## Ohm's law. History and pattern

Ohm's Law is a formula that expresses the mathematical relationship between current, voltage, and resistance in an electrical circuit. It is an experimental law and in some materials (mainly metals) it is quite accurately fulfilled for the specified current flow conditions. What is the history of this law? What's the pattern?

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## 1. What is Ohm's Law?

Ohm's law says that the current flowing through a conductor is proportional to the voltage between the ends of the conductor. It was discovered in the years 1825-1826 by a German mathematics teacher, later a physicist, professor at the University of Munich and the Nuremberg University of Technology, Georg Simon Ohm.

## 2. The history of the creation of Ohm's law

In 1822, Humphry Davy published the results of research on the conductivity of electric current in metals. As a result of these tests, the conductivity of metal wires is inversely proportional to their length and directly proportional to the cross-sectional area. This researcher also ordered conductors in terms of their ability to conduct electricity.

Some time later, George Simon Ohm, a middle school mathematics teacher at the time, studied the dependence of electric current to the dimensions of a conductor and applied voltage from 1825, but his work was complicated and unclear, and therefore did not receive much recognition.

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read the articleIn 1826, Ohm presented the results of his research in a form similar to the one known today, claiming that the current flowing in the conductor is proportional to the applied voltage. However, it was still several years before the scientific community accepted his claims.

In the years 1845-1847, another researcher, Gustav Kirchhoff, made a theoretical analysis of the current flow and related its density to the electric field inside the conductor. In 1900, Paul Drude formulated his model of the conductivity of metals, explaining the proportionality of current to voltage, as established experimentally by Ohm.

It is now known that many materials behave differently than Ohm claims. The proportionality of voltage and current is not maintained and Ohm's law is not always met. Electronic components and materials for which Ohm's law is satisfied are called linear (or ohmic), and those for which are non-linear (or non-ohmic).

Ohm's law is not a universal law of nature, but only a valid relation for materials of a certain class, within a limited range of currents and voltages. However, this law is of great historical as well as practical importance. It was the first quantitative mathematical description of an electric current.

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read the article## 3. Formula for Ohm's law

For conductors, the voltage between its ends is proportional to the current flowing through the conductor. At a certain temperature, the proportionality factor is constant and we call it the conductor resistance.

For a conductor with a resistance R, through which a current of intensity I flows, the voltage U between its ends is:

U = I x R

The unit of resistance is Ω [ohms].

We can associate the resistance with the geometry of the conductor. For a conductor of length l and a cross-section S, the resistance will be:

R = p x l / S

where p is the specific resistance and is dependent on the material the conductor is made of.

This law defines resistance as the voltage-to-current ratio. It is temperature dependent and will grow linearly with temperature for metals. If at a certain temperature T0 the resistance will be R0, then at temperature ΔT it will be:

RΔT = R0 + R0⋅α⋅ΔT

where α is the temperature coefficient of resistance

In the case of semiconductor materials, resistance will decrease exponentially with increasing temperature.

At room temperature, the specific resistance between the glass is 1.7⋅10−8Ωm, while the glass is 1018 times greater.

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