode for pH measurement.

### Electric motors and generators

When an electrical conductor moves across a magnetic field , an electrical voltage is induced in it; the faster the movement, the higher it is. Accordingly, the rotor of an electric motor rotating in the stator magnetic field or the magnetic rotor of a generator induce a voltage in its windings. This induced voltage is called back-EMF in motors. It does not matter which voltage is actually applied to the motor or generator - the difference between the two voltages drops at the ohmic resistance of the windings or is caused by leakage currents.

If the speed of a DC motor increases so much that the EMF approaches the applied voltage, the current consumption decreases and the speed does not increase any further. Knowing the back EMF of a DC motor, you can calculate its limit speed for a certain voltage.

The back EMF of a DC motor and other motors can be used to control and regulate their speed. This is used, for example, for small permanent magnet motors to drive cassette tape recorders, but also for electronically commutated motors and modern frequency converters for asynchronous motors.

Separately excited DC motors can be increased in their speed by field weakening - the back EMF now requires a higher speed in order to achieve the value of the operating voltage.

Also, asynchronous motors induce a back EMF - here the orbiting with the short-circuit armature magnetic field induced in the stator windings an alternating voltage, which counteracts the power consumption when the rotor has reached the rated speed.

The EMF of stepper motors limits their dynamics or the torque at high speeds.

The electromotive force in generators is almost equal to the open circuit voltage. The generated voltage or the EMF of generators can be changed by changing the speed or the excitation field.

### Galvanometer drives and loudspeakers

The back EMF also plays a role in galvanometer drives and electrodynamic loudspeakers : they act on the supply voltage source due to the inertia of their coils. Their EMF is usually short-circuited by the low internal resistance of the voltage sources driving them, which dampens them - ringing or overshooting is reduced.

## Field theoretical classification

Electrochemical cell in discharge mode

The current-driving electromotive force (EMF) is of a non-electrical nature (e.g. in electrochemical cells, in photocells, in thermocouples, during diffusion processes, in magnetic field-based electrical generators or motors). It can formally be traced back to an impressed (internal, non-electric) field strength that only exists within the source. is independent of the load on the source, so is the emf ${\ displaystyle V}$${\ displaystyle ^ {e} \! {\ vec {E}}}$${\ displaystyle ^ {e} \! {\ vec {E}}}$

${\ displaystyle V = \ int _ {(1)} ^ {(2)} {} ^ {e} \! {\ vec {E}} \ mathrm {d} {\ vec {s}}}$

how the source voltage is independent of the load. results positive if (1) denotes the negative and (2) the positive pole. ${\ displaystyle U_ {Q}}$${\ displaystyle V}$

In the area of ​​electromotive forces, Ohm's extended law applies . The force that moves a charge is the same there . In the battery cell shown on the right of the discharging, compensate idle ( which is embossed electric field strength) and the excited by the Polladungen electric field strength in accordance with , so that no charge is transported into the cell. The applied voltage is then with ${\ displaystyle {\ vec {J}} = ({} ^ {e} \! {\ vec {E}} + {\ vec {E}}) / \ rho}$${\ displaystyle q}$${\ displaystyle q (^ {e} \! {\ vec {E}} + {\ vec {E}})}$${\ displaystyle {\ vec {J}} = 0}$${\ displaystyle ^ {e} \! {\ vec {E}}}$${\ displaystyle {\ vec {E}}}$${\ displaystyle {\ vec {E}} = - ^ {e} \! {\ vec {E}}}$

${\ displaystyle V = \ int _ {(-)} ^ {(+)} {} ^ {e} \! {\ vec {E}} \ mathrm {d} {\ vec {s}} = \ int _ {(-)} ^ {(+)} - {\ vec {E}} \ mathrm {d} {\ vec {s}} = \ int _ {(+)} ^ {(-)} {\ vec { E}} \ mathrm {d} {\ vec {s}} = U_ {Q}}$

measurable as a source voltage at the connections.

