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This article is about the law related to electricity. For other uses, see
Ohm's acoustic law.
V, I, and R, the parameters of Ohm's law.
.^ The 'conductor' mentioned by Ohm's law is a circuit element across which the voltage is measured.- What is ohms law.? - Yahoo! Answers 11 January 2010 3:30 UTC answers.yahoo.com [Source type: FILTERED WITH BAYES]
^ With little voltage across it, its resistance is high.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Figure 1 - ohms law power consumption through a resistance .
^{[1]}
The mathematical equation that describes this relationship is:^{[2]}
where
.^ Here are the standard units of measurement for electrical current, voltage, and resistance: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ The unit of resistance is the Ohm, named after Georg Ohm .- Amateur Radio Manual/Ohm's Law and Resistors - Wikibooks, collection of open-content textbooks 11 January 2010 3:30 UTC en.wikibooks.org [Source type: FILTERED WITH BAYES]
^ I is the current in amperes , V is the potential difference in volts ,and R is a circuit parameter called the resistance (measured in ohms , also equivalent to volts per ampere).- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ Using Ohm's Law to determine current, we get: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ A similar assumption is made in the statement of Ohm's law: other things being alike, the strength of the current at each point is proportional to the gradient of electric potential.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Written as a mathematical expression, Ohms Law is Resistance(R)=voltage(V)/current(I) or R=V/I The above equation allows you to determine the value of the resistance when the voltage and the current are known.
^{[3]}
.^ Ohms Law The relationship between current(I), voltage(V or E), and resistance(R) was discovered by a German scientist named Georg Ohm.
^ In electric circuits, power is a function of both voltage and current.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ The "conductor" mentioned by Ohm's law is a circuit element across which the voltage is measured.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ He presented a slightly more complex equation than the one above to explain his experimental results.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
- What is ohms law.? - Yahoo! Answers 11 January 2010 3:30 UTC answers.yahoo.com [Source type: FILTERED WITH BAYES]
^ It's $30 more than the low voltage one.- Electricity FUBAR question [Archive] - Quarter To Three Forums 11 January 2010 3:30 UTC www.quartertothree.com [Source type: Original source]
^ So, overall, there are more electrons that make it over the various bridges in a certain amount of time than get over just the one "bridge" of the 10-ohm resistor.- Total Resistence in Parallel circuit - All About Circuits Forum 11 January 2010 3:30 UTC forum.allaboutcircuits.com [Source type: General]
.^ This equation is not a modification to Ohm's law.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ The above equation is the modern form of Ohm's law.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Equations for time-invariant AC circuits take the same form as Ohm's law, however, if the variables are generalized to complex numbers and the current and voltage waveforms are complex exponentials .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ Using Ohm's Law to determine current, we get: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Physics Physicists often use the continuum form of Ohm's Law:[3] where J is the current density (current per unit area, unlike the simpler I, units of amperes, of Ohm's law), σ is the conductivity (which can be a tensor in anisotropic materials) and E is the electric field (units of volts per meter, unlike the simpler V, units of volts, of Ohms's law).- What is ohms law.? - Yahoo! Answers 11 January 2010 3:30 UTC answers.yahoo.com [Source type: FILTERED WITH BAYES]
^ Ohm's law was probably the most important of the early quantitative descriptions of the physics of electricity.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
The simplest example of this is:
where
.^ The electrical resistance of a uniform conductor is given, in terms of conductivity, by: .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Physics Physicists often use the continuum form of Ohm's Law:[3] where J is the current density (current per unit area, unlike the simpler I, units of amperes, of Ohm's law), σ is the conductivity (which can be a tensor in anisotropic materials) and E is the electric field (units of volts per meter, unlike the simpler V, units of volts, of Ohms's law).- What is ohms law.? - Yahoo! Answers 11 January 2010 3:30 UTC answers.yahoo.com [Source type: FILTERED WITH BAYES]
^ J is the current density (current per unit area, unlike the simpler I, units of amperes, of Ohm's law), σ is the conductivity (which can be a tensor in anisotropic materials) and E is the electric field (units of volts per meter, unlike the simpler V, units of volts, of Ohm's law).- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
This reformulation of Ohm's law is due to
Gustav Kirchhoff.
^{[4]}
Microscopic origins of Ohm's law
Drude Model electrons (shown here in blue) constantly bounce between heavier, stationary crystal ions (shown in red).
.^ Current density j and field strength E may depend on the coordinates, because U and I depend on the coordinates, e.g.- Ohms Law and Materials Properties 18 September 2009 7:07 UTC www.tf.uni-kiel.de [Source type: FILTERED WITH BAYES]
^ When an electric field is applied, a slight imbalance develops and a current flows.- Total Resistence in Parallel circuit - All About Circuits Forum 11 January 2010 3:30 UTC forum.allaboutcircuits.com [Source type: General]
^ Investigate the possible advanced materials and novel nanostructures with enhanced mechanical-to-electrical power coupling efficiency to obtain power densities with magnitudes several orders of higher than the current technologies.- DARPA FY09.2 SBIR Solicitation Topics 11 January 2010 3:30 UTC www.dodsbir.net [Source type: Academic]
) A qualitative description leading to Ohm's law can be based upon
classical mechanics using the
Drude model developed by
Paul Drude in 1900.
