General definiton of Ohm's law

Question

There has been some disagreement lately on whether a diode follows Ohm's law or not: Does a diode really follow Ohm's Law?

Specifically things like

However, the truth is the resistance of a diode changes depending on the applied current and or voltages.

and

Ohm's law specifically states that R remains constant. If you try to calculate R from V/I while looking at a diodes IV curve, you will see that as you increase the voltage, "R" will change.

also historically: Why do LEDs not obey Ohm's law?

[LEDs] do [follow Ohm's law] - they just do not have a "fixed" resistance

It seems that the main disagreement comes down to what the definition of "Ohm's Law" actually is. Since I was unable to find a question here addressing it, I decided to ask one.

Below are four definitions of Ohm's law taken from a variety of introductory sources on the material. I was unable to find any in more advanced texts, probably because it is so basic it isn't worth including. Therefore, my question: which of these is correct if any. If none, what is the correct general case definition of "Ohm's Law"?

Ohm's law states that the voltage v across a resistor is directly proportional to the current i flowing through the resistor. Ohm defined the constant of proportionality for a resistor to be the resistance, R. (The resistance is a material property which can change if the internal or external conditions of the element are altered, e.g., if there are changes in the temperature.)

Charles K. Alexander "Fundamentals of Electric Circuits" 4th ed

Ohm's law is an assertion that the current through a device is always directly proportional to the potential difference applied to the device. (This assertion is correct only in certain situations; still, for historical reasons, the term "law" is used.) The device of [...] which turns out to be a 1000 ohm resistor -- obeys Ohm's law. The device of [...] which is called a pn junction diode -- does not

Halliday & Resnick "Fundamentals of Physics Extended" 10th ed

Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points. Introducing the constant of proportionality, the resistance,

Wikipedia

A well known relationship that describes the relationship between Voltage and current through a device's resistance expressed mathematically as V= IR. This formula says that voltage across the device is equal to the current through the device multiplied by the resistance.

electronics.stackexchange.com ohm's law tag description

Every single one of those is saying the same thing a different way. What's the question? — Matt Young, Nov 10 '17 at 15:19
Do you want another "*shitstorm*" to arise? All I can say is that Trevor is my man. — Harry Svensson, Nov 10 '17 at 21:15
@HarrySvensson I was hoping to clear up some of the confusion since it seemed like people were operating with different definitions of Ohm's law while debating about where it can be applied. At least with this question there seems to be agreement about what is disagreed upon. — Matt, Nov 10 '17 at 22:05
@Matt This is very close to "Is this dress yellow or blue?". In the end, does it *really* matter? Or conventional flow vs electron flow. In the end, everything works regardless how we perceive them. Right now we're all making a big fuzz about what some man said 200 years ago. - Feels like we're talking about religion. But hey, whatever floats your boat. As long as you won't use ohm's equations to kill me. I'm fine. — Harry Svensson, Nov 11 '17 at 00:38

score 8 · Accepted Answer · edited Jun 11 '20 at 15:10

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Despite all the translations and misinterpretations, there is only one definition of Ohm's theorum, the original penned by the great man himself.

In it is the answer to non-linear parts, which are clearly included, and covered in their own dedicated appendix.

See my augmented answer here.. which includes links to Ohm's paper.

The fact is Ohm simply stated, once it settles into a stable state the voltage across the circuit is the sum of the current times the resistances of the parts.

schematic

^{simulate this circuit – Schematic created using CircuitLab}

\$E = I.R1 + I.R2 + I.R3\$

The formula above is true whether R3 is a diode or not.

It goes on to say if the resistance of any part is non linear and dependent on the stimulus, one must wait until the circuit balances for the above to continue to be true.

The issue is folks tend to read more into "Ohm's Law" than is actually there, or not understand it fully enough, or worse propagate the simplified version without passing on the qualification that it is a subset of Ohm's work. But, I guess that's what happens when you try to condense a 280 something page booklet into a single paragraph.

In particular the notion mentioned in the paper that changing I will change E linearly is often miss-quoted. The paper specifically states that particular extrapolation of the Law is only true for linear parts, any change in excitation requires the circuit to rebalance with different R values.

As such, the usefulness of Ohm's Law in a circuit with non-linear components is severely limited.

edited Jun 11 '20 at 15:10

Community

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answered Nov 10 '17 at 20:22

Trevor_G

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This is absolutely the right way to apply Ohm's Law. Perhaps one way for people to look at this is that "if you know 2 of the values, you can calculate the other one". How that changes under various conditions is irrelevant. There is no precondition that they be fixed values. – Ian Bland Nov 10 '17 at 21:49
Just to add, I don't think you need to wait for the system to settle. Ohm's Law is instantaneous. In practise you will need to consider the values over some arbitrarily small fixed time period. For instance many DMMs take a considerable time to stabilise their reading, whereas an oscilloscope can consider a very short instance. Seconds vs nanoseconds. The law itself has no time component. – Ian Bland Nov 10 '17 at 22:11
In page 202-203, Ohm defines "Resistance" as a real physical quantity of a conductor, which has a definite value, which is altered only when the nature of conductor is altered. It is independent of the current flowing through and is independent of the EMF applied across it. It depends entirely on the nature of the material of which it is composed, state of aggregation of its parts and the temperature. – Mitu Raj Nov 10 '17 at 22:44
Now imagine diode. The IV curve of diode suggest that the diode doesn't even have a property called resistance, in accordance with what is told by Ohm. The "resistance" that we calculate by taking slope of that graph at some point is something which is changing with respect to I and V and is not dependent only on the nature of its composition. Now, either we have to find a resistant property, consistent with what ohm said, or say that diode doesn't obey ohm's law. – Mitu Raj Nov 10 '17 at 22:45
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The problem we have there then is that if we rigorously pursue this definition ordinary resistors don't obey Ohm's Law either, due to thermal effects. – Ian Bland Nov 10 '17 at 22:53
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Darn. I get an excuse to +1 my favorite kind of answer to this question. I believe that those who haven't fully acquired nor appreciated an infinitesimal perspective soul-deep that the *new algebra* of calculus provides, cannot really fully appreciate your answer. I personally think that Dedekind and Weierstrass both did the world a bit of a disservice in their founding differentials on the limit theorem, as it made a Rube Goldberg mess of calculus. It wasn't until Abraham Robinson's "Non-Standard Analysis", 1966, that I think a beautiful viewpoint was achieved. One I had to achieve on my own. – jonk Nov 10 '17 at 23:11
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But that's my own pet peeve about how calculus is taught these days. Aside from that, I really love the way you incorporated and researched the answer you gave. So thanks! – jonk Nov 10 '17 at 23:19
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@MITURAJ look more closely, the text you are referring to is Maxwell's interpretation of what Ohm is saying. Maxwell is talking about an entire circuit, where the parts may not be non-linear with voltage or current. The document is interesting in that the quotes from the other founders, including Kirchov, also contain out of context "quotes" from Ohm. – Trevor_G Nov 11 '17 at 01:04
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@MITURAJ as for a diode. It follows the same rule as everything else in Ohm's world. It's resistance is whatever voltage you measure across it divided by whatever current you are feeding it. It does not vary with time under a constant stimulus, at least not a short time, so it meets Ohm's criteria. Ohm explicitly does not care if that voltage changes with current, provided that changeability is recognized and adapted for in the re-measurement of the resistance under the new stimulus condition once the circuit has reached a new equilibrium. – Trevor_G Nov 11 '17 at 01:10
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@IanBland indeed, and if you had an adequate model of your diode you could indeed predict the currents and voltages at any time after some step change at To. unfortunately, gaining such a model is nigh impossible except by quantifying a particular diode. – Trevor_G Nov 11 '17 at 01:22
Hmm. Let me think. If I take ,say 10 values of V and I from diode characteristics. I will get 10 different values of V/I = resistances right? Suppose I made a look-up table with those values. Say, one of them is 0.65 V and 1.3 A , so our "resistance" = 0.5 ohms at that particular V,I, and physical conditions like temp. – Mitu Raj Nov 11 '17 at 03:41
You mean THIS would be a constant if i put this diode in any circuit in same physical conditions ? I mean if I measure 0.65 V across diode , I can look into my look-up table and blindly make prediction that the current flowing through it has be 0.5 A, regardless of what type of circuit it is and what are it's components ? cz it has to be constant at that particular conditions of V and physical conditions ? – Mitu Raj Nov 11 '17 at 03:41
Ohm mentions V/I is a constant and it depends only on nature of its composition and the temperature as well. So ohms law is obeyed even if we rigorously followed it in cases of ordinary resistors with thermal effects. No problems there. @bland – Mitu Raj Nov 11 '17 at 03:54
@MITURAJ that is correct, the diode does not know what circuit it is in. If you apply X Volts, or Y Amps to an individual diode it will have R resistance regardless of what else is around it. That is just how they work. Again, Ohm did not say that, Maxwell did. – Trevor_G Nov 11 '17 at 14:02
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Hmm interesting... Ohms law could be the most misinterpreted and mispresented law in our electrical and electronics. – Mitu Raj Nov 11 '17 at 14:34

score 4 · Answer 2 · answered Nov 10 '17 at 15:24

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1) diodes are non-linear devices meaning, if you double the voltage the current does not double.

Ohm's Law applies only to linear devices (resistors) therefore it cannot apply to the behavior of a diode.

2) All four are correct. Why do you assume any one of those is incorrect? They all describe:

\$V = I * R \$

Where

\$V\$ = voltage

\$I\$ = current

\$R\$ = The value of the resistor having that voltage \$V\$ across its terminals and having current \$I\$ flow through it.

That's Ohm's Law and all four statements describe that.

answered Nov 10 '17 at 15:24

Bimpelrekkie

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I assumed they were incorrect because the most upvoted answers on my two links at the top said they were incorrect. Generally I assume highly voted answers and high rep users are correct. Introductory texts can often make simplifying assumptions when presenting definitions. – Matt Nov 10 '17 at 15:25
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Capacitor and inductors are also linear elements. Ohms law apply to them too V= IX – Mitu Raj Nov 10 '17 at 15:29
The current through inductors and capacitors varies as a function of time as well as voltage. How can that possibly make them linear? – Finbarr Nov 10 '17 at 16:12
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@Finbarr The definition of linearity – Matt Young Nov 10 '17 at 16:40
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@Finbarr Capacitors and inductors are absolutely linear. If the applied voltage/current increases by some factor, the resultant current/voltage will increase by the same factor. If the applied voltage/current is taken to be the sum of individual voltages/currents, then the resultant current/voltage will be the sum of the individual currents/voltages taken separately. However, Ohm's law can only be applied to capacitors and inductors in the special case where the excitation source can be represented by a complex frequency. – pr871 Nov 10 '17 at 16:54
@Finbarr linearity of a system is defined by - superposition/additivity and homogeneity. R,L,C are linear. Thats why RLC circuits are called linear networks and we are able to apply thevenins theorem, KVL etc. – Mitu Raj Nov 10 '17 at 18:02
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@MITURAJ Correct, except that KVL is a result of a simplification of Maxwell's equations in which the magnetic flux through any conducting loop in a circuit is assumed constant. It has nothing to do with linearity of components. – pr871 Nov 10 '17 at 18:39
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Sorry mate, if you read his work he clearly indicates how non-linear devices work under his theorem. – Trevor_G Nov 10 '17 at 20:24
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@Trevor_G, got a link to Ohm's paper? – The Photon Jan 20 '19 at 16:38

Transistor · Answer 3 · 2017-11-10T21:34:51.833

Therefore, my question: which of these is correct if any. If none, what is the correct general case definition of "Ohm's Law"?

I will look at the question a slightly different way.

A device’s IV curve – current versus voltage curve – is a graph of the current that will flow in the device as a function of the voltage across it.

Figure 1. IV curves for various resistors. The lines can be extended through 0, 0 to show the relationship at negative voltages and currents.

As Figure shows, the slope of the IV curve for a resistor is a constant - provided temperature effects, etc., are not significant.

Figure 2. Typical IV curves for various colours of LEDs.

LEDs and diodes in general have a non-linear relationship between current and voltage. They do, however, resist the flow of current and so have resistance. It's just that it changes with the current (or voltage). e.g., The red LED of Figure 2 passes 40 mA at 2.0 V. It's resistance under these conditions is \$ R = \frac {V}{I} = \frac {2}{40m} = 50 \ \Omega \$. At 100 mA the resistance will be \$ R = \frac {V}{I} = \frac {2.5}{100m} = 25 \ \Omega \$.

My response to your question is that all of the definitions are saying the same thing in slightly different ways.

"Ohm's law states that the voltage v across a resistor is directly proportional to the current i flowing through the resistor." [So \$ V \propto I \$.]
"Ohm's law is an assertion that the current through a device is always directly proportional to the potential difference applied to the device." [So \$ I \propto V \$. This is the same as 1 - just swapped left to right.]
"Ohm's law states that the current through a conductor between two points is directly proportional to the voltage across the two points." [So \$ I \propto V \$ again. This is exactly the same as 2.]
"Voltage and current through a device's resistance expressed mathematically as V= IR." [This is the same as 1 but with the constant R eliminating the '\$ \propto \$'.]

Source: LEDnique.

score 1 · Answer 4 · answered Nov 10 '17 at 15:57

The resistance of a device is defined as the voltage/current ratio.

Ohm's Law is only meant to be applied where this ratio stays reasonably constant.

Sometimes it is, like for a typical commercial resistor, and it's worth giving a figure for it. For instance, a typical cheap 10k resistor might be sold with a 1% tolerance and a 200ppm tempco, meaning its 25C resistance is within 1% of 10k, and it won't change by more than 0.2% for every 10 degrees temperature change.

Sometimes the resistance is less constant, as for a tungsten filament bulb, which changes resistance by a factor of 10 between cold and hot.

Sometimes the device is so non-linear that it's inappropriate to give any figure for resistance, for instance a diode whose current may change by a factor of 1 million as the voltage changes from 0.6v to 0.7v.

Sometimes for diodes, we may still quote a slope resistance, which is the ratio of the change of voltage for the change of current, measured around some specified current.

All diodes are built with resistive materials, which means at high current, the slope resistance will be dominated by the residual material resistance.

score -1 · Answer 5 · answered Nov 10 '17 at 16:26

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If you apply a direct voltage (V) across a device and measure the resultant direct current (I) through it, then the resistance of the device, at that particular operating point, is R=V/I. But that is NOT Ohm's law. Ohm's law requires that the device in question must provide a constant ratio of V/I over a prescribed operating range. So if the V/I graph is not a line, Ohm's law cannot be invoked.

answered Nov 10 '17 at 16:26

Chu

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"Ohm's law requires that the device in question must provide a constant ratio of V/I over a prescribed operating range." No it doesn't, despite what you may have read or been told. You have to read the darn thing. – Trevor_G Nov 10 '17 at 20:27
@Trevor, how am I misreading it? – Chu Nov 10 '17 at 22:17
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Ohm's paper contains a whole appendix that deals with non-linear components and how to handle them. – Trevor_G Nov 10 '17 at 22:20

Tony Stewart EE75 · Answer 6 · 2017-11-10T16:05:31.200

Although Ohm's Law assumes fixed R for a set of conditions, I will show you that it can also be used for every electronic analog part including non-linear , but only if you understand the constraints where the linear value exists on impedance.

I have repeatedly written about the linear bulk resistance of diodes or ESR as a significant process variable in ALL diodes and BJT's. YOU CAN APPLY OHM's LAW on this PARAMETER. \$ESR=\Delta V /\Delta I\$ "but only when saturated" or when R dynamic < ESR. Ohm's Law only is useful for linear fixed R's which includes the bulk R of diodes, DCR of inductors and ESR of Caps. From this parameter, power dissipation limits contribute to the max current of any device.

So the rules for using Ohm's law are fixed linear R but this can be applied to non-linear devices even those with large temperature coefficents like light bulbs for a short period of time. Like estimating the surge current in a tungsten bulb R_cold ~10% R_hot thus Pd surge is 10x steady state. So the constraints for using Ohm's Law on any non-linear device must be well understood and defined and it is assumed you will understand these.(eventually)

This is the only reason why LED's have a wide tolerance on Vf (min-max) @Imax and from the nominal VI curve you can measure the tangent over a limited operating range to estimante this bulk linear resistance.

for more details

This linear characteristic only becomes dominant when the junction is well into saturation and the dynamic resistance is lower than the bulk ( linear) resistance where you can apply Ohm's Law. This is often in the 30% to 100% range of rated current but users may consider where they operate to compute heat rise or voltage source effects on current.

Even though diodes are all logarithmic, they become linear when the dynamic R< ESR.

It is important to realize Ohm's Law for incremental power dissipation applies to "Bulk" resistance to all active and passive devices. e.g. in chokes it is called DCR, in caps it is spec's using % D.F. or ESR , in BJT's we call it rCE (sat.) and in FET's it is defined as RdsOn for Vgs > 3x Vgs(th).

Note above the bulk term I use has different causes in each case but due to the conductive material in the component, each which are essential even in dielectrics and diodes.

I'm guessing it's because you don't answer the actual question being asked. — Finbarr, Nov 10 '17 at 16:16
If you can't explain it simply, you don't understand it well enough. - Einstein — Mitu Raj, Nov 10 '17 at 18:07
That's only Relative to your understanding of non-ideal characteristics . Obviously V=IR assumes R is constant but it you understand how to make R constant or derive it for non-linear parts or even use it for AC impedance , it is more complicated. ( relatively speaking) — Tony Stewart EE75, Nov 10 '17 at 18:35

General definiton of Ohm's law

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