German physicist who discovered the law, named after him, which states that the current flow through a conductor is directly proportional to the potential difference (voltage) and inversely proportional to the resistance.

Georg Simon Ohm came from a Protestant family. His father, Johann Wolfgang Ohm, was a locksmith while his mother, Maria Elizabeth Beck, was the daughter of a tailor. Although his parents had not been formally educated, Ohm's father was a rather remarkable man who had educated himself to a high level and was able to give his sons an excellent education through his own teachings. Had Ohm's brothers and sisters all survived he would have been one of a large family but, as was common in those times, several of the children died in their childhood. Of the seven children born to Johann and Maria Ohm only three survived, Georg Simon, his brother Martin who went on to become a well-known mathematician, and his sister Elizabeth Barbara. Mrs. Ohm died when Georg was ten.

When they were children, Georg Simon and Martin were taught by their father who brought them to a high standard in mathematics, physics, chemistry and philosophy. This was in stark contrast to their school education. Georg Simon entered Erlangen Gymnasium at the age of eleven but there he received little in the way of scientific training. In fact this formal part of his schooling was uninspired stressing learning by rote and interpreting texts. This contrasted strongly with the inspired instruction that both Georg Simon and Martin received from their father who brought them to a level in mathematics which led the professor at the University of Erlangen, Karl Christian von Langsdorf, to compare them to the Bernoulli family. It is worth stressing again the remarkable achievement of Johann Wolfgang Ohm, an entirely self-taught man, to have been able to give his sons such a fine mathematical and scientific education. In fact, Martin later became a mathematician of some distinction.

In 1805 Ohm entered the University of Erlangen but he became rather carried away with student life. Rather than concentrate on his studies he spent much time dancing, ice skating and playing billiards. Ohm's father, angry that his son was wasting the educational opportunity that he himself had never been fortunate enough to experience, demanded that Ohm leave the university after three semesters. Ohm went (or more accurately, was sent) to Switzerland where, in September 1806, he took up a post as a mathematics teacher in a school in Gottstadt bei Nydau.

Karl Christian von Langsdorf left the University of Erlangen in early 1809 to take up a post in the University of Heidelberg and Ohm would have liked to have gone with him to Heidelberg to restart his mathematical studies. Langsdorf, however, advised Ohm to continue with his studies of mathematics on his own, advising Ohm to read the works of Euler, Laplace and Lacroix. Rather reluctantly Ohm took his advice but he left his teaching post in Gottstadt bei Nydau in March 1809 to become a private tutor in Neuchâtel. For two years he carried out his duties as a tutor while he followed Langsdorf's advice and continued his private study of mathematics. Then in April 1811 he returned to the University of Erlangen.

His private studies had stood him in good stead for he received a doctorate from Erlangen on 25 October 1811 and immediately joined the staff as a mathematics lecturer. After three semesters Ohm gave up his university post. He could not see how he could attain a better status at Erlangen as prospects there were poor while he essentially lived in poverty in the lecturing post. The Bavarian government offered him a post as a teacher of mathematics and physics at a poor quality school in Bamberg and he took up the post there in January 1813.
 

This was not the successful career envisaged by Ohm and he decided that he would have to show that he was worth much more than a teacher in a poor school. He worked on writing an elementary book on the teaching of geometry while remaining desperately unhappy in his job. After Ohm had endured the school for three years it was closed down in February 1816. The Bavarian government then sent him to an overcrowded school in Bamberg to help out with the mathematics teaching.

As was the custom of the time, he sent the manuscript to King Wilhelm III of Prussia upon its completion. The King liked Georg's work and on 11 September 1817 he offered Ohm a position at a Jesuit Gymnasium. Due to the school's reputation for science education, Ohm found himself required to teach physics as well as mathematics. Luckily, the physics lab was well-equipped, so Ohm devoted himself to learning some physics. Being the son of a locksmith, Georg had some practical experience with mechanical equipment. He enjoyed making accurate apparatus and once, after making one accurate, but simple, device he remarked that, "I feel clearly that only that which is simple can be great." His claim certainly foreshadowed his later achievements in simplifying the theory of electric circuits.
 

