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, a Toronto home inspection, education & report writing tool company [ carsondunlop.com ].

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 ELECTRICAL RESISTANCE vs HEAT GENERATED

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 / m_ev_rms

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.

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Reader Q&A - also see RECOMMENDED ARTICLES & FAQs

Question: What do I need to hook up DC running lights and a porch light on a gutted Airstream International trailer?

I have a 1967 Airstream International planted in the backyard and want to run an extension cord out to it to run basic electric. It has 5 amber running lights and a porch light on the outside that runs on DC. It is completely gutted and I have access to the single wire from each fixture. What do I need to do to hook up the outside running lights to a power strip. - Rob

Reply: AC - DC power converter, extension cord, connectors, caution

Rob,

At your local electrical supplier or auto supply store or even at Radio Shack you should be able to pick up a small External AC to DC power converter (aka AC to DC Power Supply). What you need is a converter that will have high enough Amps output for the few trailer lights that you cited.

I used the term "External AC to DC Power converter or power supply because you don't want to have to buy a separate cabinet or case and do assembly. When shopping don't rule out existing computer or other electronic power supply "bricks" - just take a look at the DC Wattage output that the supply can provide. If it's big enough you'll be OK.

For just a few running lights and a porch light, most likely you won't even be drawing 10 watts, but to be on the safe side and to allow for expanded use of your power supply once you figure out how useful it is, I'd look at a unit with 35 watts or larger output.

Take a look at our DEFINITIONS of ELECTRICAL TERMS beginning at the top of this page for help with AC, DC, Amps, and Watts.

Run a weather-resistant outdoor-rated extension cord from an outdoor GFCI protected receptacle over to the Airstream and inside it where it will be weather protected. To that 120V (probably 15A) circuit, you'll plug in your AC to DC Converter. You'll then wire the DC output terminals to your Airstream lighting circuit.

If you're going to use this electrical supply system frequently you might want to put together a suitable plug connection feeding the DC powered circuit and a suitable connector on the wires that you run from the AC-DC converter.

For more permanent power conversion of an older Airstream or other mobile home or trailer, I'd look at what's offered by RV suppliers. Certainly I had no trouble retrofitting an AC to DC connector and power supply on an old slide-on pickup truck camper, thus allowing us to "plug in" to any 120V DC power source and run all of the DC devices in the camper.

Question: how to convert AC amps to DC Amps or vice versa

(May 26, 2015) Mike L said:
Is 1 amp AC equal to 1amp DC? My golf club stores the batteries for member's walking power carts. There are about 20 battery chargers and batteries plugged into one AC circuit that is presumably a 15 amp circuit. My charger has a 2 amp output to the battery and the others are probably the same.

If all of the batteries needed charging at the same time, drawing 40 amps, then the batteries would have to share the available 15 amps resulting in a very slow charge.
Am I correct?

Reply: apparent power (Volts Amps) vs "real" Power in Watts

Technically AC & DC amps are not precisely equivalent. The DC amperage draw will be slightly less than AC.

For example if you are selecting an electrical switch capable of handling 5A at 125VAC, it should be fine to use that switch on a DC current since the actual DC amperage draw will be a bit under 5 amps.

Apparent Power (VA) = Amps x Volts regardless of AC or DC

20A at 120VAC = 2,400 Watts (apparent power)

Also the amperage rating of a switch is increased as the voltage is decreased.

Example: a 120VAC 5-Amp switch can handle about 600 Watts and according to batterystuff.com's calculator, supports a 12-Volt DC amperage of 55.

The more-accurate formula for calculating watts is

Calculate Actual Power in Watts

Amps (A) x Volts (V) x Power Factor = Watts (W)

where the power factor of an AC circuit is the ratio of actual or "real" power consumed by the circuit (W) divided by the "apparent power" consumed by that circuit (VA).

So our first formula above is really "apparent power" in Watts.

What is the "power factor" ?

The power factor is a measure of the efficiency with which an electrical device onverts volt-amps into power. A 100% efficient electrical device would have a power-factor of 1.

But in all conventional electrical devices, some of the energy supplied by the circuit is lost in the form of heat. Thus the true power factor will be some number less than 1.

To know the actual efficiency or power factor of an electrical device we use a power meter, or a watt meter, an electrical test tool, to measure the actual power consumed in watts.

For an accurate calculation of actual energy consumed that includes the effects of AC current and power factors,

see DEFINITION of POWER FACTOR, REAL POWER

Question: how to calculate the operating cost of a well pump and booster pump

(June 18, 2015) barry said:
is there a formula i can use to calculate the cost of a water well pump, and a booster pump?

(June 18, 2015) bbrechbiel1950@gmail.com said:
hi my name is barry i had ask a question about calculating a well pump and booster pump for cost. i didn't receive an answer so i put my e-mail, by the way you do an excellent job on teaching basic electrical, keep up the good work. thanks barry 2000hrs 6-18-2015

Reply:

To convert the current draw (from the pump data tagor by actual measurement) to watts and watt hours to relate the electricity usage to what appears on your electric meter and electric bill in watt hours:

Energy E in watt-hours (Wh) = Power P (in watts W) x time period t in hours (h), or

E _(Wh) = P_(W) x t _(h)

Question: is it ok if a power inverter produces more amps than my application requires?

(July 5, 2015) layne said:
In selecting inverters for a specific product I know the Volts need to be the same, but as for the amps....if your inverter produces more Amps than needed, is this a problem?

Reply:

Layne

No not as I understand it; the amps rating is the maximum amount of current draw or demand that can be asked of the inverter. If your application draws less current that's ok.

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

Or see these

Recommended Articles

• DEFINITIONS of ELECTRICAL TERMS
  • BASIC FORMULAS Relating VOLTAGE, CURRENT (Amps), & RESISTANCE (Ohms or Ω ), Watts
  • DEFINITION of ALTERNATING CURRENT or AC
  • DEFINITION of AMPS or AMPERAGE
  • DEFINITION of DIRECT CURRENT or DC
  • DEFINITION of ELECTRICAL GROUND
  • DEFINITION of ELECTRICAL POTENTIAL
  • DEFINITION of ELECTRICAL RESISTANCE, OHM's LAW
  • DEFINITION of FAN ENERGY INDEX FEI
  • DEFINITION of JOULES HEATING LAW
  • DEFINITION of POWER FACTOR
  • DEFINITION of VOLTS or Voltage?
  • DEFINITION of VOLTAGE LEVEL DELIVERED
  • DEFINITION of WATTS or Electrical Wattage?
  • DEFINITION OF WATT-HOUR OR WH
  • DEFINITION of WATTS on a CIRCUIT

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OHM's LAW, ELECRICAL RESISTANCE at InspectApedia.com - online encyclopedia of building & environmental inspection, testing, diagnosis, repair, & problem prevention advice.

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