^{[5]} ^{[6]}
.^ When the temperature of the conductor increases, the collisions between electrons and ions increase.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ So with the red wire ALREADY FILLED with electrons Okay, tell me the diffence (physically or electrically) between the state of atoms on the red wire and the other branch of the wire; before and after power is on.- Do electrons think? [Archive] - Physics Forums 11 January 2010 3:30 UTC www.physicsforums.com [Source type: Original source]
^ He is not implying that electrons find that they cannot go one way, so they back up and go the other.- Do electrons think? [Archive] - Physics Forums 11 January 2010 3:30 UTC www.physicsforums.com [Source type: Original source]
.^ Electrons in this band can be accelerated by the field because there are plenty of nearby states on the band.- Total Resistence in Parallel circuit - All About Circuits Forum 11 January 2010 3:30 UTC forum.allaboutcircuits.com [Source type: General]
^ Its value is the difference of two large numbers - the average velocity of the individual flies in the drift direction minus the average velocity of the individual flies in the direction opposite to the drift direction.- Ohms Law and Materials Properties 18 September 2009 7:07 UTC www.tf.uni-kiel.de [Source type: FILTERED WITH BAYES]
^ For a uniform applied field and defining the voltage in the usual convention of opposite direction to the field; .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ Electronic circuits can display highly complex behaviors, even though they are governed by the same laws as simple electrical circuits.- Calculating Voltage/Temperature thresholds - BlazingPC.com 11 January 2010 3:30 UTC www.blazingpc.com [Source type: General]
^ This drift velocity is usually much smaller than the average magnitude of the velocity < v > of the individual flies.- Ohms Law and Materials Properties 18 September 2009 7:07 UTC www.tf.uni-kiel.de [Source type: FILTERED WITH BAYES]
^ Though the connecting wires take a convoluted path in forming a complete circuit, there are several electrically common points in the electrons' path.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ I have always consistently opposed high-tension and alternating systems of electric lighting...not only on account of danger, but because of their general unreliability and unsuitability for any general system of distribution."- Erroneous Predictions 18 September 2009 7:07 UTC www.foresight.org [Source type: Original source]
^ Though the connecting wires take a convoluted path in forming a complete circuit, there are several electrically common points in the electrons' path.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ An electric circuit is formed when a conductive path is created to allow free electrons to continuously move.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ "Ohm's law states that for many materials (including most metals), the ratio of the current density and electric field is a constant, which is independent of the electric field producing the current.- Ohms Law - Page 2 - Electronic Circuits Projects Diagrams Free 18 September 2009 7:07 UTC www.electro-tech-online.com [Source type: Original source]
^ J is the current density (current per unit area, unlike the simpler I, units of amperes, of Ohm's law), σ is the conductivity (which can be a tensor in anisotropic materials) and E is the electric field (units of volts per meter, unlike the simpler V, units of volts, of Ohm's law).- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ 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.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ When the temperature of the conductor increases, the collisions between electrons and ions increase.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ But on the whole, ohm's law does not apply.- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
^ When an electric field is applied, a slight imbalance develops and a current flows.- Total Resistence in Parallel circuit - All About Circuits Forum 11 January 2010 3:30 UTC forum.allaboutcircuits.com [Source type: General]
^ Using Ohm's Law to determine current, we get: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
Temperature effects
.^ Using Ohm's Law to determine current, we get: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Ohm's law states that, in an electrical circuit, the current passing through a conductor between two points is directly proportional to the potential difference (i.e.- Nikon ML-3 wireless remote review [Archive] - Digital Camera Resource Page Forums 11 January 2010 3:30 UTC www.dcresource.com [Source type: General]
^ Actually, Ohm wrote (translated): "In a point of a homogeneous conductor through which permanent currents flow, the electromotive force is identical in both amplitude and direction to the electrostatic force as given by Coulomb's law".- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
That is, that the resistance, the ratio of the applied
electromotive force (or voltage) to the current, "does not vary with the current strength ." The qualifier "in a given state" is usually interpreted as meaning "at a constant temperature," since the resistivity of materials is usually temperature dependent.
.^ However, these power equations are so commonly associated with the Ohm's Law equations relating voltage, current, and resistance (E=IR ; I=E/R ; and R=E/I) that they are frequently credited to Ohm.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ It will be one value when you just turn the lightbulb on (and the filament is cold) and a different value when the filament is hot because the filament does not obey ohm's law, resistance is variable with temperature.- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
^ Hungryhaney First of all, the resistance of your mouth can vary dramatically because the mouth contains fluids, and contaminated fluids can conduct electricity with little resistance.- Toddler gets shocked with the USB Ipod charger 11 January 2010 3:30 UTC digg.com [Source type: General]
.^ What its (specific) resistance will be, including its temperature dependence.- Ohms Law and Materials Properties 18 September 2009 7:07 UTC www.tf.uni-kiel.de [Source type: FILTERED WITH BAYES]
^ Just as the resistance of a conductor depends upon temperature, the resistance of a conductor depends upon strain .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ In the 1920s, it was discovered that the current through an ideal resistor actually has statistical fluctuations, which depend on temperature, even when voltage and resistance are exactly constant; this fluctuation, now known as Johnson–Nyquist noise , is due to the discrete nature of charge.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ Your other questions need to be answered by: Lenz's "Law" No I can't forget Mr. Maxwell !- Ohms Law - Page 2 - Electronic Circuits Projects Diagrams Free 18 September 2009 7:07 UTC www.electro-tech-online.com [Source type: Original source]
^ Ohm's work long preceded Maxwell's equations and any understanding of frequency-dependent effects in AC circuits.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ The accuracy of the assumption that flow is proportional to the gradient is more readily tested, using modern measurement methods, for the electrical case than for the heat case.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^{[7]}
Hydraulic analogy
.^ A hydraulic analogy is sometimes used to describe Ohm's Law.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Using Ohm's Law to determine current, we get: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ I usually use ohm's law for calculating resistors in LED circuits in small-time prop projects.- www.TK560.com :: View topic - Question about the voltage calculator. 11 January 2010 3:30 UTC www.tk560.com [Source type: General]
.^ Water pressure, measured by pascals (or PSI ), is the analog of voltage because establishing a water pressure difference between two points along a (horizontal) pipe causes water to flow.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Voltage is a specific measure of potential energy that is always relative between two points.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Voltage is like the size of the pipe, amps are like the pressure of water through the pipe.- Electricity FUBAR question [Archive] - Quarter To Three Forums 11 January 2010 3:30 UTC www.quartertothree.com [Source type: Original source]
.^ Water flow rate, as in liters per second, is the analog of current, as in coulombs per second.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ An Amp is a Coulomb per second.- Do electrons think? [Archive] - Physics Forums 11 January 2010 3:30 UTC www.physicsforums.com [Source type: Original source]
^ We say that the rate of water flow through an aperture restrictor is proportional to the difference in water pressure across the restrictor.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ Finally, flow restrictors — such as apertures placed in pipes between points where the water pressure is measured — are the analog of resistors.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Water pressure, measured by pascals (or PSI ), is the analog of voltage because establishing a water pressure difference between two points along a (horizontal) pipe causes water to flow.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Water begins flowing out of the faucet immediately, but water further away does not start moving until it "feels" the drop in pressure ahead of it, as water molecules start to move.- Do electrons think? [Archive] - Physics Forums 11 January 2010 3:30 UTC www.physicsforums.com [Source type: Original source]
.^ We say that the rate of water flow through an aperture restrictor is proportional to the difference in water pressure across the restrictor.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Ohm's law states that, in an electrical circuit, the current passing through a conductor between two points is directly proportional to the potential difference (i.e.- Nikon ML-3 wireless remote review [Archive] - Digital Camera Resource Page Forums 11 January 2010 3:30 UTC www.dcresource.com [Source type: General]
^ The current in a circuit is directly proportional to the electric potential difference impressed across its ends and inversely proportional to the total resistance offered by the external circuit.