This apparatus was used by Ohm. Current flowing through the metal bar in the center cylinder deflects a magnetized needle suspended above it. The deflection angle is proportional to the current. The source of electric potential is a thermocouple (discovered by Seebeck in 1821). The ends of the thermocouple are heated by steam and cooled by ice-water in the small containers on the tripods. The use of a thermocouple made the measurement possible; other sources of potential available in the 1820's were too unreliable.

As he had done for so much of his life, Ohm continued his private studies reading the texts of the leading French mathematicians Lagrange, Legendre, Laplace, Biot and Poisson. In 1820 Oersted discovered electromagnetism, and shortly afterwards, Becquerel and Barlow began their researches into the conductivity of various metals. Everywhere experimenters were making new discoveries in the young science of electricity. Yet there was also much confusion. Terms like 'tension', 'intensity', 'quantity', and 'exciting force' were used to describe various attributes of electricity, but no one was clear about the exact meanings of the terms and their relationships. At this same time, Ohm was becoming depressed. He had taught for many years and now was overburdened with students. He hadn't landed the university position that all mathematicians yearn for, and he finally realized that he would never marry. In short, he felt his life had reached a dead end. In 1825 he decided to renew his outlook and devote himself to research in electricity.

At first his experiments were conducted for his own educational benefit as were the private studies he made of the works of the leading mathematicians. To begin his researches, Ohm started with a series of three experiments. In the first, he measured the 'intensity' of electricity in a wire connected between the terminals of a voltaic pile. To measure the intensity he measured the deflection in a magnetic needle held over the wire. (He later improved the method by attaching the needle to a torsion balance.) Ohm was looking for a relationship between the measured intensity and the length of the wire. His decision to measure the loss in intensity rather than the intensity itself led him to a logarithmic relation which held only because of the high internal resistance of the voltaic pile. The pile was very cumbersome. There was an initial surge of current and the fast polarization caused the voltage to decrease steadily. He therefore had to devise elaborate methods for normalizing his data. In the third experiment, Ohm took the advice of a colleague and replaced the voltaic pile with a thermopile.

In the second of the series of experiments, Ohm determined the lengths of wires, made from different metals, that gave the same current. Ohm called these various lengths 'equivalent lengths.' Once Ohm put this experimental results together and decided to consider measuring actual intensity rather than loss in intensity, he was able to phrase his famous law in the form I = E/R.

The Jesuit Gymnasium of Cologne failed to continue to keep up the high standards that it had when Ohm began to work there so, by 1825, he decided that he would try again to attain the job he really wanted, namely a post in a university. Realising that the way into such a post would have to be through research publications, he changed his attitude towards the experimental work he was undertaking and began to systematically work towards the publication of his results [1]:

"Overburdened with students, finding little appreciation for his conscientious efforts, and realising that he would never marry, he turned to science both to prove himself to the world and to have something solid on which to base his petition for a position in a more stimulating environment."
 

In fact he had already convinced himself of the truth of what we call today "Ohm's law" namely the relationship that the current through most materials is directly proportional to the potential difference applied across the material. The result was not contained in Ohm's firsts paper published in 1825, however, for this paper examines the decrease in the electromagnetic force produced by a wire as the length of the wire increased. The paper deduced mathematical relationships based purely on the experimental evidence that Ohm had tabulated.

Ohm made only a modest living and as a result, his experimental equipment was primitive. Despite this, he made his own metal wire, producing a range of thicknesses and lengths of remarkably consistent quality. For the nine years he spent at the Jesuit's college, he did considerable experimental research on the nature of electric circuits. He took considerable pains to be brutally accurate with every detail of his work. Ohm was afraid that the purely experimental basis of his work would undermine the importance of his discovery. He tried to state his law theoretically but his rambling mathematical proofs made him an object of ridicule.

In two important papers in 1826, Ohm gave a mathematical description of conduction in circuits modelled on Fourier's study of heat conduction. These papers continue Ohm's deduction of results from experimental evidence and, particularly in the second, he was able to propose laws which went a long way to explaining results of others working on galvanic electricity. The second paper certainly is the first step in a comprehensive theory which Ohm was able to give in his famous book published in the following year.

