Editing Ohm's law (section)

==History==
[[File:Ohm3.gif|thumb|200px|[[Georg Ohm]]]]
In January 1781, before [[Georg Ohm]]'s work, [[Henry Cavendish]] experimented with [[Leyden jar]]s and glass tubes of varying diameter and length filled with salt solution. He measured the current by noting how strong a shock he felt as he completed the circuit with his body. Cavendish wrote that the "velocity" (current) varied directly as the "degree of electrification" (voltage). He did not communicate his results to other scientists at the time,<ref name=eb>{{cite EB1911|wstitle=Electricity|volume=9|page=182|first=John Ambrose |last=Fleming}}</ref> and his results were unknown until [[James Clerk Maxwell]] published them in 1879.<ref>{{cite book|isbn=9780808749080|pages=86–107|title=Volts to Hertz-- the Rise of Electricity: From the Compass to the Radio Through the Works of Sixteen Great Men of Science Whose Names are Used in Measuring Electricity and Magnetism |last1=Bordeau |first1=Sanford P. |year=1982 |publisher=Burgess Publishing Company }}</ref>

[[Francis Ronalds]] delineated "intensity" (voltage) and "quantity" (current) for the [[Voltaic pile#Dry piles|dry pile]]—a high voltage source—in 1814 using a [[Electrometer#Gold-leaf electroscope|gold-leaf electrometer]]. He found for a dry pile that the relationship between the two parameters was not proportional under certain meteorological conditions.<ref>{{Cite book|title=Sir Francis Ronalds: Father of the Electric Telegraph|last=Ronalds|first=B. F.|publisher=Imperial College Press|year=2016|isbn=978-1-78326-917-4|location=London}}</ref><ref>{{Cite journal|last=Ronalds|first=B. F.|date=July 2016|title=Francis Ronalds (1788–1873): The First Electrical Engineer?|journal=Proceedings of the IEEE|doi=10.1109/JPROC.2016.2571358|volume=104|issue=7|pages=1489–1498|s2cid=20662894}}</ref>

Ohm did his work on resistance in the years 1825 and 1826, and published his results in 1827 as the book ''Die galvanische Kette, mathematisch bearbeitet'' ("The galvanic circuit investigated mathematically").<ref>{{cite book
 |first    = G. S.
 |last     = Ohm
 |title     = Die galvanische Kette, mathematisch bearbeitet
 |year      = 1827
 |location = Berlin
 |publisher= T. H. Riemann
 |url       = http://www.ohm-hochschule.de/bib/textarchiv/Ohm.Die_galvanische_Kette.pdf
|archive-url = https://web.archive.org/web/20090326094110/http://www.ohm-hochschule.de/bib/textarchiv/Ohm.Die_galvanische_Kette.pdf
|url-status  = dead
|archive-date = 2009-03-26
}}</ref> He drew considerable inspiration from [[Joseph Fourier]]'s work on heat conduction in the theoretical explanation of his work. For experiments, he initially used [[voltaic pile]]s, but later used a [[thermocouple]] as this provided a more stable voltage source in terms of internal resistance and constant voltage. He used a galvanometer to measure current, and knew that the voltage between the thermocouple terminals was proportional to the junction temperature. He then added test wires of varying length, diameter, and material to complete the circuit. He found that his data could be modeled through the equation
<math display="block">x = \frac{a}{b + \ell},</math>
where ''x'' was the reading from the [[galvanometer]], ''ℓ'' was the length of the test conductor, ''a'' depended on the thermocouple junction temperature, and ''b'' was a constant of the entire setup. From this, Ohm determined his law of proportionality and published his results.
[[File:Internal resistance model.svg|thumb|Internal resistance model]]
In modern notation we would write,
<math display="block"> I = \frac {\mathcal E}{r+R},</math>
where <math>\mathcal E</math> is the open-circuit [[electromotive force|emf]] of the thermocouple, <math>r</math> is the [[internal resistance]] of the thermocouple and <math>R</math> is the resistance of the test wire. In terms of the length of the wire this becomes,
<math display="block"> I = \frac {\mathcal E}{r+\mathcal R \ell},</math>
where <math>\mathcal R</math> is the resistance of the test wire per unit length. Thus, Ohm's coefficients are,
<math display="block"> a = \frac {\mathcal E}{\mathcal R}, \quad b = \frac {\mathcal r}{\mathcal R} .</math>
[[File:Ohmsches Gesetz in Georg Simon Ohms Laborbuch.jpg|thumb|Ohm's law in Georg Ohm's lab book.]]
Ohm's law was probably the most important of the early quantitative descriptions of the physics of electricity. We consider it almost obvious today. When Ohm first published his work, this was not the case; critics reacted to his treatment of the subject with hostility. They called his work a "web of naked fancies"<ref>{{cite journal|doi=10.1088/0031-9120/15/1/314|title=A web of naked fancies? |year=1980 |last1=Davies |first1=Brian |journal=Physics Education |volume=15 |issue=1 |pages=57–61 |bibcode=1980PhyEd..15...57D |s2cid=250832899 }}
</ref> and the Minister of Education proclaimed that "a professor who preached such heresies was unworthy to teach science."<ref>{{cite book|last=Hart|first=Ivor Blashka|title=Makers of Science|location=London|publisher=Oxford University Press|year=1923|page=243|ol=6662681M |url=https://openlibrary.org/books/OL6662681M/Makers_of_science}}.</ref> The prevailing scientific philosophy in Germany at the time asserted that experiments need not be performed to develop an understanding of nature because nature is so well ordered, and that scientific truths may be deduced through reasoning alone.<ref>{{cite book | isbn=9780521296465|pages=78–79|title=Philosophy in Germany 1831-1933 |last1=Schnädelbach |first1=Herbert |date=14 June 1984 |publisher=Cambridge University Press }}</ref> Also, Ohm's brother Martin, a mathematician, was battling the German educational system. These factors hindered the acceptance of Ohm's work, and his work did not become widely accepted until the 1840s. However, Ohm received recognition for his contributions to science well before he died.

In the 1850s, Ohm's law was widely known and considered proved. Alternatives such as "[[Barlow's law]]", were discredited, in terms of real applications to telegraph system design, as discussed by [[Samuel F. B. Morse]] in 1855.<ref>{{cite book | title = Shaffner's Telegraph Companion: Devoted to the Science and Art of the Morse Telegraph | author = Taliaferro Preston | author-link = Taliaferro Preston Shaffner | publisher = Pudney & Russell | volume = 2 | year = 1855 | url = https://books.google.com/books?id=TDEOAAAAYAAJ&q=ohm%27s-law+date:0-1860&pg=RA1-PA43 }}</ref>

The [[electron]] was discovered in 1897 by [[J. J. Thomson]], and it was quickly realized that it was the particle ([[charge carrier]]) that carried electric currents in electric circuits. In 1900, the first ([[classical physics|classical]]) model of electrical conduction, the [[Drude model]], was proposed by [[Paul Drude]], which finally gave a scientific explanation for Ohm's law. In this model, a solid conductor consists of a stationary lattice of [[atom]]s ([[ion]]s), with [[conduction electron]]s moving randomly in it. A voltage across a conductor causes an [[electric field]], which accelerates the electrons in the direction of the electric field, causing a drift of electrons which is the electric current. However the electrons collide with atoms which causes them to scatter and randomizes their motion, thus converting kinetic energy to [[heat]] ([[thermal energy]]). Using statistical distributions, it can be shown that the average drift velocity of the electrons, and thus the current, is proportional to the electric field, and thus the voltage, over a wide range of voltages.

The development of [[quantum mechanics]] in the 1920s modified this picture somewhat, but in modern theories the average drift velocity of electrons can still be shown to be proportional to the electric field, thus deriving Ohm's law. In 1927 [[Arnold Sommerfeld]] applied the quantum [[Fermi-Dirac distribution]] of electron energies to the Drude model, resulting in the [[free electron model]]. A year later, [[Felix Bloch]] showed that electrons move in waves ([[Bloch electron]]s) through a solid crystal lattice, so scattering off the lattice atoms as postulated in the Drude model is not a major process; the electrons scatter off impurity atoms and defects in the material. The final successor, the modern quantum [[band theory]] of solids, showed that the electrons in a solid cannot take on any energy as assumed in the Drude model but are restricted to energy bands, with gaps between them of energies that electrons are forbidden to have. The size of the band gap is a characteristic of a particular substance which has a great deal to do with its electrical resistivity, explaining why some substances are [[electrical conductor]]s, some [[semiconductor]]s, and some [[insulator (electricity)|insulators]].

While the old term for electrical conductance, the [[Siemens (unit)|mho]] (the inverse of the resistance unit ohm), is still used, a new name, the [[Siemens (unit)|siemens]], was adopted in 1971, honoring [[Ernst Werner von Siemens]]. The siemens is preferred in formal papers.

In the 1920s, it was discovered that the current through a practical resistor actually has statistical fluctuations, which depend on temperature, even when voltage and resistance are exactly constant; this fluctuation, now known as [[Johnson–Nyquist noise]], is due to the discrete nature of charge. This thermal effect implies that measurements of current and voltage that are taken over sufficiently short periods of time will yield ratios of V/I that fluctuate from the value of R implied by the time average or [[ensemble average]] of the measured current; Ohm's law remains correct for the average current, in the case of ordinary resistive materials.

Ohm's work long preceded [[Maxwell's equations]] and any understanding of frequency-dependent effects in AC circuits. Modern developments in electromagnetic theory and circuit theory do not contradict Ohm's law when they are evaluated within the appropriate limits.