What to call Ohm's law when it's not Ohm's law

[rooppoorali]

For diodes, we must see the I-V curves. Following are some good write-ups regarding diodes and their characteristics.

https://www.khanacademy.org/science/electrical-engineering/ee-semiconductor-devices/ee-diode/a/ee-diode-circuit-element

https://www.theengineeringprojects.com/2018/05/introduction-to-diode.html

[Sredni]

I missed a question on a physics test once which asked if Ohm's law applies to diodes.  I said yes, but turns out Ohm's law specifically stipulates that R is a constant: I(t) = V(t) / R.  Wikipedia even mentions this explicitly, "If the resistance is not constant, the previous equation cannot be called Ohm's law,". 

So... what do I call it when I'm using not-ohm's-law to compute an effective resistance of a transistor or something? Is R(t) = V(t)/I(t) "the resistance law" the same as how P(t) = V(t)I(t) is "the power law"?

You can call it generalized Ohm's law.

There is a vicious rumor that diodes are not resistors, but they are resistors. They are nonlinear resistors (if we neglect the dynamic parasitics, of course and assume the exponential curve in the VI plane is what characterize them).
If you need to invoke the principle of authority to defend this assertion, you can always quote Chua, Desoer, Kuh, "Linear and Nonlinear Circuits". This is what I call "THE bible of circuit theory". It's not some high school or vocational school textbook for courses limited to the easiest circuits.

If we turn a blind eye on memristors, we can see three types of circuital elements only: resistors (relation between V and I), capacitors (relation between dV/dt and I) and inductors (relation between V and dI/dt). We can introduce electric charge and magnetic flux and show the relations in terms of I, V, phi, and q if we wish, but that's it.

So, a diode is a non linear resistor in the form of a one-port. A transistor can be seen as a nonlinear resistor in the form of a two-port (or just a three terminal elements, but two-ports are easier to digest, for some reason).
An incandescent lamp is a nonlinear resistor whose resistance depends on the (V,I) point it's operating because that point dictates the power dissipated and the temperature it reaches. And yes, despite being nonlinear, we use the ratio V/I.
Have you ever heard a phrase like "when cold, the filament has a resistance of x ohms, but when it's hot it shows a much higher resistance of Y ohms"? Well, that's the ratio V/I and not the differential resistance dV/dI.

In another thread I gave other examples where these sort of quantities exists: hFE and hfe are one example. And if you are familiar with dispersion relations, w/k and dw/dk are another example (w is omega, the angular frequency, k is the wavenumber).

[EPAIII]

Interesting discussion.

I do not think the word "Law" should ever be applied to anything in the scientific world. Science has observations. Science has theories. Science has more observations that either support those theories or bring them into question. But nothing in any field of science is ever absolute like the term "Law" would imply. I absolutely hate it when someone says, "The science is settled." Science is never settled. It is only our best current guess. And further observation will ALWAYS bring changes to those theories or completely new theories. That is the very nature and basis of ALL branches of science.

With that off my chest, I have always considered Ohm's Law to be one of the better theories of science. Yes, there are devices that do not have a fixed or constant resistance. Diodes? Sure! Incandescent light bulbs? Also sure! But to my mind, these really are Ohmic devices in a true sense. It is simply that one MUST substitute r(x) for the simple r when the resistance changes due to some factor, x. So if you are solving for current it is not i but i(x).

i(x) = v / r(x). i changes not only with changes in v, but also with changes of r as determined by x, whatever variable x might be. So, in this sense, Ohm's Law holds when the resistance changes with any factor by simply including the expression for that change in the basic equation of Ohm's law. No magic, just include all the variables.

And if x happens to be the Voltage, then

i(x) = v / r(v)

Again, no magic. v just appears more than once on the right side of the equation. Of course, in order to properly solve this you need to know the correct function to use for r(v) and that may not always be easy to write down.

When I first thought about the complex impedances of capacitors and inductors it gave me pause. But then if a DC Voltage is applied to a capacitor, it starts with a zero Ohm impedance; there is no resistance to the flow of current. But then, as the plates charge up to the applied DC Voltage, there is a reverse or back Voltage which effectively, over the charging time, changes that impedance/resistance from zero to infinity, going through all values between the two. The current is initially very high because i = v / r does apply and, with a constant applied Voltage, the very low value of r gives a very high value for i. But as the charge builds up and the back Voltage increases so does the resistance. So i = v / r continues to apply on an instantaneous basis and the current decreases. When the capacitor is fully charged and the back Voltage equals the applied Voltage, the resistance becomes infinite and i = v / r still CORRECTLY gives the current as zero. The DC version of Ohm's Law holds perfectly, ON AN INSTANTANEOUS BASIS, throughout this entire process. Ohm's Law never fails, even for the smallest increment of time you can imaging. It is simply i = v / r. It is just that r changes with time to make it so.

A similar argument can be made for a constant DC Voltage that is applied to an inductor. Ohm's Law applies strictly on an instantaneous basis when the effect of the induced Voltage on the resistance is included.

