Ohm's law

“ But most people remember his name in connection with his practical demonstration of electromagnetic induction.
In France Andre-Marie Ampere (1775-1836) carried out a complete mathematical study of the laws which govern the interaction between wires carrying electric currents.
In Germany in 1826 a Bavarian schoolmaster Georg Ohm (1789-1854) had defined the relationship between electric pressure (voltage) , current (flow rate) and resistance in a circuit (Ohm's law) but 16 years had to elapse before he received recognition for his work. ”

“ While in practical significance Ohm's Law, discovered nearly a half century later, is of much more import, Coulomb's discoveries are fundamental in character and, coming in the very beginnings of modern electrical science, did much to guide the infant science in the ways it should follow. The establishing of this law contributed very largely to the rapid development of the twin sciences of electricity and magnetism. It is experimental observation that means most for a rising science ”

“ It however marks one of the steps in the discovery of the law, and an examination of the experimental data shows that it represented these data very closely. Ohm was not however to be long misguided by an equation which could be easily checked by increasing the range of the experiment. He saw that, no matter how precise equation (3) might prove as an approximate formula, it could hardly represent a law of nature. He therefore prepared to test an external resistance fifteen hundred feet long. ”

“ They were so new that none of the workers in acoustics could think that Ohm had made a great discovery. His law states that the human ear perceives only pendulum-like vibration as a simple tone. Every other periodic motion it resolves into a collection of pendulum-like vibrations, which it then hears in the sound as a series of single tones, fundamentals and overtones. Ohm arrived at this law from mathematical considerations, making use of Fourier's series ”

“ Since by Ohm’s law E = Ri, where R is the resistance of the circuit, it follows that the energy dissipated as heat per unit of time in any circuit is numerically represented by Ri2, and therefore the resistance is measured by the heat produced per unit of current, provided the current is unvarying. ”

“ Lord Kelvin, himself one of the greatest of the electrical scientists of the nineteenth century, in commenting some years ago on Ohm's law, said that it was such an extremely simple expression of a great truth in electricity, that its significance is probably not confined to that department of physical phenomena, but that it is a law of nature in some much broader way. ”

“ OHM, ōm, Georg Simon (1787-1854) . A German physicist and discoverer of the famous law in electricity bearing his name. He was born and educated at Erlangen, and, after giving instruction in mathematics and physics in a number of schools, he was called in 1817 to a chair in the gymnasium at Cologne. He made a study of the laws of galvanic currents, and while investigating the relative conductivity of metals finally discovered the relation known as ‘Ohm's law,’ which underlies all electrical theory and measurement. ”

“ The first term of the right side of (3) may be transformed by substituting for the components of the total current their values in terms of the components of the magnetic intensity, while the second term, the product of the conduction current and the electromotive intensity, by Ohm's law, which states that , becomes , where C is the specific conductivity. But this is the energy appearing as heat in the circuit per unit volume according to Joule's law. ”

“ Discussion of the three fundamental hypotheses lying at the basis of his general theory and dealing with (a) the distribution of electricity in any element of a body; (b) mode of dispersion of electricity into the atmosphere; (c) law accounting for the generation of contact electricity. Of these three only the first is directly concerned with Ohm's law. Of it he says: "I have started from the supposition that the communication of electricity from one particle takes place directly to the one next to it. ”

“ The resistance of the receiver is thus not constant, but undergoes a continuous decrease with increasing E. M. F. The conductivity is therefore increased with the rise of E. M. F. The curve becomes steeper as the E. M. F. is increased, the conductivity undergoing a rapid and continuous increase.
Hence conduction in such cases does not obey Ohm's law. The resistance is not independent of the E. M. F. ”

“ If a current be passed through two resistances in series by means of an applied electromotive force, the electric potential falls from one end of the resistances to the other, and, if we apply Ohm’s law to each resistance in succession, we see that, since for each of them E = CR, and C the current is the same through both, E the electromotive force or fall of potential between the ends of each resistance must be proportional to the resistance between them. ”

“ The measurement of their fulfilment is exactly proportional to our belief in them, not from any unintelligible cause, and still less from any unreasoning feat of a capricious Deity, but by the working of an intelligible Law. If any of my readers happens to be an electrician, he will find an exact parallel in what is known as Ohm's Law. Such readers will be familiar with the formula C = E/R, but for the benefit of those to whom this formula may be unintelligible, I will give a few words of explanation. C means the current of electricity which is to be delivered for any work that is to be done. ”

“ We conclude by applying Ohm's law that the electromotive force, E, of the thermocouple may be approximately represented for small differences of temperature by the formula
2. Thermoelectric Power, Series, Inversion.—The limiting value, dE/dt, of the coefficient, p, for an infinitesimal difference, dt, between the junctions is called the Thermoelectric Power of the couple. One metal (A) is said to be thermoelectrically positive to another (B) , if positive electricity flows from A to B across the cold junction when the circuit is completed. ”

“ It is almost a universal rule in science, that no matter how distinguished an investigator may be, he makes but one cardinal discovery. Ohm, however, was destined, after having brilliantly illuminated electricity by the discovery of a great law, to throw nearly as bright a light on the domain of acoustics; and there is a law in this department of physics which is deservedly called by his name, though it is often associated with that of Helmholtz. ”

“ Here four storage cells in series have an E.M.F. of 8 volts and in accordance with Ohm's law produce a current of 2 amperes through a resistance in the circuit of 4 ohms. Now the work done or energy expended by the current in passing through the resistance between the points M and N depends upon three factors (1) the E.M.F. or potential difference; (2) the current intensity and (3) the time. The energy is measured by their product. That is, electrical energy = potential difference × current intensity × time. ”

“ For, notwithstanding its seeming subtlety, there is no force in use, or that has ever been used by men, capable of being so definitely calculated, measured, determined beforehand, as electricity is. As time passes new measurements are adopted and named, some of them being proposed as lately as 1893. An instance of the value of some of these old determinations of a time when all we now know of electrical science was unknown, may be given in what is known as Ohm's Law. ”

“ Helmholtz himself was always most emphatic in his insistence on Ohm's priority in the matter, and constantly speaks of the law in question by Ohm's name.
Perhaps no better evidence of the breadth of Ohm's interest in science, his supreme faculty for experimentation, or the originality of his investigating genius, can be found than the fact that he thus discovered, by experimental and mathematical methods, the solution to important problems in two such distinct departments of physical science as electricity and acoustics. ”

“ Accordingly, the outflow, undifferentiated, of Life and Energy from the Eternal Substantive of Spirit, is never stopped by its own current in any of its differentiated streams; it is impossible for a current to be stopped by its own flow, whether it be a current of electricity, steam, water, or anything else. What then does stop the flow of any sort of current? It is the Resistance or inertia of the channel through which it flows; so that we come back to the formula of Ohm's Law, C = E/R as a general proposition applicable to any conceivable sort of energy. ”

“ He was one of the first in this country to appreciate the importance of Ohm's simple law of the relation between electromotive force, resistance of conductors, and resulting current—the law which is today the foundation of all electrical engineering. ”

“ A typical example of the sort of opposition which a modern discoverer in science meets with is to be found in the life of Ohm, after whom, because of his discovery of the law of electrical resistance, the unit of resistance is called. When he made his discovery Ohm was working in the Gymnasium at Cologne. The leading physicists of the day could not bring themselves to believe that this comparatively young man--he was scarcely forty at the time--could have made a discovery that went far beyond their knowledge. ”

“ The arguments in favour of the surface form are, in the opinion of the author, deductions from exploded theories, from imperfect experiments, or from erroneous interpretations of well ascertained facts. (133) No direct experiments have ever been made to solve the question, as far as the author knows. Quantities of electricity, that is static discharges from condensers, are in incessant use for telegraphic purposes, and are found to follow exactly Ohm’s laws, even with the most delicate apparatus. ”

“ If we had supposed that a body when raised to a high potential becomes electrified throughout its substance as if electricity were compressed into it, we should have arrived at equations of this very form. It is remarkable that Ohm himself, misled by the analogy between electricity and heat, entertained an opinion of this kind, and was thus, by means of an erroneous opinion, led to employ the equations of Fourier to express the true laws of conduction of electricity through a long wire, long before the real reason of the appropriateness of these equations had been suspected. ”

“ But in many other cases we have to consider not merely the laws which regulate the actions of our ultimate causes, but a system of mechanism, or a structure of parts, through the intervention of which their effects become sensible to us. Thus, in the delicate and curious electro-dynamic theory of Ampere, the mutual attraction or repulsion of two magnets is referred to a more universal phenomenon, the mutual action of electric currents, according to a certain fundamental law. ”

“ The formulation of such a connecting theory is the task to which Ohm set himself, approaching the problem from the experimental side. The workers of the early nineteenth century had already in a measure identified and separated the factors at play in the galvanic circuit. Examples of such factors are: the "contact force" at the terminals of the circuit, the "flow of current" along the wire, the "electroscopic force" between any two points of a circuit, the tendency of electricity to escape into the air, and the polarization of the electrodes. ”

“ As a unit of resistance, the International Ohm, which is based upon the ohm equal to 109 units of resistance of the C.G.S. system of electromagnetic units, and is represented by the resistance offered to an unvarying electric current by a column of mercury at the temperature of melting ice 14·4521 grammes in mass, of a constant cross-sectional area and of the length of 106·3 cm. ”

“ In acoustics Ohm discovered that the ear of itself analyzes any complex sound into simple tones in the manner contemplated in Fourier's theorem, a fact which later proved of great importance in the hands of Helmholtz. In 1852 Ohm was appointed to the chair of physics at the University of Munich. His most important work, by all odds, is his theorem concerning the galvanic circuit. ”

“ We still carry our ordinary mechanical notions down into the realm of small electric effects, and still talk, for instance, about non-electrical forces which hold an electron together. Nor are there experiments affording sufficient basis for believing that all the mass of a positive nucleus is electrical in character. We also think of electrical charges as having the property of identifiability, which involves the possession of sharp edges and a change in the law of force at small distances, and this is certainly a property carried over from our large scale experience. ”

“ The electroscopic force in the open pile was generally identified with the thickness of the electrical stratum at the place tested; while Ohm, recognizing that electric currents are not confined to the surface of the conductors, but penetrate their substance, seems to have thought of the electroscopic force at a place in a circuit as being proportional to the volume-density of electricity there—an idea in which he was confirmed by the relation which, in an analogous case, exists between the temperature of a body and the volume-density of heat supposed to be contained in it. ”