Ohm's law

ohmicOhmohmic losseslawOhms Lawdelineationelectrical principlesfamous law that bears his nameI-V (current-voltage) curvenow-famous circuital relation
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.wikipedia
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Scientific law

laws of physicsphysical lawlaws of nature
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.
Ohm's law only applies to linear networks, Newton's law of universal gravitation only applies in weak gravitational fields, the early laws of aerodynamics such as Bernoulli's principle do not apply in case of compressible flow such as occurs in transonic and supersonic flight, Hooke's law only applies to strain below the elastic limit, Boyle's law applies with perfect accuracy only to the ideal gas, etc. These laws remain useful, but only under the conditions where they apply.

Voltage

potential differenceVvoltages
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
, but more often simply as V, for instance in the context of Ohm's or Kirchhoff's circuit laws.

Electrical resistance and conductance

resistanceelectrical resistanceconductance
Introducing the constant of proportionality, the resistance, one arrives at the usual mathematical equation that describes this relationship: 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.
This proportionality is called Ohm's law, and materials that satisfy it are called ohmic materials.

Georg Ohm

Georg Simon OhmOhmOhm, Georg
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. 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.
This relationship is known as Ohm's law.

Volt

VkVvolts
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.
It can also be expressed as amperes times ohms (current times resistance, Ohm's law), webers per second (magnetic flux per time), watts per ampere (power per unit current, definition of electric power), or joules per coulomb (energy per unit charge), which is also equivalent to electronvolts per elementary charge:

Ohm

Ωohmsmegohm
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.
The formula is a combination of Ohm's law and Joule's law:

Francis Ronalds

Sir Francis RonaldsRonalds
Francis Ronalds delineated “intensity” (voltage) and “quantity” (current) for the dry pile – a high voltage source – in 1814 using a gold-leaf electrometer.
His theoretical contributions included an early delineation of the parameters now known as electromotive force and current; an appreciation of the mechanism by which dry piles generated electricity; and the first description of the effects of induction in retarding electric signal transmission in insulated cables.

Drude model

DrudeLorentz modelDrude behavior
In 1900 the first (classical) model of electrical conduction, the Drude model, was proposed by Paul Drude, which finally gave a scientific explanation for Ohm's law.
The latter expression is particularly important because it explains in semi-quantitative terms why Ohm's law, one of the most ubiquitous relationships in all of electromagnetism, should be true.

Ampere

AmAamp
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.
The standard ampere is most accurately realized using a Kibble balance, but is in practice maintained via Ohm's law from the units of electromotive force and resistance, the volt and the ohm, since the latter two can be tied to physical phenomena that are relatively easy to reproduce, the Josephson junction and the quantum Hall effect, respectively.

Internal resistance

where \mathcal E is the open-circuit emf of the thermocouple, r is the internal resistance of the thermocouple and R is the resistance of the test wire.
When the power source delivers current, the measured voltage output is lower than the no-load voltage; the difference is the voltage drop (the product of current and resistance) caused by the internal resistance.

Electric current

currentelectrical currentcurrents
Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points.
In such conditions, Ohm's law states that the current is directly proportional to the potential difference between two ends (across) of that metal (ideal) resistor (or other ohmic device):

Drift velocity

driftdrift speeddrift velocities
The drift velocity then determines the electric current density and its relationship to E and is independent of the collisions.
Thus Ohm's law can be explained in terms of drift velocity.

Henry Cavendish

CavendishCavendish balanceCavendish, Henry
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.
According to the 1911 edition of Encyclopædia Britannica, among Cavendish's discoveries were the concept of electric potential (which he called the "degree of electrification"), an early unit of capacitance (that of a sphere one inch in diameter), the formula for the capacitance of a plate capacitor, the concept of the dielectric constant of a material, the relationship between electric potential and current (now called Ohm's Law) (1781), laws for the division of current in parallel circuits (now attributed to Charles Wheatstone), and the inverse square law of variation of electric force with distance, now called Coulomb's Law.

Free electron model

free electronselectron gasDrude–Sommerfeld model
In 1927 Arnold Sommerfeld applied the quantum Fermi-Dirac distribution of electron energies to the Drude model, resulting in the free electron model.
Mainly, the free electron model and the Drude model predict the same DC electrical conductivity σ for Ohm's law, that is

Galvanometer

D'Arsonval galvanometertangent galvanometernull detector
: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.
The ability to measure quantitatively voltage and current allowed Georg Ohm, in 1827, to formulate Ohm's Law – that the voltage across a conductor is directly proportional to the current through it.

Resistor

Resistor controlresistorsResistance
Resistors are circuit elements that impede the passage of electric charge in agreement with Ohm's law, and are designed to have a specific resistance value R.
The behaviour of an ideal resistor is dictated by the relationship specified by Ohm's law:

Barlow's law

In the 1850s, Ohm's law was known as such and was widely considered proved, and alternatives, such as "Barlow's law", were discredited, in terms of real applications to telegraph system design, as discussed by Samuel F. B. Morse in 1855.
Ohm's law is now considered the correct law and Barlow's false.

Electromotive force

EMFelectromotive force (EMF)
where \mathcal E is the open-circuit emf of the thermocouple, r is the internal resistance of the thermocouple and R is the resistance of the test wire.
As shown in the figure, for a load resistance R L, the cell develops a voltage that is between the short-circuit value V = 0, I = I L and the open-circuit value V oc, I = 0, a value given by Ohm's law V = I R L, where the current I is the difference between the short-circuit current and current due to forward bias of the junction, as indicated by the equivalent circuit (neglecting the parasitic resistances).

Current–voltage characteristic

current-voltage characteristiccharacteristic curveI-V curve
There are, however, components of electrical circuits which do not obey Ohm's law; that is, their relationship between current and voltage (their I–V curve) is nonlinear (or non-ohmic).
The simplest I–V curve is that of a resistor, which according to Ohm's law exhibits a linear relationship between the applied voltage and the resulting electric current; the current is proportional to the voltage, so the I–V curve is a straight line through the origin with positive slope.

Series and parallel circuits

seriesparallelin series
Resistors which are in series or in parallel may be grouped together into a single "equivalent resistance" in order to apply Ohm's law in analyzing the circuit.
The current in each individual resistor is found by Ohm's law.

Maxwell's equations

Maxwell equationsMaxwell equationMaxwell’s equations
Ohm's work long preceded Maxwell's equations and any understanding of frequency-dependent effects in AC circuits.
E.g., the original equations given by Maxwell (see History of Maxwell's equations) included Ohm's law in the form

Fick's laws of diffusion

Fick's law of diffusionFick's lawdiffusion constant
The Fick's law is analogous to the relationships discovered at the same epoch by other eminent scientists: Darcy's law (hydraulic flow), Ohm's law (charge transport), and Fourier's Law (heat transport).

Joule heating

resistive heatingohmic heatingJoule's law
Because the conduction of current is related to Joule heating of the conducting body, according to Joule's first law, the temperature of a conducting body may change when it carries a current.
Joule heating is referred to as ohmic heating or resistive heating because of its relationship to Ohm's Law.

Electrical resistivity and conductivity

electrical conductivityresistivityconductivity
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.
It starts from the tensor-vector form of Ohm's law, which relates the electric field inside a material to the electric current flow.

Green–Kubo relations

Green-Kubo relationsforce-flux lawGreen-Kubo
In broad terms, they fall under the topic of constitutive equations and the theory of transport coefficients.
The standard example of an electrical transport process is Ohm's law, which states that, at least for sufficiently small applied voltages, the current I is linearly proportional to the applied voltage V,