Ohm's law in differential and integral form states that the current through the conductor between two points is directly proportional to the voltage at two points. The equation with a constant looks like this:
I = V / R,
where I is the current point through the conductor in units of amperes, V (Volt) is the voltage measured with the help of the conductor in units of volts, R is the resistance of the conducted material in Ohms. More specifically, Ohm's law states that R in this respect is constant, independent of current.
What can be understood by Ohm's Law?
Ohm's law in differential and integral form is an empirical relation that accurately describes the conductivity of the vast majority of conductive materials. However, some materials are not subject to Ohm's law, they are called "neomic." The law was named after the scientist George Ohm, who published it in 1827. It describes voltage and current measurements using simple electrical circuits containing various wire lengths. Om explained his experimental results with a slightly more complex equation than the modern form above.
The concept of Ohm's law in diff. form is also used to denote various generalizations, for example, its vector form is used in electromagnetism and materials science:
J = σE,
where J is the number of electrical particles in a particular place of the resistive material, e is the electric field at this place, and σ (sigma) is a material that depends on the conductivity parameter. Gustav Kirchhoff formulated the law in this way.
History
History
In January 1781, Henry Cavendish experimented with a Leiden jar and a glass tube of various diameters filled with a salt solution. Cavendish wrote that speed changes directly as a degree of electrification. Initially, the results were unknown to the scientific community. But Maxwell published them in 1879.
Om did his work on resistance in 1825 and 1826 and published his results in 1827 in the book "Galvanic circuit is proved mathematically." He was inspired by the work of the French mathematician Fourier, who described thermal conductivity. For experiments, he initially used galvanic piles, but later switched to thermocouples, which could provide a more stable voltage source. He operated on the concepts of internal resistance and direct current voltage.
Also in these experiments, a galvanometer was used to measure current, since the voltage between the thermocouple terminals is proportional to the connection temperature. He then added test leads of various lengths, diameters and materials to complete the circuit. He found that his data can be modeled using the following equation
x = a / b + l,
where x is the readings of the measuring device, l is the length of the test conductor, a is dependent on the temperature of the thermocouple connection, b is the constant (constant) of the whole equation. Om proved his law on the basis of these proportionality calculations and published his results.
The Importance of Ohm's Law
Ohm's law in differential and integral form was probably the most important of the early descriptions of the physics of electricity. Today, we think this is almost obvious, but when Om first published his work, this was not so. Critics reacted with hostility to his interpretation. They called his work "naked fantasies," and the German Minister of Education stated that "a professor who preaches such a heresy is not worthy to teach science."
The prevailing scientific philosophy in Germany at that time claimed that there was no need to conduct experiments to develop an understanding of nature. In addition, Geogra’s brother, Martin, a mathematician by profession, struggled with the German educational system. These factors impeded the acceptance of Ohm's work, and his work did not gain wide recognition until the 1840s. Nevertheless, Om received recognition for his contribution to science long before his death.
Ohm's law in differential and integral form is an empirical law, a generalization of the results of many experiments, which showed that the current is approximately proportional to the voltage of the electric field for most materials. It is less fundamental than the Maxwell equations, and is not suitable in all situations. Any material will be destroyed by the strength of a sufficient electric field.
Ohm's law has been observed on a wide range of scales. At the beginning of the 20th century, Ohm's law was not considered on an atomic scale, but experiments confirm the opposite.
Quantum beginning
The dependence of the current density on the applied electric field has a fundamentally quantum mechanical character (classical quantum permeability). A qualitative description of Ohm's law can be based on classical mechanics using the Drude model developed by the German physicist Paul Drude in 1900. Because of this, Ohm's law has many forms, for example, the so-called Ohm's law in differential form.
Other forms of Ohm's law
Ohm's law in differential form is an extremely important concept for electrical engineering / electronics, since it describes both voltage and resistance. All this is interconnected at the macroscopic level. Studying electrical properties at the macro- or microscopic level, a more related equation is used, which can be called the Ohm equation, which has variables that are closely related to the scalar variables V, I and R of Ohm's law, but which are a constant function of the position in the conductor.
Magnetism effect
If an external magnetic field (B) is present and the conductor is not at rest, but moves at a speed of V, it is necessary to add an additional variable to take into account the current induced by the Lorentz force on the charge carriers. Also called Ohm's law of integral form:
J = σ (E + v * B).
In the rest system of a moving conductor, this term falls out because V = 0. There is no resistance, since the electric field in the rest system is different from the E-field in the laboratory system: E '= E + v × B. Electric and magnetic fields are relative. If J (current) is variable due to the fact that the applied voltage or E-field changes in time, then reactance must be added to the resistance in order to take into account self-induction. The reactance can be strong if the frequency is high or the conductor is wound.