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 three mathematical equations used to
describe this relationship:
V, I, and R, the parameters of Ohm's law
where I is the current through the conductor, V is the voltage measured across the conductor
and R is the resistance of the conductor. More specifically, Ohm's law states that the R in this
relation is constant, independent of the current.[3] If the resistance is not constant, the
previous equation cannot be called Ohm's law, but it can still be used as a definition
of static/DC resistance.[4] 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.
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.[5]
What Is Ohm’s Law?
Ohm’s law states that the electrical current through a conductor is proportional to the
potential difference across it. Furthermore, the electrical resistance of the conductor is
constant. This leads to the mathematical equation:
where R the resistance in ohms (Ω), V the voltage in volts (V), and I is the current in amperes
(A). To illustrate: a resistor of 1 Ω subjected to a current of 1 A has a voltage difference of 1
V across its terminals. The equation is named after Georg Ohm. In 1827 he published his
findings that form the basis of the formula that is used today. He performed a large series of
experiments that showed the relation between applied voltage and current through a
conductor. The law is therefore empirical. Although Ohm’s law is one of the fundamentals of
electrical engineering, at the time of publication it was received with criticism. The ohm is
adopted as the official SI unit for electrical resistance. Gustav Kirchhoff (known
from Kirchhoff’s circuit laws) made a generalization that is used more often in physics:
where σ is the conductivity parameter (material specific), J is the current density, and E is the
electric field.
Ohm’s Law and Resistors
Resistors are passive elements that introduce resistance to the flow of electric current in a
circuit. A resistor that functions according to Ohm’s law is called an Ohmic resistor. When
current passes through an Ohmic resistor, the voltage drop across the terminals is
proportionally to the magnitude of resistance. Ohm’s formula is also valid for circuits with
varying voltage or current, so it can be used for alternating current (AC) circuits as well. For
capacitors and inductors, Ohm's law cannot used since their I-V curves are inherently not
linear (not Ohmic).
Ohm’s formula is valid for circuits with multiple resistors that can be connected in series,
parallel or both. Groups of resistors in series or parallel can be simplified with an equivalent
resistance. The articles Resistors in Series and Resistors in Parallel describe this process in
more detail.
