Ohm discovered the proportional relationship between current and voltage in resistance, that is, the famous ohm's law; He also proved that the resistance of a conductor is directly proportional to its length and inversely proportional to its cross-sectional area and conductivity. In the case of stable current, the charge moves not only on the surface of the conductor, but also on the whole cross section of the conductor. The international system of units "ohm" of resistance is named after him. The name of ohm is also used in other physical and related technical contents, such as "ohmic contact", "ohmic sterilization" and "ohmmeter".

The first stage of ohm experiment is to explore the relationship between the electromagnetic force attenuation caused by current and the length of wire. The results were published in his first scientific paper 1825 in May. In this experiment, he met with the difficulty of measuring the current intensity. Inspired by the galvanometer invented by German scientist Schveger, he skillfully combined the current magnetic effect discovered by Oster with Coulomb torsion balance method, designed a current torsion balance, and used it to measure the current intensity. Ohm comes from preliminary experiments, and the electromagnetic force of current is related to the length of conductor. This relationship is not directly related to today's ohm's law expression. Ohm did not relate the potential difference (or electromotive force), current intensity and resistance at that time.

Before ohm, although there was no concept of resistance, some people studied the conductivity of metals. 1825 In July, Ohm also studied the relative conductivity of metals with the device used in the previous experiment. He measured various metals by making wires with the same diameter, and determined the relative conductivity of metals such as gold, silver, zinc, brass and iron. Although the experiment was rough and there were many mistakes, the fact that Ohm thought the current was constant in the whole wire showed that the current intensity could be used as an important basic quantity of the circuit, and he decided to study it as a main observation in the next experiment.

In the previous experiment, the battery used by Ohm was a voltaic pile, and the electromotive force of this pile was unstable, which made him very headache. Later, it was suggested to use bismuth-copper thermocouple as power supply, thus ensuring the stability of electromotive force of power supply.

1826, ohm deduced his law with the experimental device shown above. A current torsion balance is installed on the wooden stand, DD' is the glass cover of the torsion balance, CC' is the dial, S is the magnifying glass for observation, M and M' are the mercury cups, abb'a' is the bismuth stand, and one leg of bismuth and copper stand contacts each other, thus forming a thermocouple. A and B are two tin containers used to generate temperature difference. In the experiment, the conductor to be studied is inserted into two cups containing mercury, M and M' respectively, which become the two poles of a thermoelectric battery.

Ohm prepares conductors with the same cross section but different lengths, connects each conductor into the circuit in turn for experiment, observes the deflection angle of the torsion drag pin, and then repeats the operation under different conditions. According to the experimental data, the following relations are summarized:

X=q/(b+l) where x represents the current flowing through the wire, which is proportional to the current intensity, A and B are two parameters of the circuit, and L represents the length of the experimental wire.

Ohm published a paper in April 1826, rewriting Ohm's law as follows: x=ksa/ls is the cross-sectional area of a conductor, k is the conductivity, a is the potential difference between two ends of the conductor, l is the length of the conductor, and x is the current intensity passing through L. If the resistance l'=l/ks is substituted into the above formula, X=a/I' is obtained, which is Ohm's law.

1 ohm is defined as the resistance that just passes the ampere current when the potential difference is 1 volt.