Ohm's law
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This article is about the law related to electricity. For other uses, see Ohm's acoustic law.
V, I, and R, the parameters of Ohm's law
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Ohm's law
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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,[1] one arrives at the usual mathematical equation that
describes this relationship:[2]
where I 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. [3] Ohm's law is an empirical
relation which accurately describes the conductivity of the vast majority
of electrically conductive materials over many orders of magnitude of current.
However some materials do not obey Ohm's law, these are called non-ohmic.
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. Ohm explained his
experimental results by a slightly more complex equation than the modern form
above (see § History below).
In physics, the term Ohm's law is also used to refer to various generalizations of the
law; for example the vector form of the law used in electromagnetics and material
science:
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.[4]
Contents
1History
2Scope
3Microscopic origins
4Hydraulic analogy
5Circuit analysis
o 5.1Resistive circuits
o 5.2Reactive circuits with time-varying signals
o 5.3Linear approximations
6Temperature effects
7Relation to heat conductions
8Other versions
o 8.1Magnetic effects
o 8.2Conductive fluids
9See also
10References
11External links and further reading
History
Georg Ohm
In January 1781, before Georg Ohm's work, Henry Cavendish experimented
with Leyden jars and glass tubes of varying diameter and length filled with salt
solution. He measured the current by noting how strong a shock he felt as he
completed the circuit with his body. Cavendish wrote that the "velocity" (current)
varied directly as the "degree of electrification" (voltage). He did not
communicate his results to other scientists at the time, [5] and his results were
unknown until Maxwell published them in 1879.[6]
Francis Ronalds delineated “intensity” (voltage) and “quantity” (current) for
the dry pile—a high voltage source—in 1814 using a gold-leaf electrometer. He
found for a dry pile that the relationship between the two parameters was not
proportional under certain meteorological conditions. [7][8]
Ohm did his work on resistance in the years 1825 and 1826, and published his
results in 1827 as the book Die galvanische Kette, mathematisch
bearbeitet ("The galvanic circuit investigated mathematically"). [9] He drew
considerable inspiration from Fourier's work on heat conduction in the theoretical
explanation of his work. For experiments, he initially used voltaic piles, but later
used a thermocouple as this provided a more stable voltage source in terms of
internal resistance and constant voltage. He used a galvanometer to measure
current, and knew that the voltage between the thermocouple terminals was
proportional to the junction temperature. He then added test wires of varying
length, diameter, and material to complete the circuit. He found that his data
could be modeled through the equation
where x was the reading from the galvanometer, l was the length of the test
conductor, a depended on the thermocouple junction temperature, and b was
a constant of the entire setup. From this, Ohm determined his law of
proportionality and published his results.
Internal resistance model
In modern notation we would write,
where is the open-circuit emf of the thermocouple, is
the internal resistance of the thermocouple and is the resistance
of the test wire. In terms of the length of the wire this becomes,
where is the resistance of the test wire per unit length. Thus,
Ohm's coefficients are,
