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# Definition of Ohm's LawExplanation & measurement of electrical resistance

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Plain language definition of Ohms & Ohm's Law of electrical resistance:

What are Ohms and how are ohms or resistance measured & used in understanding electrical circuits, electrical resistance, and heat?

We also give a little of the history of the development of Ohm's law as well as links to supporting research.

This article series gives definitions of amps, volts, watts, resistance, current, ohms, electrical phases. We include basic formulas relating amps, volts, resistance, watts, and we explain what these electrical terms mean in practical applications such as for building or appliance electrical power, electrical wiring, and basic troubleshooting.

## What is the definition of Electrical Resistance & what is Ohm's Law?

Electrical Resistance is illustrated at left courtesy of Carson Dunlop Associates.

Electrical resistance is measured in Ohms Ω and is related to Watts and Volts by the simple equations we show here:

Watts = Volts 2 / Ohms

Current (Amps) = Potential (Volts) / Resistance (Ohms)

Electrical resistance can be thought of as how easily electricity flows through a material. Where resistance is high more effort is needed. A smaller-diameter electrical wire has more resistance to electrical flow than a larger-diameter wire.

A reason that the light bulb filament has high resistance is that it is very small in diameter.

Beginning with Thomas Edison, researchers discovered that if resistance in a wire is high enough the wire will get hot enough to glow (produce light) or even to start a fire (which is why the inside of an incandescent light bulb is a vacuum - to deny oxygen and thus protect the filament from simply burning up).

Ohm's Law, written about as early as 1791 and first formally published by Georg Simon Ohm (1789-1854) in 1827, states very simply the relationship between electrical current (Amps), electrical voltage (Volts) and the resistance of movement of electrical energy in a metallic conductor (Ohms).

I = V / R

tells us that the current (Amps) through a conductor (wire) between two points on a circuit is proportional to the potential difference (Voltage drop) across the two points and that the current (Amps) between the same two points is inversely proportional to the resistance between them (Ohms or Ω).

We can re-write Georg Ohm's law to describe each of amps, volts, or resistance in terms of the other parameters, as shown below.

I = the current, measured in Amps; I = V / R

and using simple algebra to re-write the Ohm's Law equation,

V = the difference in potential between the same two points, measured in Volts;

V = I x R

R = Ω or the resistance in the conductor or circuit between the same two points, measured in Ohms;

R = V / I

Also See JOULES HEATING LAW

## What is the Relationship Between Resistivity and Conductivity?

Resistivity

Resistivity or electrical resistance describes how strongly a material opposes or "resists" the flow of electric current. Low resistance means easy flow. High resistance means more-limited flow of electricity.

Symbols for resistivity are the greek letter ρ (rho) or the SI unit of electrical resistivity the ohm-metre (Ω . m)

The resistance between two contacts at two points of an electrical circuit is expressed in ohms or Ω.

Resistivity is the reciprocal of conductivity.

Technically, resistivity or electrical resistance is a measure of the scattering of electrons, where when more electrons are scattered the resistance is higher and can be written as

σ = ne2ℓ / mevrms

Where

σ = electrical conductivity [S/m]
n = density of free electrons [e/m3]
e = charge of an electron (1.60 × 10−19 C)
me = mass of an electron (9.11 × 10−31 kg)
vrms = root-mean-square speed of electrons [m/s]
ℓ = mean free path length [m]

Conductivity Electrical conductivity is a measure of the degree to which a material will conduct electricity.

Similarly, heat conductivity is the rate with which heat passes through a material, or the amount of heat that flows per unit of time through a unit area with a temperature gradient of one degree per unit of distance.

Conductivity can be calculated as the ratio of current density in the material to the electric field that causes the current flow.

The conductivity between two contacts at two points of an electrical circuit is expressed by the greek letter σ (sigma) as you'll see making a cameo appearance in Glenn Elert's homely formula above. Some texts use kappa κ or gamma γ or in SI units (S/m) (Siemens per metre) to express conductivity.

Conductivity is most-easily expressed as the reciprocal of resistivity.

Technically, conductivity in metals is a statistical/thermodynamic quantity. But that's not going to help us undestand how the little electric heater works in a room thermostat heat anticipator.