In my mind, that is what the AC form of Ohm's Law is all about. And it is just as precise as the DC form, but harder to envision. And all the math with complex numbers (a + bi) is just a way to simplify the calculations in real world AC circuits. But it is never introduced to the students in that manner.

Thus, I see Ohm's Law as being very precise for both DC and, using complex numbers, AC. I am sure there are places where Ohm's Law does break down and become inaccurate but ordinary devices and circuits are not among them.

What to call Ohm's Law when it is not Ohm's Law? I can not even imagine an example of this. And until one is found, the question is pointless.

[Kleinstein]

For everyday use science and especially physics has pretty much settled. There is a long known in consistency between quantum mechanics and general relativity - so we know that our current best therories are not perfect and 100% as they are incompatible. However on there own they worked out fine and for normal use there is not problem - that starts with sub µm back holes or siminar strange things that are very small and very heavy.

R = U/I is just a definition of resistance, not ohms law. The ohms law states that the resistance of metals is independent of the current as long as other parameters are constant. So it tells that metals (without the effect of self heating) are linear resistors. In that sense an ohmic resistor has to be linear. If it gets notably nonlinear there is nothing left of ohms law.

Relating current to voltage or on the microscopic scale current density to the electric flield the ohms law is a materials equation and on it's own not a theory. Initially it was just an empirical observation, that turned out to be quite good. There are than theories (e.g. Drude / Sommerfeld) that want to explain resistivity based on the structure / chemistry. These theories than usually also explain why ohms law holds and most reistors are linear. These theories can also give more detailed material laws, that may include the exffect of temperature, strain and similar.  E.g. to a first approximatio the resistance of simple metals goes up about proportional to the absolute temperature.

[magic]

Have you ever heard a phrase like "when cold, the filament has a resistance of x ohms, but when it's hot it shows a much higher resistance of Y ohms"? Well, that's the ratio V/I and not the differential resistance dV/dI.

Yes, and it has nothing to do with nonlinearity. You can push 10A through a lightbulb and still enjoy your low resistance if you keep it cool.


There is absolutely no use for the ratio of V/I. The only thing you can do is to calculate it and then immediately go back to either V or I by multiplying/dividing by the other. It's 100% useless.

Here's a much more interesting problem I can solve using resistance:
- measure the voltage drop of 680Ω resistor at 1mA to be 0.68V
- know that the voltage at 10mA will be 6.8V

And another interesting problem I can solve, knowing that diodes aren't resistors:
- measure the voltage drop of a diode at 1mA to be 0.68V at room temerature
- know that the voltage at 10mA will be 0.686~0.69V

Your definition of "resistance" doesn't help with either of these problems, because it makes no sense for the latter and only adds unnecessary confusion to the former.

[armandine2]

I may have found another term albeit a bit general "Electric Characteristics"

- from Hans Kammer ? Brussels Workshop on TI NSpire data acquisition calculator / school experiment workshop.

Edited to make more sense to the author

[Sredni]

Have you ever heard a phrase like "when cold, the filament has a resistance of x ohms, but when it's hot it shows a much higher resistance of Y ohms"? Well, that's the ratio V/I and not the differential resistance dV/dI.

Yes, and it has nothing to do with nonlinearity.

It has ALL to do with nonlinearity. The nonlinearity of an incandescent bulb is the consequence of the fact that the resistivity of the material increases with temperature. Have you ever drawn the VI curve of a light bulb from experimental data? You set the voltage (or current), wait for temperature to stabilize and measure the current (or voltage). You end up with a lot of points on the VI plane that follows a square rootish shape. That nonlinear shape is the non linear characteristic of the nonlinear resistor.

You can push 10A through a lightbulb and still enjoy your low resistance if you keep it cool.

And it would not be incandescent. What you do by placing an active cooling system is to create a new component that has a different VI characteristic (most likely still nonlinear, but even if it was linear, it would not be the incandescent bulb you started with).

There is absolutely no use for the ratio of V/I.

Well, I just gave you an example of its use. You are free to disregard it, if it makes you feel better.

Here's a much more interesting problem I can solve using resistance:
- measure the voltage drop of 680Ω resistor at 1mA to be 0.68V
- know that the voltage at 10mA will be 6.8V

And another interesting problem I can solve, knowing that diodes aren't resistors:
- measure the voltage drop of a diode at 1mA to be 0.68V at room temerature
- know that the voltage at 10mA will be 0.686~0.69V

Your definition of "resistance" doesn't help with either of these problems, because it makes no sense for the latter and only adds unnecessary confusion to the former.

R = V/I adds confusion to the problem of finding the voltage drop at 10 mA when we know the voltage drop at 1 mA? What confusion?

And as for the diode:
This is just simple math applied to the nonlinear characteristic of the nonlinear resistor that is the diode. It's done routinely with exponential curves. Ever heard of the Newton's cooling problem? You know the temperature of the liver at time t1 and you can recover the temperature it had at time t0 - (or, as they do in CSI, determine the time of death computing the time the temperature was normal body temp).
The exponential curve of the diode is just a nonlinear curve of a component whose behavior is described by the values of current and voltage (and not their derivative or integrals).