Ohm’s Law: History and Biography of George Ohm

Everyone who studies basic electricity or physics learns Ohm’s law. But did you know that when Georg Ohm published his work in 1827, it was widely hated so much that he basically lost his job?

Georg Simon Ohm was born in 1787 in Bavaria the oldest of three children who survived to adulthood (out of seven) to a self-educated locksmith and the daughter of a tailor. His father wished for Ohm and his younger brother to be locksmiths and join the family business.

However, his father loved mathematics and thought his sons would have advantages in their field if they learned more mathematics in school. Thus, unusually for sons of a tradesman at the time, both Georg and his younger brother Martin Ohm went to high school (or Gymnasium). In 1804, when Georg was 16 years old, a local mathematics professor was so impressed with what he heard about them that he wrote Ohm’s father that the Ohm brothers were so talented they would soon “emulate the brothers Bernoulli”[1] (Jacob and Johann Bernoulli were Swiss mathematical scientists who were famous for their influence on Bernoulli numbers, infinitesimal calculus and more).

Georg Ohm’s father was so impressed with this letter that he agreed to let his sons stay in academia and end the generational family business of locksmithing (Georg Ohm’s younger brother eventually became a prominent mathematician).  

In 1804, Georg Ohm then went off to college at the University of Erlangen but left after 18 months as he ran low on funds so he went to Switzerland to become a math tutor. It took Ohm a further five years to finish his degree and another six years after that, 1817, for him to get a permanent position as a math professor and physics teacher at a respected high school called the Great Gymnasium at Cologne which had an excellent science laboratory.

In July of 1820, a Danish scientist and philosopher named Hans Christian Oersted discovered that current in a wire could move a magnet on a compass, the first instance of a relationship between electricity and magnetism. One of the important effects of Oersted’s discovery was that it allowed people to use the force on a compass to directly measure both the direction and the intensity of current.

In 1825 Ohm decided to systematically and mathematically study how the metals connecting the circuits affected the magnetic effect of the current. Interestingly, Ohm also said that he chose this topic as he felt that it had less competition from other researchers, as he felt that it was not a particularly popular subject in Germany.[2] Ohm started with an experiment to test the effect of the length of the wire between terminals of a simple battery on the current. To measure the current, Ohm had a magnetized needle suspended over a wire and then used a tension measuring machine (first invented by Charles Coulomb to measure the electric force) to measure the force between the wire and the magnet. As Ohm knew that his battery had a current that would quickly dissipate over time: he created a “standard conductor” which was a short and thick piece of metal that he alternated with the pieces he was experimenting with.

He then took the average value of the “standard force” from the “standard conductor” as the average value of the force from current from this battery and then measured how much that changed when a test sample was used. In this convoluted way, Ohm found a complicated equation that he admitted didn’t work for long wires, but it was a start, and clearly demonstrated that the length of the wire decreased the current (eventually, Ohm’s first, incorrect equation was found to work as an approximation with Ohm’s laws that he made later as long as the external resistance is much smaller than the internal resistance).[3] Ohm’s next experiment was conducted in a similar manner with wires of different material, where he experimentally determined the lengths of materials that would have equivalent currents, and thus what is called the conductivity of different materials compared to each other. It was at this point that Ohm’s former professor, the one who said he and his brother could have been like the brothers Bernoulli, suggested that he might have better luck with something called a thermocouple as his voltage source as it is “far more steady”.[4] 

A tiny background on the thermocouple. In 1821, a German physicist named Thomas Seebeck discovered that if two metals were soldered together and kept at a temperature difference and then the ends were connected to a wire, the wire would cause a magnet to turn. Seebeck thought it was a magnetic effect (as it moved a magnet), but within a year Hans Christian Oersted (the same man who discovered the electromagnetic effect in 1820) suggested that the temperature difference with the two metals was creating a current in the wire which was moving the magnet and called this a “thermoelectric” effect, a name we still use to this day. Then, in 1824, André-Marie Ampère and his friend Antoine Becquerel found that the “tension” of a thermocouple was a function of the temperature difference.[5] In 1826, Ohm tried out the thermocouple with a hot end under boiling water and the cold in ice water and found to his delight that the current was steady and strong for over 30 minutes.