What is now known as Ohm's law appears in this famous book "Die galvanische Kette, mathematisch bearbeitet" (The Galvanic Circuit Investigated Mathematically) (1827) in which he gave his complete theory of electricity. The book begins with the mathematical background necessary for an understanding of the rest of the work. While his work greatly influenced the theory and applications of current electricity, it was coldly received. We should remark here that such a mathematical background was necessary for even the leading German physicists to understand the work, for the emphasis at this time was on a non-mathematical approach to physics. We should also remark that, despite Ohm's attempts in this introduction, he was not really successful in convincing the older German physicists that the mathematical approach was the right one. To some extent, as Caneva explains in [1], this was Ohm's own fault:

"... in neither the introduction nor the body of the work, which contained the more rigorous development of the theory, did Ohm bring decisively home either the underlying unity of the whole or the connections between fundamental assumptions and major deductions. For example, although his theory was conceived as a strict deductive system based on three fundamental laws, he nowhere indicated precisely which of their several mathematical and verbal expressions he wished to be taken as the canonical form."

It is interesting that Ohm's presents his theory as one of contiguous action, a theory which opposed the concept of action at a distance. Ohm believed that the communication of electricity occurred between "contiguous particles" which is the term Ohm himself uses. The paper [8] is concerned with this idea, and in particular with illustrating the differences in scientific approach between Ohm and that of Fourier and Navier. A detailed study of the conceptual framework used by Ohm in formulating Ohm's law is given in [6].

Ohm's famous law states that the flow of current is directly proportional to voltage and inversely proportional to resistance. Using this law, scientists could for the first time work out the amounts of current, voltage and resistance in electric currents, and the variations of one through changes in the others. By altering circuit components such as resistances, they could then design circuits to perform specific functions. His formulation of the relationship between current, electromotive force, and resistance, is the basic law of current flow.
 

As we described above, Ohm was at the Jesuit Gymnasium of Cologne when he began his important publications in 1825. He was given a year off work in which to concentrate on his research beginning in August 1826 and although he only received the less than generous offer of half pay, he was able to spend the year in Berlin working on his publications. Ohm had believed that his publications would lead to his receiving an offer of a university post before having to return to Cologne but by the time he was due to begin teaching again in September 1827 he was still without such an offer.

 

Unfortunately, Ohm's law was met with resistance. Many of his countrymen were used to experimenting with voltage and current, but they considered these to be entirely separate phenomena. Now Ohm was claiming a connection between the two. Ohm's work was also ignored in administrative channels due, perhaps, to his brother, Martin, who was continually criticizing the ministry of education. The Prussian minister of education announced that "a professor who preached such heresies was unworthy to teach science." Unfortunately, Georg was caught in the ensuing political storm. One science 'critic' reviewed Ohm's book, claiming that its "sole effort is to detract from the dignity of nature." This hinted at the Hegelian philosophy that was just then sweeping German science. Ohm's feeling were hurt, he decided to remain in Berlin and, in March 1828, he formally resigned his position at Cologne. He took some temporary work teaching mathematics in schools in Berlin.

He accepted a position at Nüremberg in 1833 and although this gave him the title of professor, it was still not the university post for which he had strived all his life. For whatever reasons, Ohm's work was accepted abroad before it was in his own country. Joseph Henry in America recognized that Ohm had cleared away nearly all the confusion surrounding electrical circuits. His work was eventually recognised in England by the Royal Society with its award of the Copley Medal in 1841 with the inscription "he had clarified in a remarkable way what had been previously wrapped in mystery and confusion." He became a foreign member of the Royal Society in 1842. Other academies such as those in Berlin and Turin elected him a corresponding member, and in 1845 he became a full member of the Bavarian Academy.
 

This belated recognition was welcome but there remains the question of why someone who today is a household name for his important contribution struggled for so long to gain acknowledgement. This may have no simple explanation but rather be the result of a number of different contributary factors. One factor may have been the inwardness of Ohm's character while another was certainly his mathematical approach to topics which at that time were studied in his country a non-mathematical way. There was undoubtedly also personal disputes with the men in power which did Ohm no good at all. He certainly did not find favour with Johannes Schultz who was an influential figure in the ministry of education in Berlin, and with Georg Friedrich Pohl, a professor of physics in that city.

Electricity was not the only topic on which Ohm undertook research, and not the only topic in which he ended up in controversy. Ohm also experimented with optics, acoustics, and the electrical conductivity of liquids, though he didn't achieve any real progress in these fields. In 1843 he stated the fundamental principle of physiological acoustics, concerned with the way in which one hears combination tones. However the assumptions which he made in his mathematical derivation were not totally justified and this resulted in a bitter dispute with the physicist August Seebeck. He succeeded in discrediting Ohm's hypothesis and Ohm had to acknowledge his error. See [10] for details of the dispute between Ohm and Seebeck. This result was rediscovered by Hermann von Helmholtz in 1860.

