# Ohm s law

V is the voltage across the resistor I is the current through the resistor A linear resistor has a constant resistance value over all applied voltages or currents; many practical resistors are linear over a useful range of currents. Non-linear resistors have a value that may vary depending on the applied voltage or current. Where alternating current is applied to the circuit or where the resistance value is a function of timethe relation above is true at any instant but calculation of average power over an interval of time will require integration of "instantaneous" power over that interval. We consider it almost obvious today. When Ohm first published his work, this was not the case; critics reacted to his treatment of the subject with hostility.

They called his work a "web of naked fancies"  and the German Minister of Education proclaimed that "a professor who preached such heresies was unworthy to teach science. These factors hindered the acceptance of Ohm's work, and his work did not become widely accepted until the s.

However, Ohm received recognition for his contributions to science well before he died. In the s, Ohm's law was known Ohm s law 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. Thomsonand it was quickly realized that it is the particle charge carrier that carries electric currents in electric circuits. In the first classical model of electrical conduction, the Drude modelwas proposed by Paul Drudewhich finally gave a scientific explanation for Ohm's law.

In this model, a solid conductor consists of a stationary lattice of atoms ionswith conduction electrons moving randomly in it. A voltage across a conductor causes an electric fieldwhich accelerates the Ohm s law in the direction of the electric field, causing a drift of electrons which is the electric current.

However the electrons collide with and scatter off of the atoms, which randomizes their motion, thus converting the kinetic energy added to the electron by the field to heat thermal energy.

Using statistical distributions, it can be shown that the average drift velocity of the electrons, and thus the current, is proportional to the electric field, and thus the voltage, over a wide range of voltages.

The development of quantum mechanics in the s modified this picture somewhat, but in modern theories the average drift velocity of electrons can still be shown to be proportional Ohm s law the electric field, thus deriving Ohm's law. In Arnold Sommerfeld applied the quantum Fermi-Dirac distribution of electron energies to the Drude model, resulting in the free electron model.

A year later, Felix Bloch showed that electrons move in waves Bloch waves through a solid crystal lattice, so scattering off the lattice atoms as postulated in the Drude model is not a major process; the electrons scatter off impurity atoms and defects in the material.

The final successor, the modern quantum band theory of solids, showed that the electrons in a solid cannot take on any energy as assumed in the Drude model but are restricted to energy bands, with gaps between them of energies that electrons are forbidden to have.

The size of the band gap is a characteristic of a particular substance which has a great deal to do with its electrical resistivity, explaining why some substances are electrical conductorssome semiconductorsand some insulators. While the old term for electrical conductance, the mho the inverse of the resistance unit ohmis still used, a new name, the siemenswas adopted inhonoring Ernst Werner von Siemens.

The siemens is preferred in formal papers. In the s, it was discovered that the current through a practical resistor actually has statistical fluctuations, which depend on temperature, even when voltage and resistance are exactly constant; this fluctuation, now known as Johnson—Nyquist noiseis due to the discrete nature of charge.

Ohm's work long preceded Maxwell's equations and any understanding of frequency-dependent effects in AC circuits. Modern developments in electromagnetic theory and circuit theory do not contradict Ohm's law when they are evaluated within the appropriate limits.

Scope Ohm's law is an empirical lawa generalization from many experiments that have shown that current is approximately proportional to electric field for most materials. It is less fundamental than Maxwell's equations and is not always obeyed.

Any given material will break down under a strong-enough electric field, and some materials of interest in electrical engineering are "non-ohmic" under weak fields. In the early 20th century, it was thought that Ohm's law would fail at the atomic scalebut experiments have not borne out this expectation.

As ofresearchers have demonstrated that Ohm's law works for silicon wires as small as four atoms wide and one atom high. Drude model The dependence of the current density on the applied electric field is essentially quantum mechanical in nature; see Classical and quantum conductivity.

A qualitative description leading to Ohm's law can be based upon classical mechanics using the Drude model developed by Paul Drude in Electrons will be accelerated in the opposite direction to the electric field by the average electric field at their location.

With each collision, though, the electron is deflected in a random direction with a velocity that is much larger than the velocity gained by the electric field. The net result is that electrons take a zigzag path due to the collisions, but generally drift in a direction opposing the electric field.

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The drift velocity then determines the electric current density and its relationship to E and is independent of the collisions. Since both the momentum and the current density are proportional to the drift velocity, the current density becomes proportional to the applied electric field; this leads to Ohm's law.

Hydraulic analogy A hydraulic analogy is sometimes used to describe Ohm's law. Water pressure, measured by pascals or PSIis the analog of voltage because establishing a water pressure difference between two points along a horizontal pipe causes water to flow.

Water flow rate, as in liters per second, is the analog of current, as in coulombs per second.

## Ohm's Law Calculators

Finally, flow restrictors—such as apertures placed in pipes between points where the water pressure is measured—are the analog of resistors.

We say that the rate of water flow through an aperture restrictor is proportional to the difference in water pressure across the restrictor. Similarly, the rate of flow of electrical charge, that is, the electric current, through an electrical resistor is proportional to the difference in voltage measured across the resistor.

Flow and pressure variables can be calculated in fluid flow network with the use of the hydraulic ohm analogy.Resisting Current The collisions between electrons and atoms in a conductor cause resistance to the flow of charge. We measure that resistance in order to determine the effect that it will have on current.

Ohm's Law. There are 2 base formulae which will help you to understand the relationship between current, voltage, resistance and kaja-net.com you have any two of .

Simple to use Ohm's Law Calculator. Calculate Power, Current, Voltage or Resistance. Just enter 2 known values and the calculator will solve for the others. Experiment with an electronics kit! Build circuits with batteries, resistors, light bulbs, and switches. Determine if everyday objects are conductors or insulators, and take measurements with an ammeter and voltmeter.

View the circuit as a schematic diagram, or switch to a lifelike view. Ohm's Law and Formulas. Ohm's Law [after physicist Georg Ohm] states that: In an electrical circuit, the current which passes through a conductor between two points is proportional to the potential difference (i.e.

voltage drop or voltage) across the two points, and inversely proportional to the resistance between the two point. The Ohm's law equation is often explored in physics labs using a resistor, a battery pack, an ammeter, and a voltmeter.

An ammeter is a device used to measure the current at a given location. A voltmeter is a device equipped with probes that can be touched to two locations on a circuit to determine the electric potential difference across those.

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