Ohm then repeated the experiment with a thermocouple source and then measured the magnetic force from the wire for 8 wires of different lengths. Ohm found that the “strength of magnetic action” decreased with the length, x, according to the equation a/(b + x). Ohm instantly was quite sure that the values for a and b depended in some way on the “resistance of the other parts of the circuit” and what he called the “exciting force”, although he needed more experiments to determine their dependance.[6] Ohm then very cleverly redid the experiment with a reduced temperature difference, and, thus, a reduced “exciting force” or “tension” of his thermocouple. In this case, as he varied the length of the wire, the “strength of magnetic action” also varied by the same equation where the numerator (a) was much reduced but b was the same. In other words, it seemed to Ohm that the current in a wire was related to a simple fraction, where the numerator had to do with the “strength” of the battery or thermocouple, and the denominator had to do with the length of the wires, or what Ohm called the “resistance length”.

Then, Ohm made a profound deduction from these experiments, what he called a “pure law of nature”.[7] He decided that the “tension” was from the battery or thermocouple and then it dissipated over the length of the circuit as the current flowed over the circuit. Like a pump for an artificial waterfall raising water to a certain height, and then the water falls down, and no matter the path, the change in height is the same as it returns to the bottom of the waterfall.

Ohm was quite happy with his conclusions, but felt they were missing mathematical derivations and asked the Prussian Minister of Culture for a year off to create a mathematical formulation of his theories, which was accepted. Ohm then spent a year living with his younger brother on half pay and by 1837, published his book, “The Galvanic Circuit Investigated Mathematically”.[8]

This book was not a success, to put it mildly. Critics called it, “a web of naked fancies” and “the result of an incurable delusion, whose sole effort is to detract from the dignity of nature.”[9] It is worthwhile to delve into why this work brought up such negative reactions. First, Ohm’s mathematics were complex and his ideas were not expressed well. For example, a translator of Ohm’s book written in 1891, added many sections from other scientists’ papers and books that explain it better so that the reader could have a chance of understanding what Ohm meant. In other words, even with, by then, 54 years of hindsight and acknowledgement of the correctness of his conclusions, it still is not an easy read.

Secondly, Ohm’s conclusions fell in opposition to what was considered established fact in the 1820s, namely, that the current produced by a battery is independent of the electric “force” from a battery. This all started with an experiment conducted by André-Marie Ampère in 1820. Ampère wanted to see the relationship between the strength of a battery and the current so he measured the magnetic deflection from a wire connected to a battery and then redid the experiment with several batteries in series and found to his surprise that, to the accuracy of the galvanometer, the magnetic deflection, and therefore the current, was the same! As the multiple batteries produced a bigger shock if one held the ends with wet hands, would charge an early form of a capacitor called a Leyden jar more, would decompose more water into hydrogen and oxygen gas and would cause gold foil to deflect more, it was clear that multiple batteries in series had more “tension”, so it seemed clear that the “tension” of the battery was unrelated to the current in the wire. This experiment was repeated in different ways and was considered one of the few foundations of early electronics.[10] However, what Ampère and other contemporaries didn’t know was that batteries have something called internal resistance, and their batteries had very high internal resistance. By using several batteries, you do get more “tension” or voltage, but you also get more internal resistance. As the total resistance in this experiment is mostly from the internal resistance, increasing the number of batteries increases the total resistance almost as much as it increases the voltage and therefore, the current only increases by a minute amount, too small to be observed by their simple compasses. 

Thirdly, Ohm was talking about “tension” in a new way. At the time tension came from the battery or the thermocouple, one did not talk about the “tension” (or what we now call the potential difference) between two points on a circuit. This is a difficult concept to appreciate, and like I said before, Ohm was brilliant enough to come up with it but not great at describing it in a convincing manner.

Fourthly, and possibly most damaging, Ohm’s theories were opposed by a physicist and philosopher named Georg Fredrich Pohl. Pohl, who was supported by the philosopher Georg Hegel (lots of Georg’s), had just published his own work on the science of circuits and was, not surprisingly, not too favorable to Ohm. In addition, Pohl believed in the “Hegelian school of science” which, at least for Pohl, rejected using experiment to come to conclusions, and Pohl called Ohm’s results “an unmistakable failure” and Pohl convinced the German Minister of Education that, “a physicist who professed such heresies was unworthy to teach science”.[11] Ohm was devastated, especially by feeling that his superiors at the Gymnasium were offended by his work, and he declared that it was impossible for him to retain his position there, and quit, full of, as a biographer put it, “mortification and grief”.[12] Ohm then spent the next several years struggling to find a position with room to experiment and mostly made a living as a tutor to a military school. It took Ohm until 1833, after continually sending entrees to the King of Bavaria, for Ohm to find a new position, as a Professor at a Polytechnic school in Nuremberg, although he still struggled with getting recognition for his work.[13]

Ohm’s work actually ended up being first promoted in England, not Germany. See, in the mid 1830s, an English shoemaker who invented the electromagnet named William Sturgeon got into a fight with the people at the Royal Society of London. Frustrated and basically blackballed, in mid-1836, Sturgeon started his own newspaper where he published a description of a motor he had made, that he claimed was very powerful, “upon the same scale as we see pieces of machinery put into motion by the large models of steam engines,”[14] although it was obviously basically a spinning toy. Soon, many English tinkerers were attempting their own electric motor or device and scouring Sturgeon’s magazine for advice. In 1837, Sturgeon published a translation of an article written by a Russian architect living in Germany named Moritz Jacobi who had invented his own motor 3 years earlier, which was clearly superior to Sturgeons. In addition, Jacobi, whose brother was a mathematician, was a fan of Ohm and wrote a paper on the theory behind his devices where he clearly described Ohm’s law as he felt that, “the theory established by Mr. Ohm… offers so much simplicity, and agrees so well with all the phenomena of the voltaic pile, that I have not hesitated to adopt it.”[15] Within weeks, the articles in Sturgeon’s magazine regularly referenced Ohm’s law or at least Ohm’s idea of resistance, although it was generally ignored by most established scientists especially at the Royal Society.

Luckily, there was an engineer named Charles Wheatstone who bridged the gap between the tinkerers who read William Sturgeon’s magazine and the scientists at the Royal Society. Wheatstone first became interested in sending acoustic signals when, as a teen in 1821, he invented an “enchanted lyre” as a gimmick to attract attention to his uncle’s music shop, where he caused a musical instrument to ring by playing a piano hidden in another room that was connected with wires. Wheatstone continued to study sound propagation and invent musical instruments for many years, which eventually caused him to be interested in electrical devices as well. In 1834, Wheatstone demonstrated a method of measuring the speed of electricity in a wire that turned out (eventually) to be erroneous but caused him to be quite famous in the scientific circles. He was instantly hired as a professor at King’s College of London where he almost never lectured, as he had a terrible fear of public speaking. Despite this by 1836, Wheatstone’s work was so impressive he was made a member of the Royal Society. Then, in February of 1837, a soldier named William Cooke met with Wheatstone for help with an idea of an electric telegraph. They soon formed a partnership, and Wheatstone scoured the papers for electric help, which is when he read Sturgeon’s magazine and Jacobi’s article and became an Ohm superfan.

Then, in 1838, the British Association for the advancement of science decided to allocate 100 pounds for translating and publishing scientific memoirs.[16] With Wheatstone’s help and encouragement (he was a member of the committee) they decided to translate and published Ohm’s entire 1827 book[17] in the second volume of “selected transactions of the foreign academies of science and from foreign journals”[18] in 1841, and, suddenly, many England scientists became Ohm fans. That year, Ohm was awarded England’s Royal Society’s highest honor, the Copley Medal for his “researches into the laws of electric currents.”[19] Soon, the scientific papers were full of scientists writing about Ohm’s theories and Wheatstone continued to promote Ohm’s work including in 1842 when he asked his friend Ida Lovelace to make a better translation of Ohm’s work, and in 1843, when he introduced what is now called the “Wheatstone bridge” where Wheatstone said that, “the instruments and processes I am about to describe being all founded on the principles established by Ohm in his theory of the voltaic circuit, and this beautiful and comprehensive theory”.)[20]

Ohm felt indebted to the people at the Royal Society (he, apparently didn’t know about Wheatstone), and dedicated his 1849 book on molecular physics to them as he said that their support gave him the courage, “which had previously been softened by disheartening treatment, to renewed efforts in the field of science”. Ohm hoped to publish three books on molecular physics or, “if God gives me length of days for it, a fourth,” however, when he found that his ideas had already been published, he gave up on the entire project.[21] Ohm died in July of 1854 at the age of 65 from an “attack of apoplexy”.[22] Eventually, Ohm’s results were called “Ohm’s Law”, and it is simply written as Voltage = Resistance x Current. In 1861, the British Association for the Advancement of Science proposed a standard unit for resistance to be an Ohma in Georg Ohm’s honor (which was shortened to Ohms by 1867). As a capital O looks close to zero, the units of ohms were given the Greek letter Omega as Omega starts with the letter O and we use this nomenclature to this day.[23] As a side note, I was amused to learn that conductivity, or how easy it is for materials to measure how electricity flows, is measured in mho’s in reverse Ohm honor.

So that was a little biography of Georg Ohm and how he discovered Ohm’s law and how it became accepted in scientific circles. There was another person besides Wheatstone who learned of Ohm’s law through Sturgeon’s magazine and, although he was just a young beer brewer, he eventually used those ideas to change the world. His name… James Prescott Joule. And his story is next time on the lightning tamers.

[1] Karl Christian von Langsdorf to Johann Ohm (1804) found in “Obituary notices of deceased Fellows: George Simon Ohm” Proceedings of Royal Society of London (Jan 1, 1856) vol. 7 p. 599

[2] According to Jungnickel, C and McCormmach, R Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein, Volume 1 (1990) p. 52

[3] Ohm, G “Ueber Elektricitätsleiter” Journal für Chemie und Physik (herausgegeben von Dr. Schweigger u Dr. Meinecke) vol 44 (1825) p. 12

[4] Poggendorf letter to the editor quoted in Schagrin, M “Resistance to Ohm’s Law” (Feb 4, 1963) American Journal of Physics vo. 31 No. 7 p. 542

[5] Schagrin, M “Resistance to Ohm’s Law” (Feb 4, 1963) American Journal of Physics vo. 31 No. 7 p. 545

[6] Ohm, G “Bestimmung des Gesetzes…” Journal für Chemie und Physik vol. 46 (1826) p. 25 translated and found in Schagrin, M “Resistance to Ohm’s Law” (Feb 4, 1963) American Journal of Physics vo. 31 No. 7 p. 543

[7] Georg Ohm in 1826 translated and quoted in Appleyard, R Pioneers of Electrical Communication (1968) p. 199

[8] Jungnickel, C and McCormmach, R Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein, Volume 1 (1990) p. 53

[9] Quoted and translated by Tyndall, J “Reports on the Progress of the Physical Sciences” London, Edinburgh and Dublin Phil. Mag. [Forth Series] (May 1852) p. 322

[10] Schagrin, M “Resistance to Ohm’s Law” (Feb 4, 1963) American Journal of Physics vo. 31 No. 7 p. 540

[11] Found in Lloyd William, T Physics, the pioneer science (1959) p. 668

[12] Dr. J. Lamont “Obituary notices of deceased Fellows: George Simon Ohm” Proceedings of Royal Society of London (Jan 1, 1856) vol. 7 p. 600

[13] According to Jungnickel, C and McCormmach, R Intellectual Mastery of Nature: Theoretical Physics from Ohm to Einstein, Volume 1 (1990) p. 57-8

[14] Sturgeon, W “Description of an Electro-magnetic Engine” The Annals of Electricity, vol. 1(October, 1836) p. 78

[15] Jacobi, M “On the application of Electro-magnetism to the moving of Machines” (April 1835) The Annals of Electricity, Magnetism, and Chemistry (Oct 1837) p. 422

[16] “On the translation of Foreign Scientific Memoirs” British Association for the Advancement of Science Report of the Annual Meeting vo. 10 (1841) p. 446

[17] Bowers, B Sir Charles Wheatstone FRS (2001) p. 102

[18] Taylor, R Scientific Memoirs Selected from The Transactions … vol. 2 (1841) p. 401

[19] Copley Medal 1841 “George Simon Ohm” The Royal Society https://royalsociety.org/grants-schemes-awards/awards/copley-medal/

[20] Wheatstone, C “The Bakerian Lecture” (June 15, 1843) Philosophical Transactions of the Royal Society vol. 133 p. 303

[21] Found in Alois, K Christianity and the Leaders of Modern Science (1911) p. 132-3

[22] Dr. J. Lamont “Obituary notices of deceased Fellows: George Simon Ohm” Proceedings of Royal Society of London (Jan 1, 1856) vol. 7 p. 602

[23]  Report of the British Association for the Advancement of Science (1865) Foldout between p. 348 and 349

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