In the summarizing chain of equations for the electrochemical cell sketched on the right

${\ displaystyle I {\ stackrel {\ circ} {R}} = I \ oint {\ frac {\ rho} {A}} \ mathrm {d} s = \ oint \ rho {\ vec {J}} \ mathrm {d} {\ vec {s}} = \ oint ({} ^ {e} \! {\ vec {E}} + {\ vec {E}}) \ mathrm {d} {\ vec {s}} = \ oint {} ^ {e} \! {\ vec {E}} \ mathrm {d} {\ vec {s}} = V}$

means the circulation resistance of the circuit, i.e. the sum of the internal and external resistance, the location-dependent cross-sectional area and the location-dependent specific electrical resistance. The sense of rotation of the integrals is oriented like the path from the minus to the plus pole in the source. ${\ displaystyle {\ stackrel {\ circ} {R}}}$${\ displaystyle A}$${\ displaystyle \ rho}$

If the conductor circle moves in a magnetic field ( e.g. in electrical machines), the field strength of the Lorentz force is to be calculated as the applied electrical field strength . The circuit becomes the source as a whole. If the magnetic field varies over time ( ), the circulation of the electric field strength is no longer zero, as assumed in the chain of equations above. Rather, it is true ${\ displaystyle {\ vec {v}} \ neq 0}$${\ displaystyle {\ vec {v}} \ times {\ vec {B}}}$${\ displaystyle ^ {e} \! {\ vec {E}}}$${\ displaystyle \ partial {\ vec {B}} / \ partial t \ neq 0}$

${\ displaystyle \ oint {\ vec {E}} \ cdot \ mathrm {d} {\ vec {s}} = - \ int {\ frac {\ partial {\ vec {B}}} {\ partial t}} \ mathrm {d} {\ vec {A}}}$

according to the law of induction . The induced voltage

${\ displaystyle U_ {i} = - \ int \ limits _ {{\ mathcal {A}} (t)} {\ frac {\ partial {\ vec {B}}} {\ partial t}} {\ text { d}} {\ vec {A}} + \ oint _ {\ partial {\ mathcal {A}} (t)} {\ vec {v}} \ times {\ vec {B}} \ {\ text {d }} {\ vec {s}}}$

forms part of the electromotive force.

If one takes into account the current driving effect of the sources not through their source voltage, but through their EMF, the Kirchhoff set of meshes takes on the form instead . The clearer form with , which differentiates between “engine” and “chassis”, is less common. ${\ displaystyle \ sum U = 0}$${\ displaystyle \ sum V = \ sum U}$${\ displaystyle V}$

The statement that EMF is an outdated term for source voltage suggests that these are synonyms for the same physical quantity. This is only correct as far as the EMF and source voltage are equal. Their directions are opposite and their definitions, as shown above, are based on different field sizes. In a hydraulic analogy, the EMF corresponds to the pressure generated by a pump and the source voltage corresponds to the (supposed) pressure drop that is measured on the pump from the pressure to the suction side.

The EMF drives an electric current in its direction, the source voltage in the opposite direction.

## Individual evidence

1. DIN 1304-1: 1994 Formula symbols - General formula symbols ; Cape. 3.4
2. EN 80000-6: 2008 Quantities and units - Part 6: Electromagnetism ; Entry 6-11.3
3. IEC 60050, see DKE German Commission for Electrical, Electronic and Information Technologies in DIN and VDE: Internationales Electrotechnical Dictionary Search term Electromotoric force
4. http://www.goetz-automation.de/Schrittmotor/SchrittmotorEMK.htm EMK for stepper motors.
5. Becker / Sauter: Theory of Electricity 1, BG Teubner Stuttgart, 21st edition 1973, section 4.3 Applied forces

## literature

• Paul B. Arthur Linker : Electrotechnical measurement . 3rd, completely revised and expanded edition. Julius Springer, Berlin 1920.
• Max Le Blanc : Textbook of Electrochemistry. 9th and 10th edition. Oskar Leiner, Leipzig 1922