For most of his life Ohm held only indifferent, poorly paid teaching jobs. In 1849, just five years before his death, Ohm's lifelong dream was realized when he was given a post in Munich as curator of the Bavarian Academy's physical cabinet and he began to lecture at the University of Munich. Only in 1852, two years before his death, did Ohm achieve his lifelong ambition of being appointed to the chair of physics at the University of Munich.
 

On July 7, 1854, Georg Ohm passed away in Munich, at the age of 65. The picture shows his grave located at the Southern Cemetery (Suedfriedhof) in Munich.

 

The ultimate honor came in 1881, after his death, when the Electrical Congress in Paris voted to adopt the 'ohm' as the international standard of electrical resistance. "Ohm's work stands alone, and, reading it at the present time, one is filled with wonder at his presience, respect for his patience and prophetic soul,and admiration at the immensity and variety of ground covered by his little book, which is indeed his best monument." Ohm's Law has stayed the test of time, being proven true by J. Clerk Maxwell and George Chrystal, and it is now universally known and used in physics.

 

Georg Ohm is commemorated in Erlangen with a technical Gymnasium (UK equivalent - grammar school) and a square just outside the centre of the city, both of which bear his name.

References for Georg Simon Ohm:

1. Biography in Dictionary of Scientific Biography (New York 1970-1990).
2. Biography in Encyclopaedia Britannica. (WWW version)

Books:
3.  E Deuerlein, Georg Simon Ohm, 1789-1854 (Erlangen, 1939).
4. C Jungnickel and R McCormmach, Intellectual Mastery of Nature:
    Theoretical physics from Ohm to Einstein, 2 Volumes (Chicago, 1986).
5. H von Füchtbauer, Georg Simon Ohm. Ein Forscher wächst aus seiner Väter Art
    (Berlin, 1939).

Articles:
6. T Archibald, Tension and potential from Ohm to Kirchhoff, Centaurus 31 (2) (1988),
    141-163.
7. G Baker, Georg Simon Ohm, Short wave magazine 52 (1953), 41.
8. B Pourprix, G S Ohm théoricien de l'action contigue, Arch. Internat. Hist. Sci. 45
    (134) (1995), 30-56.
9. B Pourprix, La mathématisation des phénomènes galvaniques par G S Ohm (1825-1827),
    La mathématisation 1780-1830, Rev. Histoire Sci. 42 (1-2) (1989), 139-154.
10. R S Turner, The Ohm-Seebeck dispute, Hermann von Helmholtz, and the origins of
     physiological acoustics, British J. Hist. Sci. 10 (34) (1) (1977), 1-24.
 

Ohm's law in electricity, experimentally discovered relationship that the amount of steady current through a large number of materials is directly proportional to the potential difference, or voltage, across the materials. Thus, if the voltage V (in units of volts) between two ends of a wire made from one of these materials is tripled, the current I (amperes) also triples; and the quotient V/I remains constant. The quotient V/I for a given piece of material is called its resistance, R, measured in units named ohms. The resistance of materials for which Ohm's law is valid does not change over enormous ranges of voltage and current. Ohm's law may be expressed mathematically as V/I = R. That the resistance, or the ratio of voltage to current, for all or part of an electric circuit at a fixed temperature is generally constant had been established by 1827 as a result of the investigations of the German physicist Georg Simon Ohm.

Alternate statements of Ohm's law are that the current I in a conductor equals the potential difference V across the conductor divided by the resistance of the conductor, or simply I = V/R, and that the potential difference across a conductor equals the product of the current in the conductor and its resistance, V = IR. In a circuit in which the potential difference, or voltage, is constant, the current may be decreased by adding more resistance or increased by removing some resistance. Ohm's law may also be expressed in terms of the electromotive force, or voltage, E, of the source of electric energy, such as a battery. For example, I = E/R.
 

The diagram shows exactly how Ohm's Law works with a common battery. The yellow light represents a bulb which is powered by the battery. The tan wire shows where the resistence occurs.

