What is "ohm's law"

Ohm \Ohm\ ([=o]m), n. [So called from the German electrician, G. S. Ohm.] (Elec.) The standard unit in the measure of electrical resistance, being the resistance of a circuit in which a potential difference of one volt produces a current of one amp['e]re. As defined by the International Electrical Congress in 1893, and by United States Statute, it is a resistance substantially equal to 10^ 9 units of resistance of the C. G. S. system of electro-magnetic units, and is represented by the resistance offered to an unvarying electric current by a column of mercury at the temperature of melting ice 14.4521 grams in mass, of a constant cross-sectional area, and of the length of 106.3 centimeters. As thus defined it is called the international ohm.

Ohm's law (Elec.), the statement of the fact that the strength or intensity of an electrical current is directly proportional to the electro-motive force, and inversely proportional to the resistance of the circuit.

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship:

$$I = \frac{V}{R},$$

where is the current through the conductor in units of amperes, V is the voltage measured across the conductor in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current.

The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. He presented a slightly more complex equation than the one above (see History section below) to explain his experimental results. The above equation is the modern form of Ohm's law.

In physics, the term Ohm's law is also used to refer to various generalizations of the law originally formulated by Ohm. The simplest example of this is:

J = σE, 

where J is the current density at a given location in a resistive material, E is the electric field at that location, and σ ( Sigma) is a material-dependent parameter called the conductivity. This reformulation of Ohm's law is due to Gustav Kirchhoff.