### Research & History of Ohms Law & Electrical Resistance

• Appleyard, Rollo. Pioneers of electrical communication. London, 1930.
• Elert, Glenn, Electric Resistance, The Physics Hypertextbook, [Web article] retrieved 2017/10/31, original source: https://physics.info/electric-resistance/
• Geddes, Leslie A., and L. E. Geddes. "How did Georg Simon Ohm do it?[Ohm's law]." IEEE Engineering in Medicine and Biology Magazine 17, no. 3 (1998): 107-109.
Abstract:

The "it" in the title refers to what is now known as Ohm's law. Georg Simon Ohm (1789-1854) lived at a time when there were no calibrated indicators for electric current. There was no volt or amp; these were established much later by the 1881 International Electrical Congress. The resources available to Ohm were:

1) the discovery of Oersted, who in 1520 showed that a magnetic field surrounded a wire carrying electric current;

2) the electrochemical cell, described by Volta in 1800; and

3) the thermoelectric effect, discovered by Seebeck in 1822.

How Ohm discovered his law with these varied and limited resources is the subject of this article.
• Jaffe, Lionel F., and R. Nuccitelli. "Electrical controls of development." Annual review of biophysics and bioengineering 6, no. 1 (1977): 445-476.
• Johnson, Don H. "Origins of the equivalent circuit concept: the voltage-source equivalent." Proceedings of the IEEE 91, no. 4 (2003): 636-640.
• Langley, Pat. "Data‐driven discovery of physical laws." Cognitive Science 5, no. 1 (1981): 31-54.
• Nazarov, Yuli V. "Generalized Ohm’s law." In Quantum Dynamics of Submicron Structures, pp. 687-704. Springer Netherlands, 1995.
• Olson, Richard G. "Sir John Leslie and the laws of electrical conduction in solids." American Journal of Physics 37, no. 2 (1969): 190-194.
Abstract:

It is contended that Sir John Leslie provided both a theoretical discussion and a limited experimental confirmation of Ohm's Law in a paper written in 1791 and published in 1824, three years prior to Ohm's presentation in Die galvanische Kette mathematische bearbeitet.
• Reingold, Nathan, and Ida H. Reingold, eds. Science in America: A documentary history, 1900-1939. University of Chicago Press, 1981.
• Schagrin, Morton L. "Resistance to Ohm's law." American Journal of Physics 31, no. 7 (1963): 536-547.
Abstract:

It is argued that the usual account of the discovery and subsequent rejection, or criticism, of Ohm's law is both a misleading and an inadequate explanation. A close logical examination of Ohm's experimental work reveals a conceptual structure quite different from that of the electrical science of his time.

As a result of this analysis, it is claimed that the conceptual shift in Ohm's experimental work was the basis for the reaction of his contemporaries.
• Teichmann, Jürgen. VOLTA AND THE QUANTITATIVE CONCEPTUALIZATION OF ELECTRICITY: FROM ELECTRICAL CAPACITY TO THE PRECONCEPTION OF OHM’S LAW [PDF] Nuova Voltiana: studies on Volta and his times 3 (2001): 53-80. Retrieved 2017/11/01, original source: http://ppp.unipv.it/Collana/Pages/Libri/Saggi/Nuova%20Voltiana3_PDF/cap3/3.pdf

Excerpt:
... Volta’s scientific concepts of – especially – “capacity”, (capacità), “tension” (tensione), “load” (quantità) became fruitful ground for new researches, e.g. for his electric battery programme, for his astonishing remarks about what was later called Ohm’s law, and for Ohm’s research itself in 1825-6.

These concepts were very closely related to simple mechanical ones and to refined but commonly reproducible measurements. The latter were importantly different from the electrostatic experiments of Charles-Augustin Coulomb (1786) and Henry Cavendish (1771); their measurements could not be handled so transparently.
• Turner, R. Steven. "The Ohm-Seebeck dispute, Hermann von Helmholtz, and the origins of physiological acoustics." The British journal for the history of science 10, no. 1 (1977): 1-24.

Abstract:
The term ‘Ohm's law’ traditionally denotes the formula of Georg Simon Ohm relating voltage, current, and resistance in metallic conductors. But to students of sensory physiology and its history, ‘Ohm's law’ also denotes another relationship: the fundamental principle of auditory perception that Ohm announced in 1843.

This aspect of Ohm's science has attracted very little attention, partly because his galvanic researches so thoroughly eclipsed it in success and importance, and partly because Ohm's work in physiological acoustics had so little immediate impact on the science of his time.

On announcing his hypothesis in 1843, Ohm found himself drawn into a bitter dispute with the physicist August Seebeck, who successfully discredited the hypothesis and forced Ohm to withdraw from the field.

...

Continue reading at JOULES HEATING LAW that explains resistive heating or ohmic heating, or select a topic from closely-related articles below, or see our complete INDEX to RELATED ARTICLES below.

Or see HEAT ANTICIPATOR OPERATION that explains the principles of Ohms law and Jules Heating Law applied to a tiny electric heater in a room thermostat.

Or see this

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