Is it true that not all components obey Ohm's law?

Question

After explaining Ohm's law to someone who knew nothing about electronics, I was corrected by another guy, pointing out that not all components obey Ohm's law. I replied with the usual "I know, that's why I said in a simple resistive circuit."

However since I also know very little about electronics, that made me curious if that were really true. Is there any component for which the relation I = V/R is broken?

I always took that to just mean that this relation was constant, not that I could expect R to be constant and/or independent of the other two values or time. I wonder if, when people say that a diode (for instance) does not obey Ohm's law, do they actually just mean that you can't use it to set I by varying V or R independently?

Does a diode behave differently than a variable resistor which attempts to keep the voltage drop across it constant, and which offers maximum resistance when voltage across the terminals are reversed?

After reading the accepted answer here Does a diode really follow Ohm's Law?, I conclude that the answer to the last question is "no", that is, a diode does really "obey" Ohm's law. Can I also conclude that this is true for all components, if we use Ohm's original formulation, not later simplifications?

Does it even make sense to say that Ohm's law can be "broken"?

Answer 1

Ohms original work was trying to understand the relationship between the length of a telegraph cable and the amount of voltage required to get a certain current. When he did this work, the concept of a resistor, as a component that you may intentionally introduce into a circuit specifically for the purpose of throwing away valuable bits of EMF, was unheard of.

His major contribution was to discover -- or at least to do the work that pointed a big fat arrow at -- the fact that the voltage drop in a circuit made of metal was proportional to current. It wasn't that voltage was proportional to current squared, or the square root of current, or current raised to any non-unity exponent.

As has been mentioned repeatedly, Ohms law isn't a basic law of physics -- it's the culmination of an great amount of empirical experience, both deliberate and inadvertent that lead us to realize that for most conductive materials, we can make a hunk of said material and assign a resistance to it such that \$E = I\ R\$.

It's found a solid place in circuit analysis because if you assume that all the resistive elements obey it, then (along with some other simplifying assumptions for other components that are usually true enough for the purpose) it reduces system analysis down to solving systems of linear differential equations -- and while solving linear differential equations is mildly mind-bending, there's no general solution at all to solving nonlinear differential equations.

So -- does every component out there follow Ohms law? No. Does every resistor out there follow Ohms law? Not if you take heating into account, not (if high voltages are present) if you take corona discharge or other leakage paths into account, not if you take aging into account, etc.

But there's enough components out there that follow it that it's useful. In addition, because you can take much of the remainder and you can wrangle your circuit description into a linear differential equation that you can analyze on paper, it's useful. It's this tremendous usefulness that's kept it alive all these years, and refined it into the form that we all know and love.

Answer 2

The Wikipedia article explains it fairly well:

If the resistance is not constant, the previous equation cannot be called Ohm's law, but it can still be used as a definition of static/DC resistance.[4] Ohm's law is an empirical relation which accurately describes the conductivity of the vast majority of electrically conductive materials over many orders of magnitude of current. However some materials do not obey Ohm's law; these are called non-ohmic.

Diodes do not have a linear relationship between current and voltage so they cannot be modeled as simply as a resistor using Ohm’s Law, V = IR. We can, however, make a simplification and model them over a range of currents as a combination of a resistor and a voltage source.

Figure 1. This green LED has a "resistance" of 15 Ω with a voltage offset of 2.0 V. Image source: Resistance of an LED.

Figure 2. If this was our region of interest we could use a resistance value of 37.5 Ω and a voltage offset of 1.5 V.

Does a diode behave differently than a variable resistor which attempts to keep the voltage drop across it constant, and which offers maximum resistance when voltage across the terminals are reversed?

See if my article What is an LED helps with the non-return valve analogy.

Does it even make sense to say that Ohm's law can be "broken"?

I don't think so. It makes sense to say that it applies to resistors and not to other things.

Answer 3

All resistances do obey the law. It's just that it will be difficult to find ideal pure resistances anywhere else except in text books. Nevertheless it is an useful concept.

Even real world resistors are not pure resistances, as they have stray inductance and stray capacitance over them so a 100 ohm resistor at DC won't look like 100 ohm resistor when measured at 10 GHz frequency. A 100 ohm resistor might be approximated as a ideal 100 ohm resistor when used within some reasonable range of frequencies, currents and voltages. If you put 200 volts over the resistor, it will most likely measure a different resistance than at 100 volts due to whatever nonlinearities it may have.

Diodes and other semiconductors are not resistances so the law does not apply to them, but an ideal resistor as a part of modeling a semiconductor diode might be a good enough approximation, depending on how accurately you want to model a diode.

Answer 4

I will attempt to answer my own question with a summary.

It seems it all boils down to whether Ohm's law implies that R is constant or not. I had always taken it to not imply this, that it is a simple mathematical relation which states that I = V/R, regardless of whether R is constant or not. As such it could be seen as a definition formula for R, on the form R = V/I.

