# Ohm's law

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## Ohm's law

(ōm) [for G. S. Ohm**Ohm, Georg Simon**

, 1787–1854, German physicist. He was professor at Munich from 1852. His study of electric current led to his formulation of the law now known as Ohm's law. The unit of electrical resistance (see ohm) was named for him.

**.....**Click the link for more information. ], law stating that the electric current

*i*flowing through a given resistance

*r*is equal to the applied voltage

*v*divided by the resistance, or

*i*=

*v*/

*r.*For general application to alternating-current circuits where inductances and capacitances as well as resistances may be present, the law must be amended to

*i*=

*v*/

*z,*where

*z*is impedance

**impedance,**

in electricity, measure in ohms of the degree to which an electric circuit resists the flow of electric current when a voltage is impressed across its terminals.

**.....**Click the link for more information. . There are conductors in which the current that flows is not proportional to the applied voltage. These do not follow this law and are called nonohmic conductors.

## Ohm's law

The direct current flowing in an electrical circuit is directly proportional to the voltage applied to the circuit. The constant of proportionality *R*, called the electrical resistance, is given by the

*V*is the applied voltage and

*I*is the current. Numerous deviations from this simple, linear relationship have been discovered.

*See*Electrical resistance

## Ohm’s Law

a law that states that the steady current density *I* in a conductor is directly proportional to the potential difference (voltage) *U* between two fixed points or cross sections of the conductor:

(1) *RI = U*

The proportionality constant *R*, which depends on the geometric and electric properties of the conductor and on temperature, is called the ohmic resistance, or simply the resistance, of the given section of the conductor. Ohm’s law was discovered in 1826 by the German physicist G. S. Ohm.

In the general case, the relationship between *I* and *U* is nonlinear; however, in practice it is always possible to assume it to be linear for a certain range of voltages and to apply Ohm’s law for this range. For metals and their alloys the range is virtually unlimited.

Ohm’s law in form (1) is valid for those sections of a circuit that do not contain any sources of electromotive force (emf). If such sources (storage batteries, thermocouples, or dynamos) are present, Ohm’s law assumes the form

(2) *RI*= *U + E*

where *E* is the emf of all sources connected in the section of the circuit that is being considered. For a closed circuit, Ohm’s law assumes the following form:

(3) *R _{t}I* =

*E*

where *R _{t}* =

*R*+

*R*is the total resistance of the entire circuit, which is equal to the sum of the external resistance

_{i}*R*of the circuit and the internal resistance

*R*of the source of emf. Kirchhoff’s laws generalize Ohm’s law for the case of branched circuits.

_{i}Ohm’s law can also be written in differential form, which links the current density j and the total electric field strength for each point of the conductor. The potential electric field of intensity E generated in conductors by the microscopic charges—electrons and ions—of the conductors themselves cannot support steady motion of free charges (a current), since the work done by the field in a closed loop is equal to zero. The current is supported by nonelectrostatic forces of various origins (induction, chemical, thermal, and so on) that are active in the emf sources and can be represented as some equivalent, nonpotential field of intensity E_{ext}, called the external field. In the general case, the total strength of the field acting on the charges in the conductor is E + E_{ext}. Correspondingly, the differential Ohm’s law assumes the form

(4) ρj = E + E_{ext} or j = σ(E + E_{ext})

where ρ is the specific electric resistivity of the conductor material and σ = 1/ρ is the specific electrical conductivity.

Ohm’s law in complex form is also valid for sinusoidal quasi-stationary currents:

(5) *ZI = E*

where *Z* is the total complex impedance, equal to *R + iX*, and *R* and *iX* are the resistance and reactance of the circuit, respectively. If an inductance *L* and a capacitance *C* are present in a circuit carrying a quasi-stationary current of frequency ω, then *X*= ω*L* - 1/ω*C.*

### REFERENCES

*Kursfiziki*, vol. 2. Edited by N. D. Papaleksi. Moscow-Leningrad, 1948.

Kalashnikov, S. G.

*Elektrichestvo.*Moscow, 1964. (

*Obshchii kurs fiziki*, vol. 2.)

*Fizicheskie osnovy elektrotekhniki.*General editor, K. M. Polivanov. Moscow-Leningrad, 1950.

## Ohm's law

[′ōmz ‚lȯ]## Ohm's law

The direct current flowing in an electrical circuit is directly proportional to the voltage applied to the circuit. The constant of proportionality *R*, called the electrical resistance, is given by the

*V*is the applied voltage and

*I*is the current. Numerous deviations from this simple, linear relationship have been discovered.