.^ We say that the rate of water flow through an aperture restrictor is proportional to the difference in water pressure across the restrictor.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ As the current encounters the 5 Ω resistance, voltage is dropped across the resistor's ends.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Electric current is the flow of electric charge by moving electrons.- Do electrons think? [Archive] - Physics Forums 11 January 2010 3:30 UTC www.physicsforums.com [Source type: Original source]
.^ A hydraulic analogy is sometimes used to describe Ohm's Law.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Flow and pressure variables can be calculated in fluid flow network with the use of the hydraulic ohm analogy.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ It may not always be useful, especially if you are dealing with active components, and if you have a few inductors or capacitors then you have to convert to the frequency domain to use (a variation of)ohm's law on them.- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
^{[8]}^{[9]} .^ The method can be applied to both steady and transient flow situations.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ Poiseuille's law Scientific laws named after people Ohm's acoustic law Hydraulic analogy Hopkinson's Law ("Ohm's Law for magnetics") Sheet resistance Walking along the resistive film - building various resistive circuits by reproducing Ohm's experiment nowadays .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Ohm's Law states that I=V/R. The toddlers skin would have to have an EXTREMELY low resistance for enough current to flow at 12v.- Toddler gets shocked with the USB Ipod charger 11 January 2010 3:30 UTC digg.com [Source type: General]
^ If the resistance to water flow stays the same and the pump pressure increases, the flow rate must also increase.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
Circuit analysis
In
circuit analysis, three equivalent expressions of Ohm's law are used interchangeably:
.^ That's one of three values in Ohm's Law.- www.TK560.com :: View topic - Question about the voltage calculator. 11 January 2010 3:30 UTC www.tk560.com [Source type: General]
^ "We stress that the relationship V=IR is not a statement of Ohm's law.- Ohms Law - Page 2 - Electronic Circuits Projects Diagrams Free 18 September 2009 7:07 UTC www.electro-tech-online.com [Source type: Original source]
^ All Ohm's law says is that Voltage is directly proportional to amps.- crap economy? watch your speed guys [Archive] - Steam Users' Forums 11 January 2010 3:30 UTC forums.steampowered.com [Source type: Original source]
^{[14]}^{[15]}
Resistive circuits
.^ Resistors are conductors that slow down the passage of electric charge.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ This symbol represents a resistor, and the R designates its resistance.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Ohm's law states that, in an electrical circuit, the current passing through a conductor between two points is directly proportional to the potential difference (i.e.- Nikon ML-3 wireless remote review [Archive] - Digital Camera Resource Page Forums 11 January 2010 3:30 UTC www.dcresource.com [Source type: General]
.^ The most common schematic symbol for a resistor is a zig-zag line: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Real resistors look nothing like the zig-zag symbol.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Sometimes resistor symbols are used in schematic diagrams to designate a non-specific load, rather than an actual resistor.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ That's one of three values in Ohm's Law.- www.TK560.com :: View topic - Question about the voltage calculator. 11 January 2010 3:30 UTC www.tk560.com [Source type: General]
^ The resistance of most resistive devices ( resistors ) is constant over a large range of values of current and voltage.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ When a resistor is used under these conditions, the resistor is referred to as an ohmic device (or an ohmic resistor ) because a single value for the resistance suffices to describe the resistive behavior of the device over the range.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ Equations for time-invariant AC circuits take the same form as Ohm's law, however, if the variables are generalized to complex numbers and the current and voltage waveforms are complex exponentials .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ However, the resistance will not be constant and it will NOT equal voltage/current.- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
^ Using Ohm's Law to determine current, we get: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ Ohm's law states that, in an electrical circuit, the current passing through a conductor between two points is directly proportional to the potential difference (i.e.- Nikon ML-3 wireless remote review [Archive] - Digital Camera Resource Page Forums 11 January 2010 3:30 UTC www.dcresource.com [Source type: General]
^ Equations for time-invariant AC circuits take the same form as Ohm's law, however, if the variables are generalized to complex numbers and the current and voltage waveforms are complex exponentials .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Resistor values in ohms are usually shown as an adjacent number, and if several resistors are present in a circuit, they will be labeled with a unique identifier number such as R 1 , R 2 , R 3 , etc.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ Well, not really, it's a circuit with parallel resistors.- www.TK560.com :: View topic - Question about the voltage calculator. 11 January 2010 3:30 UTC www.tk560.com [Source type: General]
^ But on the whole, ohm's law does not apply.- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
^ Ohm's law states that, in an electrical circuit, the current passing through a conductor between two points is directly proportional to the potential difference (i.e.- Nikon ML-3 wireless remote review [Archive] - Digital Camera Resource Page Forums 11 January 2010 3:30 UTC www.dcresource.com [Source type: General]
.^ Ohm's Law is a very simple and useful tool for analyzing electric circuits.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Using Ohm's Law to determine current, we get: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ How electrical engineers use Ohm's law .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
Reactive circuits with time-varying signals
.^ Equations for time-invariant AC circuits take the same form as Ohm's law, however, if the variables are generalized to complex numbers and the current and voltage waveforms are complex exponentials .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ That's one of three values in Ohm's Law.- www.TK560.com :: View topic - Question about the voltage calculator. 11 January 2010 3:30 UTC www.tk560.com [Source type: General]
^ The complex generalization of resistance is impedance , usually denoted Z ; it can be shown that for an inductor, .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ Using Ohm's Law to determine current, we get: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Ohm's law for power: Power equals Voltage times Current.- Backlinks to www.sengpielaudio.com back links - Mikrofonaufnahme und Tonstudiotechnik Some Back Links - Senkpiel ist immer Sengpiel - sengpielaudio Eberhard Sengpiel Berlin 11 January 2010 3:30 UTC www.sengpielaudio.com [Source type: FILTERED WITH BAYES]
^ Ohm's law states that, in an electrical circuit, the current passing through a conductor between two points is directly proportional to the potential difference (i.e.- Nikon ML-3 wireless remote review [Archive] - Digital Camera Resource Page Forums 11 January 2010 3:30 UTC www.dcresource.com [Source type: General]
^{[16]}
.^ Now that we know the current, we can take that value and multiply it by the voltage to determine power: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ If you hook up a lightbulb to a battery, both the voltage and the current will be constant (for some small amount of time as the battery does drain).- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
^ Ohm expressed his discovery in the form of a simple equation, describing how voltage, current, and resistance interrelate: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ Equations for time-invariant AC circuits take the same form as Ohm's law, however, if the variables are generalized to complex numbers and the current and voltage waveforms are complex exponentials .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ In this approach, a voltage or current waveform takes the form A e s t , where t is time, s is a complex parameter, and A is a complex scalar.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ In any linear time-invariant system , all of the currents and voltages can be expressed with the same s parameter as the input to the system, allowing the time-varying complex exponential term to be canceled out and the system described algebraically in terms of the complex scalars in the current and voltage waveforms.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
The complex generalization of resistance is
impedance, usually denoted
Z; it can be shown that for an inductor,
and for a capacitor,
We can now write,
where
.^ V and I are the complex scalars in the voltage and current respectively and Z is the complex impedance.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ In any linear time-invariant system , all of the currents and voltages can be expressed with the same s parameter as the input to the system, allowing the time-varying complex exponential term to be canceled out and the system described algebraically in terms of the complex scalars in the current and voltage waveforms.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ The real parts of such complex current and voltage waveforms describe the actual sinusoidal currents and voltages in a circuit, which can be in different phases due to the different complex scalars.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ How about, instead, we discuss the form of "torture" which is, you know, the topic of this thread, and when TPM starts a thread about electric-shock to testicles, or even Ohm's Law in general, I will be happy to discuss that in minute detail with you?- TPMmuckraker | Talking Points Memo | Mukasey Says Waterboarding "Repugnant" But Refuses Outright Condemnation 11 January 2010 3:30 UTC tpmmuckraker.talkingpointsmemo.com [Source type: Original source]
- TPMMuckraker | Talking Points Memo | Mukasey Says Waterboarding "Repugnant" But Refuses Outright Condemnation 11 January 2010 3:30 UTC tpmmuckraker.talkingpointsmemo.com [Source type: FILTERED WITH BAYES]
^ No - they don't follow Ohm's law in a strictly linear fashion - nothing about ohm's law says anything about linearity in the first place.- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
^ There are other mathematical principles of electricity that do take polarity into account through the use of signs (+ or -), but not Ohm's Law.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
When
Z is complex, only the real part is responsible for dissipating heat.
.^ In the general AC circuit, Z will vary strongly with the frequency parameter s , and so also will the relationship between voltage and current.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ In any linear time-invariant system , all of the currents and voltages can be expressed with the same s parameter as the input to the system, allowing the time-varying complex exponential term to be canceled out and the system described algebraically in terms of the complex scalars in the current and voltage waveforms.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ When such reactive elements, or transmission lines, are involved in a circuit, the relationship between voltage and current becomes the solution to a differential equation.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ For the common sinusoidal case, the s parameter is taken to be j ω , corresponding to a complex sinusoid A e j ω t .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ The real parts of such complex current and voltage waveforms describe the actual sinusoidal currents and voltages in a circuit, which can be in different phases due to the different complex scalars.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ V and I are the complex scalars in the voltage and current respectively and Z is the complex impedance.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ In this approach, a voltage or current waveform takes the form A e s t , where t is time, s is a complex parameter, and A is a complex scalar.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
Linear approximations
.^ That's one of three values in Ohm's Law.- www.TK560.com :: View topic - Question about the voltage calculator. 11 January 2010 3:30 UTC www.tk560.com [Source type: General]
^ This equation is not a modification to Ohm's law.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ How electrical engineers use Ohm's law .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ It applies to both metal conductors and circuit components ( resistors ) specifically made for this behaviour.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ There are circuit components specifically engineered to provide nonlinear resistance curves, one of them being the varistor .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ So far, we've been analyzing single-battery, single-resistor circuits with no regard for the connecting wires between the components, so long as a complete circuit is formed.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ Both are ubiquitous in electrical engineering.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Now, Mr. Electrical Engineer, it is time for both of us to "put-up or shut-up."- Toddler gets shocked with the USB Ipod charger 11 January 2010 3:30 UTC digg.com [Source type: General]
.^ That's one of three values in Ohm's Law.- www.TK560.com :: View topic - Question about the voltage calculator. 11 January 2010 3:30 UTC www.tk560.com [Source type: General]
^ But on the whole, ohm's law does not apply.- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
^ With current steady, voltage follows resistance (an increase in resistance means an increase in voltage).- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ The plot is no longer a straight line.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ A "linear" function in mathematics is one that tracks a straight line when plotted on a graph.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ So although current and voltage stay the same, the resistance changes.- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
.^ The resistance of most resistive devices ( resistors ) is constant over a large range of values of current and voltage.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ With little voltage across it, its resistance is high.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ If we know the values of any two of the three quantities (voltage, current, and resistance) in this circuit, we can use Ohm's Law to determine the third.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ How voltage, current, and resistance relate .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Ohm's law states that, in an electrical circuit, the current passing through a conductor between two points is directly proportional to the potential difference (i.e.- Nikon ML-3 wireless remote review [Archive] - Digital Camera Resource Page Forums 11 January 2010 3:30 UTC www.dcresource.com [Source type: General]
^ "In a true ohmic device, the same value of resistance will be calculated from R = V/I regardless of the value of the applied voltage V. That is, the ratio of V/I is constant, and when current is plotted as a function of voltage the curve is linear (a straight line)."- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
.^ Plot of I–V curve of an ideal p-n junction diode at 1μA reverse leakage current.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Ohm%27s_law Since we're agreed that when current is plotted against voltage, the curve is not linear for a light bulb, it's obviously not ohmic.- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
Failure of the device to follow Ohm's law is clearly shown since the curve is not a straight line.
.^ In electric circuits, power is a function of both voltage and current.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ 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.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Calculation of Ohm's law · The Magic Triangle Calculation of electric power, voltage, current and resistance .- Backlinks to www.sengpielaudio.com back links - Mikrofonaufnahme und Tonstudiotechnik Some Back Links - Senkpiel ist immer Sengpiel - sengpielaudio Eberhard Sengpiel Berlin 11 January 2010 3:30 UTC www.sengpielaudio.com [Source type: FILTERED WITH BAYES]
.^ An example is the p-n junction diode .- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Plot of I–V curve of an ideal p-n junction diode at 1μA reverse leakage current.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ As it progresses to the right we see the line flattening out, the circuit requiring greater and greater increases in voltage to achieve equal increases in current.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ If we were to plot current over voltage on a graph as we did with the lamp circuit, the effect of ionization would be clearly seen as nonlinear: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Swipecat, on 10/03/2009 , -0/+1 A light bulb filament is a metal, which is Ohmic, meaning that the current is (near enough) proportional to the applied voltage at a given temperature.- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
.^ That's one of three values in Ohm's Law.- www.TK560.com :: View topic - Question about the voltage calculator. 11 January 2010 3:30 UTC www.tk560.com [Source type: General]
^ If we know the values of any two of the three quantities (voltage, current, and resistance) in this circuit, we can use Ohm's Law to determine the third.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ If we try to apply Ohm's Law to find the resistance of this lamp circuit with the voltage and current values plotted above, we arrive at several different values.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ As it progresses to the right we see the line flattening out, the circuit requiring greater and greater increases in voltage to achieve equal increases in current.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Because the slope of the current/voltage for this phenomenon is negative (angling down instead of up as it progresses from left to right), it is known as negative resistance .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Swipecat, on 10/03/2009 , -0/+1 A light bulb filament is a metal, which is Ohmic, meaning that the current is (near enough) proportional to the applied voltage at a given temperature.- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
.^ Here is a further statement, " This quantity is sometimes called simply resistance, although the two definitions are equivalent only for an ohmic component such as an ideal resistor."- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
^ There are circuit components specifically engineered to provide nonlinear resistance curves, one of them being the varistor .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ It will be one value when you just turn the lightbulb on (and the filament is cold) and a different value when the filament is hot because the filament does not obey ohm's law, resistance is variable with temperature.- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
.^ The resistance of most resistive devices ( resistors ) is constant over a large range of values of current and voltage.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ With current steady, voltage follows resistance (an increase in resistance means an increase in voltage).- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ However, in some diode applications, the AC signal applied to the device is small and it is possible to analyze the circuit in terms of the dynamic , small-signal , or incremental resistance, defined as the slope of the V–I curve (or inverse slope of the I–V curve, that is, the derivative of current with respect to voltage).- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ That's one of three values in Ohm's Law.- www.TK560.com :: View topic - Question about the voltage calculator. 11 January 2010 3:30 UTC www.tk560.com [Source type: General]
^ For sufficiently small signals, the dynamic resistance allows the Ohm's law proportionality to be applied as an approximation.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ A similar assumption is made in the statement of Ohm's law: other things being alike, the strength of the current at each point is proportional to the gradient of electric potential.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^{[20]}
Relation to heat conductions
Ohm's principle predicts the flow of electrical charge (i.e. current) in electrical conductors when subjected to the influence of voltage differences;
Jean-Baptiste-Joseph Fourier's principle predicts the flow of
heat in heat conductors when subjected to the influence of temperature differences.
.^ Both phenomena can exist simultaneously in the same system.- TPMmuckraker | Talking Points Memo | Mukasey Says Waterboarding "Repugnant" But Refuses Outright Condemnation 11 January 2010 3:30 UTC tpmmuckraker.talkingpointsmemo.com [Source type: Original source]
- TPMMuckraker | Talking Points Memo | Mukasey Says Waterboarding "Repugnant" But Refuses Outright Condemnation 11 January 2010 3:30 UTC tpmmuckraker.talkingpointsmemo.com [Source type: FILTERED WITH BAYES]
^ Horsepower and watts are merely two different units for describing the same kind of physical measurement, with 1 horsepower equaling 745.7 watts.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Ohm's law describes both an instantaneous and average value because it's only applicable to a linear relationship between V and I where the instantaneous and average values are the same.- xkcd - A Webcomic - Ohm 11 January 2010 3:30 UTC digg.com [Source type: Original source]
Specifically, solving a heat conduction (Fourier) problem with
temperature (the driving "force") and
flux of heat (the rate of flow of the driven "quantity", i.e. heat energy) variables also solves an analogous
electrical conduction (Ohm) problem having
electric potential (the driving "force") and
electric current (the rate of flow of the driven "quantity", i.e. charge) variables.
The basis of Fourier's work was his clear conception and definition of
thermal conductivity.
.^ He assumed that, all else being the same, the flux of heat is strictly proportional to the gradient of temperature.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ A similar assumption is made in the statement of Ohm's law: other things being alike, the strength of the current at each point is proportional to the gradient of electric potential.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Although undoubtedly true for small temperature gradients, strictly proportional behavior will be lost when real materials (e.g.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ Although undoubtedly true for small temperature gradients, strictly proportional behavior will be lost when real materials (e.g.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ He assumed that, all else being the same, the flux of heat is strictly proportional to the gradient of temperature.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
ones having a thermal conductivity that is a function of temperature) are subjected to large temperature gradients.
.^ A similar assumption is made in the statement of Ohm's law: other things being alike, the strength of the current at each point is proportional to the gradient of electric potential.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
^ Using Ohm's Law to determine current, we get: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Ohm's law was probably the most important of the early quantitative descriptions of the physics of electricity.- Ohm's Law 11 January 2010 3:30 UTC jugandi.com [Source type: Academic]
.^ In this case, however, power (P) is exactly equal to current (I) multiplied by voltage (E), rather than merely being proportional to IE. When using this formula, the unit of measurement for power is the watt , abbreviated with the letter "W." .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Newer houses suffer the same possibility but usually with less frequency because they use Copper now and modern wire can withstand heat better.- Electricity FUBAR question [Archive] - Quarter To Three Forums 11 January 2010 3:30 UTC www.quartertothree.com [Source type: Original source]
^ As odd as it may seem, the actual mathematical relationship between pressure, flow, and resistance is actually more complex for fluids like water than it is for electrons.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
Other versions of Ohm's law
.^ If we know the values of any two of the three quantities (voltage, current, and resistance) in this circuit, we can use Ohm's Law to determine the third.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Here are the standard units of measurement for electrical current, voltage, and resistance: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Using Ohm's Law to determine current, we get: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ Using Ohm's Law to determine current, we get: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ The law was proposed by physicist Georg Ohm, who also proposed famous electrical law, which is similarly called Ohm's law."- Belkin's RockStar channels jams to five others -- Engadget 11 January 2010 3:30 UTC www.engadget.com [Source type: FILTERED WITH BAYES]
^ Ohm's law states that, in an electrical circuit, the current passing through a conductor between two points is directly proportional to the potential difference (i.e.- Nikon ML-3 wireless remote review [Archive] - Digital Camera Resource Page Forums 11 January 2010 3:30 UTC www.dcresource.com [Source type: General]
Physicists often use this continuum form of Ohm's Law:
^{[21]}
where
.^ Calculation of Ohm's law · The Magic Triangle Calculation of electric power, voltage, current and resistance .- Backlinks to www.sengpielaudio.com back links - Mikrofonaufnahme und Tonstudiotechnik Some Back Links - Senkpiel ist immer Sengpiel - sengpielaudio Eberhard Sengpiel Berlin 11 January 2010 3:30 UTC www.sengpielaudio.com [Source type: FILTERED WITH BAYES]
^ Here are the standard units of measurement for electrical current, voltage, and resistance: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Using Ohm's Law to determine current, we get: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
The above equation is sometimes written
^{[22]} as
J =
σE where "σ" is the
conductivity which is the reciprocal of ρ.
Current flowing through a uniform cylindrical conductor (such as a round wire) with a uniform field applied.
The potential difference between two points is defined as:^{[23]}
with
the element of path along the integration of electric field vector
E. If the applied
E field is uniform and oriented along the length of the conductor as shown in the figure, then defining the voltage V in the usual convention of being opposite in direction to the field (see figure), and with the understanding that the voltage V is measured differentially across the length of the conductor allowing us to drop the Δ symbol, the above vector equation reduces to the scalar equation:
Since the E field is uniform in the direction of wire length, for a conductor having uniformly consistent resistivity ρ, the current density J will also be uniform in any cross-sectional area and oriented in the direction of wire length, so we may write:^{[24]}
Substituting the above 2 results (for E and J respectively) into the continuum form shown at the beginning of this section:
where
.^ That step function in voltage propagates down the twisted pair wire at c/n, where n is related to the capacitance and inductance per unit length of the transmission line.- Do electrons think? [Archive] - Physics Forums 11 January 2010 3:30 UTC www.physicsforums.com [Source type: Original source]
^ The conductivity ( ) of a material is determined by taking the reciprocal of the measured electrical resistance (R) to the flow of electricity in a length (L) of material divided by the cross-sectional area (A).- Calculating Voltage/Temperature thresholds - BlazingPC.com 11 January 2010 3:30 UTC www.blazingpc.com [Source type: General]
^ With wire resistance being zero, the voltage drop across any continuous stretch of wire can be determined through Ohm's Law as such: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
After substitution of R from the above equation into the equation preceding it, the continuum form of Ohm's law for a uniform field (and uniform current density) oriented along the length of the conductor reduces to the more familiar form:
.^ The bus speed can be increased for a stable OC as long as the resistance is low enough for the signal to flow unimpeded along the circuit.- Calculating Voltage/Temperature thresholds - BlazingPC.com 11 January 2010 3:30 UTC www.blazingpc.com [Source type: General]
^ In such a case, there would be zero resistance, a lot of heat and possibly sparks just prior and just after every moment the metal made contact.- Toddler gets shocked with the USB Ipod charger 11 January 2010 3:30 UTC digg.com [Source type: General]
^ Likewise, if we were to have a short circuit constructed of a loop of superconducting wire (absolutely zero resistance), we could have a condition of current in the loop with zero voltage, and likewise no power would be dissipated.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ All of this makes sense, of course, so long as the lamp continues to provide exactly the same amount of friction (resistance) to the flow of electrons through it: 3 Ω.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ The amount of current in a circuit depends on the amount of voltage available to motivate the electrons, and also the amount of resistance in the circuit to oppose electron flow.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ As odd as it may seem, the actual mathematical relationship between pressure, flow, and resistance is actually more complex for fluids like water than it is for electrons.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ How about, instead, we discuss the form of "torture" which is, you know, the topic of this thread, and when TPM starts a thread about electric-shock to testicles, or even Ohm's Law in general, I will be happy to discuss that in minute detail with you?- TPMmuckraker | Talking Points Memo | Mukasey Says Waterboarding "Repugnant" But Refuses Outright Condemnation 11 January 2010 3:30 UTC tpmmuckraker.talkingpointsmemo.com [Source type: Original source]
- TPMMuckraker | Talking Points Memo | Mukasey Says Waterboarding "Repugnant" But Refuses Outright Condemnation 11 January 2010 3:30 UTC tpmmuckraker.talkingpointsmemo.com [Source type: FILTERED WITH BAYES]
^ It will be critically important in the analysis of more complex circuits involving multiple resistors and/or batteries.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ For purposes of this discussion I am focusing on electrical breakdown as it relates to an electrical circuit and in particular current (electron) migration (more on this later).- Calculating Voltage/Temperature thresholds - BlazingPC.com 11 January 2010 3:30 UTC www.blazingpc.com [Source type: General]
In broad terms, they fall under the topic of
constitutive equations and the theory of
transport coefficients.
Magnetic effects
The continuum form of the equation is only valid in the
reference frame of the conducting material. If the material is moving at velocity
v relative to a
magnetic field B, a term must be added as follows:
See
Lorentz force for more on this and
Hall effect for some other implications of a magnetic field.
.^ However, these power equations are so commonly associated with the Ohm's Law equations relating voltage, current, and resistance (E=IR ; I=E/R ; and R=E/I) that they are frequently credited to Ohm.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Surveying our array of Ohm's Law equations, we find two equations that give us answers from known quantities of voltage and current: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ It should be understood that polarity has nothing to do with Ohm's Law: there will never be negative voltages, currents, or resistance entered into any Ohm's Law equations!- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ There are other mathematical principles of electricity that do take polarity into account through the use of signs (+ or -), but not Ohm's Law.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ If we were to triple the voltage in our last example circuit from 10 to 30 volts and keep the circuit resistance unchanged, we would expect the current to triple as well.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
Ohm's law in a plasma
In plasma physics, the generalized Ohm's law is given by
where
.^ As odd as it may seem, the actual mathematical relationship between pressure, flow, and resistance is actually more complex for fluids like water than it is for electrons.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ Cast in these terms, current is the rate of electric charge motion through a conductor.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
The resistive electric field is given by
.
.^ As odd as it may seem, the actual mathematical relationship between pressure, flow, and resistance is actually more complex for fluids like water than it is for electrons.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
The divergence of the electron pressure is given by
.
.^ Notice how there are only two variable terms on the right-hand side of the equation, S and T. All the other terms on that side are constant: 2, pi, and 33,000 are all constants (they do not change in value).- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
Magnetic topology cannot be changed by the convective electric field, the Hall electric field, or an electric field due to scalar electron pressure.
.^ As odd as it may seem, the actual mathematical relationship between pressure, flow, and resistance is actually more complex for fluids like water than it is for electrons.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ REVIEW: The polarity of the voltage drop across any resistive component is determined by the direction of electron flow through it: negative entering, and positive exiting.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ A varistor is a component that changes resistance with the amount of voltage impressed across it.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
The generalized Ohm's law plays a particularly important role in
magnetic reconnection.
History
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.
.^ If we have a water pump that exerts pressure (voltage) to push water around a "circuit" (current) through a restriction (resistance), we can model how the three variables interrelate.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ In addition to voltage and current, there is another measure of free electron activity in a circuit: power .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ In my circuits 1 class we spent the last day of class talking about how much current it takes to kill some one.- Toddler gets shocked with the USB Ipod charger 11 January 2010 3:30 UTC digg.com [Source type: General]
.^ Ohm's Law is not very useful for analyzing the behavior of components like these where resistance varies with voltage and current.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ For this reason we can regard the resistance of many circuit components as a constant, with voltage and current being directly related to each other.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ In circuits where resistance varies with changes in either voltage or current, the plot of current over voltage will be nonlinear (not a straight line).- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
He did not communicate his results to other scientists at the time,
^{[26]} and his results were unknown until
Maxwell published them in 1879.
^{[27]}
.^ When George Simon Ohm's theory of electricity was published in 1827 in his book "The Galvanic Chain, Mathematically Worked Out," it was called .- Erroneous Predictions 18 September 2009 7:07 UTC www.foresight.org [Source type: Original source]
^ The first, and perhaps most important, relationship between current, voltage, and resistance is called Ohm's Law, discovered by Georg Simon Ohm and published in his 1827 paper, The Galvanic Circuit Investigated Mathematically .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ By observing the results of a computer simulation, a student can gain an intuitive grasp of circuit behavior without the intimidation of abstract mathematical analysis.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^{[28]} He drew considerable inspiration from
Fourier's work on heat conduction in the theoretical explanation of his work.
.^ Resistors, which are manufactured to provide a definite, stable value of resistance, behave very much like the plot of values seen above.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ In the above circuit, there is only one source of voltage (the battery, on the left) and only one source of resistance to current (the lamp, on the right).- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ The increase in resistance will decrease the current to the amp, as well as its supply voltage: E = I R. Voltage sources do not "compensate" by increasing current.- VWvortex Forums: Lights dim 11 January 2010 3:30 UTC forums.vwvortex.com [Source type: General]
.^ If we know the values of any two of the three quantities (voltage, current, and resistance) in this circuit, we can use Ohm's Law to determine the third.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Electrical power is almost always measured in "watts," and it can be calculated by the formula P = IE. Electrical power is a product of both voltage and current, not either one separately.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Ohm's Law is not very useful for analyzing the behavior of components like these where resistance varies with voltage and current.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ Does the wire length or circuit "shape" matter to our calculations?- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ So far, we've been analyzing single-battery, single-resistor circuits with no regard for the connecting wires between the components, so long as a complete circuit is formed.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Though the connecting wires take a convoluted path in forming a complete circuit, there are several electrically common points in the electrons' path.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
He found that his data could be modeled through the equation
where
.^ It is worth mentioning that temperature dependence does not make a substance non-ohmic, because at a given temperature R does not vary with voltage or current (V / I = constant).- Calculating Voltage/Temperature thresholds - BlazingPC.com 11 January 2010 3:30 UTC www.blazingpc.com [Source type: General]
^ The resistance of an Ohmic substance depends on temperature in the following way: R = L/A * P = L/A * Po(@(T-To)+1) Where ρ is the resistivity, L is the length of the conductor, A is its cross-sectional area, T is its temperature, T0 is a reference temperature (usually room temperature), and ρ0 and α are constants specific to the material of interest.- Calculating Voltage/Temperature thresholds - BlazingPC.com 11 January 2010 3:30 UTC www.blazingpc.com [Source type: General]
.^ Using Ohm's Law to determine current, we get: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ If we know the values of any two of the three quantities (voltage, current, and resistance) in this circuit, we can use Ohm's Law to determine the third.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ With wire resistance being zero, the voltage drop across any continuous stretch of wire can be determined through Ohm's Law as such: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ There are other mathematical principles of electricity that do take polarity into account through the use of signs (+ or -), but not Ohm's Law.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ The first, and perhaps most important, relationship between current, voltage, and resistance is called Ohm's Law, discovered by Georg Simon Ohm and published in his 1827 paper, The Galvanic Circuit Investigated Mathematically .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ I am probably incorrect with my point about it being an oversimplification to rely on Ohm's Law while using nominal values, to summarize the toddler mouth-burns.- Toddler gets shocked with the USB Ipod charger 11 January 2010 3:30 UTC digg.com [Source type: General]
We consider it almost obvious today.
.^ When George Simon Ohm's theory of electricity was published in 1827 in his book "The Galvanic Chain, Mathematically Worked Out," it was called .- Erroneous Predictions 18 September 2009 7:07 UTC www.foresight.org [Source type: Original source]
They called his work a "web of naked fancies"
^{[29]} and the German Minister of Education proclaimed that "a professor who preached such heresies was unworthy to teach science."
^{[30]} The prevailing scientific philosophy in Germany at the time, led by
Hegel, asserted that experiments need not be performed to develop an understanding of nature because nature is so well ordered, and that scientific truths may be deduced through reasoning alone. Also, Ohm's brother Martin, a mathematician, was battling the German educational system. These factors hindered the acceptance of Ohm's work, and his work did not become widely accepted until the 1840s. Fortunately, Ohm received recognition for his contributions to science well before he died.
In the 1850s, Ohm's law was known as such, and was widely considered proved, and alternatives such as "
Barlow's law" discredited, in terms of real applications to telegraph system design, as discussed by
Samuel F. B. Morse in 1855.
^{[31]}
.^ Ohm's Law is not very useful for analyzing the behavior of components like these where resistance varies with voltage and current.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Ohm's Law is a very simple and useful tool for analyzing electric circuits.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Each unit of measurement is named after a famous experimenter in electricity: The amp after the Frenchman Andre M. Ampere, the volt after the Italian Alessandro Volta, and the ohm after the German Georg Simon Ohm.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
The siemens is preferred in formal papers.