I had referenced another electronics SE answer, which argued this way: Does a diode really follow Ohm's Law?. He argues that the implication that R must be constant comes from a later simplification by Maxwell. It seemed very convincing because it actually went back to the original source, hundreds of pages written by Ohm himself on the subject.

However another answerer here referenced https://en.wikipedia.org/wiki/Ohm%27s_law stating that when R is not constant it can't be called Ohm's law, even if it could be used as a definition formula for R. Wikipedia has anonymous contributors, but the article referenced a university textbook which surely weighs heavily: https://books.google.no/books?vid=ISBN9780321501219&redir_esc=y

Seen this way, Ohm's law is more of an empirical law, which can be used if you know a constant R, to determine V from I or vice versa. But that would only hold for components with a constant R.

I reckon it doesn't really matter that much exactly what Ohm originally meant. It seems clear from the answers here that if I say "Ohm's law", the overwhelming majority of electronics engineers and amateurs alike will take it to imply that R is constant. The main goal is to be correctly understood.

Answer 5

Is there any component for which the relation I = V/R is broken?

And, from a comment (just to be sure I haven't misinterpreted what was asked): -

As pointed out in the question, I wanted to know whether this could be said for all components, not just for diodes.

Here you talk about any (or all) components i.e. you are not talking about ideal components because you said any component. All practical, real components can be made by composites of ideal components and indeed the relationship between V and I is not determined by a constant value called R. Even some ideal components (as in a capacitor or inductor for instance) do not have a linear relationship between voltage and current. In a capacitor for example: -

Image from here. In this "ideal" example the relationship between current and voltage is not a simple "X": -

$$I = C\cdot\dfrac{dv}{dt}$$

In other words current is proportional to the rate of change of voltage across the terminals of the component. It's a similar story for an inductor.

If you focussed down to the current and voltage across an ideal resistance then ohm's law is true but, in the bigger picture it is not so clear because all real components have parasites that muddy the clear ohm's law water.

Answer 6

You have realised that R is not necessarily constant for many components. That's not just semiconductors. Even the tungsten filament lamp has a resistance that varies with how hot the filament is.

So does Ohm's Law apply to all components? If you allow R to be a function of V or I, then you can argue that any two-terminal component obeys Ohm's Law. You measure V and I, calculate R using R = V/I, and then discover that I = V/R. But it becomes a meaningless circular argument.

Answer 7

Ohm's law is an empirical statement about the relation between voltage and current through a conductor. It can also be derived using simplified atomic models of conductors. In either case, it describes a simple linear relationship between voltage and current through conducting materials: metallic conductors, or nonmetallic like soil, concrete, electrolytes, plasmas, biological tissues etc...

The key concern here is that it's a linear relationship between device's voltage and current, and which is identified by a line that passes through the origin on the I-V plane.

From this point of view, any electrical device whose i-v curve is not a line, or which does not pass through the origin is called a nonlinear device, and ohm's law is not valid for nonlinear devices.

In this reagrd, all semiconductor electronic devices such as diodes, transistors, photocells, etc, or many electrical devices such as fluorescent lamp, will globally violate Ohm's law.

Note, however, that electrical engineers can talk about linearisation of a nonlinear device (or a circuit with nonlinear devices) through an operating point, and making use of small signal analysis to deduce its behaviour around that specific operation point. In such a case, the device or the whole circuit will be replaced by its linear model with linear resistors, whose iv behavior will obey Ohm's law in that restricted range of analysis. But that does not make such devices ohmic. They are eventually nonlinear devices, and violate Ohm's law.

Answer 8

Ohm's law describes a linear relationship between current, voltage, and resistance.

If you plot the current as a function of the voltage applied to a resistor, you will get a straight line - it is a linear function.

If you plot the current as a function of the voltage applied to a diode, the graph is not a straight line.

The diode doesn't follow Ohm's law in that sense.

On the other hand, from any point on the diode graph, you can write Ohm's law as \$R=\frac{E}{I}\$ to calculate an equivalent resistance for that point.

You can't apply Ohm's law to just any circuit and expect the linear relationship to hold true - if you measure the current drawn by the circuit at 5V, you can't use Ohm's law to predict how much current it will draw at 10V. Not, that is, unless the circuit is purely resistive.

Along with that, there are tunnel diodes.

The equation \$E=IR\$ is totally twisted for tunnel diodes. There are places in the current to voltage plot where you get the same resistance more than once.

Ohm's law doesn't hold for all components in all conditions. Even for simple resistors it is only an approximation of the real behavior. For non-linear devices (diodes, transistors, etc.) it doesn't describe their behavior in general though it can be used to calculate an equivalent resistance given current and voltage in a particular circuit.

Answer 9

Indeed, Ohm's law applies to very few loads: resistive loads.

I prepared this chart to show which loads Ohm's law applies to: