# Ohm’s law for complete chain

Ohm's law for a complete circuit - a mathematical expression describing the relationship between current and voltage, taking into account the source resistance. So originally written formula. Those who wish will see the section on Ohm’s law for the chain section.

## Again the story of

There have been and will be white spots in history.

Inductance Coil

The father of the inductor is unknown. The reason - scientists are constantly exchanging experience. At the congresses of the academies of sciences there was an intensive process of discussing various points of view. The idea was born together. In the treatise of George Ohm about the mathematical study of electroplating circuits there is no information about measuring devices - it is not clear what the husband of science was oriented on. One has only to look at the set of reports of that time, it becomes clear: the information is omitted due to the lack of choice. At the time of the second decade of the 20th century, only a magnetic needle was considered the only indicator of current strength. A series of events:

1. July 21, 1820 Oersted in Latin writes about his own experiments in the field of electromagnetism. It turns out that an electric current can deflect a compass needle. The effect appears when the contour is closed — the scientist writes — and is absent when open. It has been suggested that the angle of deviation depends on the "intensity of the moving electricity."
2. A little later in Geneva, physicists came to see how Sh. G. De la Reeve would demonstrate an unusual phenomenon.
3. September 4, Arago at a congress of the Academy of Sciences informed the scientists about the new discovery. Ampere, who was present at the meeting for a short time, made a number of discoveries: the solenoid with current is oriented in the magnetic field of the earth, the direction of deflection of the arrow can be predicted in advance, the conductors with current interact with each other.
4. At the indicated academy meeting( September 25), where Ampere spoke, physicists Biot and Savard reported on the discovery of the relationship between the conductor current and the magnetic field generated by it.

Scientist Schweiger

In September 1820, Schweiger presented the first galvanometer to the public, completing the preparation of the material base for George Ohm's research. The device scientist called the multiplier for the ability to multiply the effect of individual turns of wire. For example, a single specimen rejected the compass needle by 30 degrees, and three by 90. The contribution to the multiplier design was made by Poggendorf, who used an inductor of many turns of small radius for measuring purposes. Then Seebeck, using a new tool, discovered the thermoelectric effect used by Georg Om( on the advice of Poggendorf) to create a power source for his own pilot plant.

In close contact, scientists have made a lot of discoveries in a short period of time. And each became known to the interested public. Therefore, Georg Om lowered in his narration about the mathematical study of electroplating circuits such smallness as information about an experimental setup. It is noteworthy that the electric current has already been investigated, the idea of ​​the intensity of the magnetic field appeared in science, but a quantitative relationship between the simplest, as it seems today, values ​​was not noted. No one had a clue about voltage drops and conductor resistances.

George Ohm's merit: quantitatively able to describe what is used today in any electrical engineering calculations. The titans of science fought over this task:

• Humpfrey Davy;
• Becquerel;
• Barlow;
• Mariani;
• Petrov.

Researchers, including Ritter, Fourcroix, Tenar and Davy, noticed that the wire, while connected to a volt column, was constantly heated. The question arose: what does the temperature depend on? From the length, material, shape? Diverse metals emptied a source of energy at different times, the concept of electrical conductivity began to break through in everyday life. After the reports of Oersted were published, they tried to characterize the angle of deflection of the magnetic needle.

## The path of George Ohm to the discovery of the law for the complete chain

Strange, but the name of George Ohm today is known more than Michael Faraday, who presented the first electric motor to mankind( more precisely, the true inventor wished to remain anonymous, sending a letter published later in a scientific journal).Without a simple law, the branches of science would not have arisen, technology has degenerated into labor with a shovel. No radio, television and personal computers.

Initially, George Om worked as a mechanic's apprentice, but his father wanted to educate his children. Money for the books was discharged regardless of material well-being. Georg Om quickly mastered the science, becoming a talented mathematician. The husband of science manifested itself as a talented athlete and an excellent dancer who had no equal at student parties.

Not having completed his education, the father of the law for the full circuit went to a primary school teacher. He worked simultaneously as a tutor. George Omu liked being a teacher in the Swiss city of Gottstadt: picturesque nature and good earnings, but a true triumph awaited the discoverer of the law for a complete chain through adversity in the future. In 1809, the prose of life is again on the threshold: the son, a mathematician by education, returns to the local priest. Georg is offered to leave the post of teacher.

Georg Om

For more than ten years, Om moved from one job to another, not finding a satisfactory place to teach. Until the will of fate is not invited to the Jesuit school of Cologne. The teaching load is small, but the institution has an extensive storage of instruments, mostly obsolete or broken. It is curious that Georg Om is not in a hurry to run with a petition for material assistance to the rectors. Instead, recalling the old skills of a locksmith, is taken to make with his own hands. With interest in his letters to his father, he talks about new designs, conventional and hydrostatic, perfected the fatherly method of grinding amber to create electrical sources.

At the same time, George Om devotes a great deal of time to designing an instrument called an electrometer( charge measurement based on the experience of Charles Coulomb).Rumors about Schweigerger's galvanometers have already been heard on the stage, and Om realizes that in the harmony of science is far from perfect. In 1821, he wrote to his father that he sensed some kind of discovery and was closely following developments in this industry.

Initially, Om took a volt an element of copper and zinc, charged with hydrochloric acid, and with torsion weights measured the force required to bring the arrow to the magnetic meridian of the Earth, while the current-carrying conductor acted on the compass. Wire George Om oriented along the meridian, excluding the error. The volt pillar was discharged relatively quickly, the angle of deflection of the arrow gradually changed. Om saw that the source in the usual quality for the experimental setup is not suitable.

Wire samples were initially lowered into a bowl with mercury( having a relatively low conductivity) and carefully cleaned by the scientist for better contact. Liquid medium prevented the oxidation of the material and at the same time limited the growth of current to reasonable limits.5 samples of copper wire of different lengths took part in the experiment. Designating the samples in Latin letters a, b, c, d, e, the newly-made scientist Georg Om finds his first law in logarithmic form:

Ohm's first law

Where x is the length of the wire in feet, U characterizes the magnetic field. The results do not satisfy the scientist and, over time, he adds two constants to the dependency:

U = m ln( 1 + x / a) - the original formulation of Ohm's law for the complete circuit.

## From logarithms to a simple law for the complete chain

So, if m equals 0.525, with a = 2.9, the resulting dependence allows us to predict the results of the experiment in advance. In parallel, the scientist was engaged in the study of the conductivity of various metals, as a reference using a piece of copper with a length of 1 foot. The prototype was shortened until the deflection of the magnetic needle became the same. Lead, gold, silver, zinc, iron, brass, platinum and tin were investigated in this way, but the results often did not coincide with the science that is now available. The scientist saw discrepancies and explained that the purity of the samples was rarely 100%.

Failures were also expected in determining the dependence of the deviation of the arrow on the sectional area. There was no tool to accurately estimate the diameter of the wire. However, it was possible to establish that the conductivity clearly depends linearly on the cross-sectional area and length.

In its original form, the law was published by the Journal of Physics and Chemistry, published by Schweiger. At the time of 1825, George Om is unknown to the scientific community, and the formula, as can be seen, is not entirely correct and convenient. The scientist in the text made the reservation that the study was not completed. I bother to issue a treatise( discussed in the topic according to Ohm’s law for the chain section), where he described what he relied on, and set forth his conclusions in detail. First: the current strength is the same throughout the circuit. This is evident in the degree of deviations of the magnetic needle. Note that the relationship was considered rather an assumption, although we should not forget about the law of Bio-Savart( 1820).

At the same time, the scientist finally realized that the element of Wollaston( Wulston) is no good. This was determined by the weakened glow of the wire, but as soon as the circuit was opened and a little wait, the temperature reached the initial value after the restart. This clearly indicated instability in the first place and renewability in the second place of such a source. At the same time, Becquerel and Barlow used a similar technique - both published erroneous conclusions on the dependencies between the parameters of the conductor. Moreover, scientists put forward various formulas, which clearly indicated the need to continue the search.

Poggendorf came to the rescue, who, when analyzing Ohm's printed work, stated that it is better to use thermo-emf as a source. And brought information to Martin - younger brother George. The thermocouple of copper and bismuth in the installation was on a tripod tripod, equipped with screws for the exhibition to the horizon. The magnetic needle with torsional weights served as a cover for a transparent glass cap protecting the working part from air flow fluctuations. The Mauch collegium mechanic helped Ohm create a precise adjustment system with a graduated washer in order to accurately detect the effort needed to return the arrow to the Earth's magnetic meridian.

Even the compass needle was made special: made of steel, with ivory tips, the only one crowned with a brass pointer, aimed at a scale. As far as the experiment was conducted responsibly, the result of 1926 was closer to the truth:

X = a / b + x.

This is Ohm’s law for the complete circuit( I = U / R + r), where X is the magnetic field strength directly proportional to the current I, and is the thermo-emf U, x is the conductor length directly proportional to the resistance R, b is the restpart of the circuit, implying today the internal resistance r of the source and the installation contacts.

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