.^ Then it displays the current through each voltage source.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ How voltage, current, and resistance relate .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ As the current encounters the 5 Ω resistance, voltage is dropped across the resistor's ends.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ Calculation of Ohm's law · The Magic Triangle Calculation of electric power, voltage, current and resistance .- Backlinks to www.sengpielaudio.com back links - Mikrofonaufnahme und Tonstudiotechnik Some Back Links - Senkpiel ist immer Sengpiel - sengpielaudio Eberhard Sengpiel Berlin 11 January 2010 3:30 UTC www.sengpielaudio.com [Source type: FILTERED WITH BAYES]
^ How voltage, current, and resistance relate .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Here are the standard units of measurement for electrical current, voltage, and resistance: .- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ However, these power equations are so commonly associated with the Ohm's Law equations relating voltage, current, and resistance (E=IR ; I=E/R ; and R=E/I) that they are frequently credited to Ohm.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
.^ I didn't say that Ohms Law is a theory.- Toddler gets shocked with the USB Ipod charger 11 January 2010 3:30 UTC digg.com [Source type: General]
^ Resistor values in ohms are usually shown as an adjacent number, and if several resistors are present in a circuit, they will be labeled with a unique identifier number such as R 1 , R 2 , R 3 , etc.- Lessons In Electric Circuits -- Volume I (DC) - Chapter 2 18 September 2009 7:07 UTC openbookproject.net [Source type: FILTERED WITH BAYES]
^ Electronic circuits can display highly complex behaviors, even though they are governed by the same laws as simple electrical circuits.- Calculating Voltage/Temperature thresholds - BlazingPC.com 11 January 2010 3:30 UTC www.blazingpc.com [Source type: General]
See also
References
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- ^ ^{a} ^{b} Robert A. Millikan and E. S. Bishop (1917). Elements of Electricity. American Technical Society. p. 54. http://books.google.com/books?id=dZM3AAAAMAAJ&pg=PA54&dq=%22Ohm%27s+law%22++current+directly+proportional&lr=&as_brr=3&as_pt=ALLTYPES&ei=V4wPStPrI4jSkwS4vN3UCQ.
- ^ Oliver Heaviside (1894). Electrical papers. 1. Macmillan and Co. p. 283. http://books.google.com/books?id=lKV-AAAAMAAJ&pg=PA284&dq=ohm%27s+law+constant+ratio&lr=&as_brr=1&ei=ZNLPSt2_OZuOkQSj-dTjBQ#v=onepage&q=ohm's%20law%20constant%20ratio&f=false.
- ^ Olivier Darrigol, Electrodynamics from Ampère to Einstein, p.70, Oxford University Press, 2000 ISBN 0198505949.
- ^ Drude, Paul (1900). "Zur Elektronentheorie der metalle". Annalen der Physik 306 (3): 566. http://www3.interscience.wiley.com/cgi-bin/fulltext/112485959/PDFSTART.
- ^ Drude, Paul (1900). "Zur Elektronentheorie der Metalle; II. Teil. Galvanomagnetische und thermomagnetische Effecte". Annalen der Physik 308 (11): 369. http://www3.interscience.wiley.com/cgi-bin/fulltext/112485893/PDFSTART.
- ^ Normal Lockyer, ed (Sept. 21, 1876). "Reports". Nature (Macmillan Journals Ltd) 14: 452. http://books.google.com/books?id=-8gKAAAAYAAJ&pg=PA452&dq=ohm%27s-law+temperature&lr=&as_drrb_is=q&as_minm_is=0&as_miny_is=&as_maxm_is=0&as_maxy_is=&as_brr=3&ei=_BPJSqDeIqW6lATGusiuAw#v=onepage&q=ohm's-law%20temperature&f=false.
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- ^ A. Esposito, "A Simplified Method for Analyzing Circuits by Analogy", Machine Design, October 1969, pp. 173–177.
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- ^ Dale R. Patrick and Stephen W. Fardo (1999). Understanding DC circuits. Newnes. p. 96. ISBN 9780750671101. http://books.google.com/books?id=wyC5SFtZskMC&pg=PA96&dq=%22Ohm%27s+law%22+%22R+%3D%22+%22V+%3D%22+%22I+%3D%22&lr=&as_brr=3&as_pt=ALLTYPES&ei=V3cQSrCMG4uSkASxiKXSCQ#PPA96,M1.
- ^ Thomas O'Conor Sloane (1909). Elementary electrical calculations. D. Van Nostrand Co. p. 41. http://books.google.com/books?id=e89IAAAAIAAJ&pg=PA41&dq=R%3D+%22Ohm%27s+law%22+proportional&lr=&as_brr=1&as_pt=ALLTYPES&ei=unMQSteUF5CGkAS3zdnPCQ.
- ^ Linnaeus Cumming (1902). Electricity treated experimentally for the use of schools and students. Longman's Green and Co. p. 220. http://books.google.com/books?id=3iUJAAAAIAAJ&pg=PA220&dq=V%3DIR+%22Ohm%27s+law%22&lr=&as_drrb_is=q&as_minm_is=0&as_miny_is=&as_maxm_is=0&as_maxy_is=&as_brr=1&as_pt=ALLTYPES&ei=rXIQSvWZDIvUkwSd9azYCQ.
- ^ Benjamin Stein (1997). Building technology (2nd ed.). John Wiley and Sons. p. 169. ISBN 9780471593195. http://books.google.com/books?id=J_RSbj_KzAQC&pg=PA169&dq=%22Ohm%27s+law+that+V%3D%22&lr=&as_brr=3&as_pt=ALLTYPES&ei=U3UQStD7Oo6ukASXjf25AQ.
- ^ Rajendra Prasad (2006). Fundamentals of Electrical Engineering. Prentice-Hall of India. http://books.google.com/books?id=nsmcbzOJU3kC&pg=PA140&dq=ohm%27s-law+complex+exponentials&lr=&as_brr=3&ei=k1rwR4ffNo2AsgPNhtnCBg&sig=mjShqNIvu1F9qL5g7I7ET2JrOg8#PPA138,M1.
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- ^ Kenneth L. Kaiser (2004). Electromagnetic Compatibility Handbook. CRC Press. p. 13–52. ISBN 9780849320873. http://books.google.com/books?id=nZzOAsroBIEC&pg=PT1031&dq=%22static+resistance%22+%22dynamic+resistance%22+nonlinear&lr=&as_brr=3&ei=Kk50Ser1MJeOkAS9wNTwDg#PPT1031,M1.
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- ^ Taliaferro Preston (1855). Shaffner's Telegraph Companion: Devoted to the Science and Art of the Morse Telegraph. Vol.2. Pudney & Russell. http://books.google.com/books?id=TDEOAAAAYAAJ&pg=RA1-PA43&dq=ohm%27s-law+date:0-1860&lr=&as_brr=1&ei=EljwR83SIJTQtgPvxOmCBw.
External links
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