 

The geometrically-independent quantity that is used is called resistivity and is usually indicated by the Greek symbol r. In the case of a wire, resistivity is defined as the resistance in the wire, times the cross-sectional area of the wire, divided by the length of the wire. The units associated with resistivity are thus, ohm-m (ohm x meters). The diagram shows this equation as it would work with a common wire, represented by the tan cylinder.

With modifications, Ohm's law also applies to alternating-current circuits, in which the relation between the voltage and the current is more complicated than for direct currents. Precisely because the current is varying, besides resistance, other forms of opposition to the current arise, called reactance. The combination of resistance and reactance is called impedance, Z. When the impedance, equivalent to the ratio of voltage to current, in an alternating current circuit is constant, a common occurrence, Ohm's law is applicable. For example, V/I = Z.

With further modifications Ohm's law has been extended to the constant ratio of the magnetomotive force to the magnetic flux in a magnetic circuit.

The power in the Ohm's experiments was provided by a thermoelectric conductor, developed by a Russian named Seebeck. This was very important because it provided a large current and a constant electromagnetic force. Other generators could not do this and were really nothing but crude batteries. He used a galvanic circuit and a galvonmeter in the experiment also. The galvonmeter was a compass over the wire that would turn as current passed through the wire. This movement was measured by a Ohm as the "restoring angle of torsion head in the division". These figures when looked at with the length of copper conductor in inches provided Ohm with enough information to produce the equation X=a/(b+x). X is the reading of the torsion head, x the length of the conductor (wire), while a and b were constants that had to be determined by more experiments. X is really a measure of the electric current, while Ohm found that the resistance was represented by b. After trying the experiment with different metals and temperatures Ohm's Law was published in The Galvanic Circuit Mathematically Worked Out. It was written out in these five statements:
1) Resistance is a unique property of a given conductor.
2) The current flowing in a given circuit is directly proportional to the difference potential at the two ends of the circuit.
3) The current is directly proportional to the section of wire, and the current passing through the wire is everywhere the same.
4) The current is directly proportional to the specific conductivity of the material of which the conductor is composed.
5) The potential of a circuit connected to the source of electricity is highest at the positive pole of the source, and lowest at the negative pole.

Ohmic vs. Nonohmic

Ohm's Law is only applicable under the assumption that resistance is constant. If the resistance is changing then the law is no longer true. For this reason some people consider Ohm not to have developed a law of nature, but just a mathematical explanation for a certain circumstance. Nonetheless, Ohm is credited with a law because of its wide range of application. Materials with a constant resistance will obey Ohm's Law and result in a graph of I versus V with a straight line. If the material is not constant in resistance then the graph looks something like the square root of y equals x.

Potential Difference and Current

There were some studies done in these areas before Ohm introduced his law. Experiments done in the area of conductivity and potential were normally very crude, but served as a basis for others to build upon. One example of this is Henry Cavendish. He explored the relationship between current and potential by using his body to complete the circuit and he would estimate the "degree of electrification". Somehow his findings were somewhat accurate. Neither of these terms were standard properties among scientists. Most scientists dealing in the area would use different terms to describe something similar, such as "intensity" and "tension" to describe something close to what we call current. Current was fairly new to the scientists because most earlier studies dealt with electrostatic properties. Although meanings and measurements were not standardized, scientists knew a lot more about current and potential difference before Ohm, than they did about resistance. Potential is defined today as the electric potential energy over the charge of the test particle. This test particle's charge is supposed to be very small. It is measured by the volt. The current is defined today as the charge that passes through a surface per unit time. It is measured by the ampere.

Resistance

This was the first electrical property to become standardized by committees. It was given the name Ohm, as recognition to the man that first put a mathematical value with it. Resistance is the ease of transportation of the electrons through the material. When a current is placed over a wire then the electrons slowly drift in a direction opposite current. This drift velocity is opposed by resistance. If electrons do not travel well inside the material then the material is said to be a insulator. If they do travel well, then the material is said to be a conductor. If the material allows for only some passage of electrons, then the material is a semiconductor. Many studies have been done to understand resistance. Resistivity is a constant characteristic of different metals. Each metal will have its own resistivity value. The value for the conductor will depend upon this, the conductor's dimensions, and the temperature. The dimension of the wire affects the current and resistance. For more information on factors of resistance click here...Conductors and Resistors.
 

The Ohm's law was illustrated in a stamp. The stamp shows an electrical resistance with special color code.

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