# Ohm's Law or not Ohm's Law... That is the question

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#### CDRIVE

##### Hauling 10' pipe on a Trek Shift3
May 8, 2012
4,960

(solidus)

Sure they do. For BJT's it's the "Collector Resistor". It doesn't matter if we're talking Tubes, BJT's, MOSFETs, JFETs, Resistors, Light Bulbs, Inductors, Capacitors or even Wire. All components in an electronics circuit are governed by Ohms Law.

Chris

#### BobK

Jan 5, 2010
7,682
All components in an electronics circuit are governed by Ohms Law.

Chris
That's news to me. Tell me how an inductor is governed by Ohm's law.

Bob

#### KrisBlueNZ

##### Sadly passed away in 2015
Nov 28, 2011
8,393
Oh dear. I've been through this business before (not here though). In my case it was an argument about whether Ohm's law applies to the human body when it is being electrocuted. That's a much greyer area than inductors and capacitors.

From what I learnt from that argument, Ohm's law is normally only used when I and V are proportional; its purpose is to demonstrate the proportionality of I and V, and the quantity R that relates them to each other.

It's also used with small-signal quantities i and v when the incremental resistance can be defined over a limited range, for example in a semiconductor junction.

Applying it to components that are not ohmic may be meaningful to some degree - for example, I think it's kind of meaningful to say that when a neon bulb ionises, its "resistance" suddenly drops, but trying to apply Ohm's law doesn't help when you're dealing with reactive components (capacitors and inductors).

Except at DC, where inductors are ohmic (in answer to BobK's question).

I'd welcome comments from Steve on this point, too.

#### CDRIVE

##### Hauling 10' pipe on a Trek Shift3
May 8, 2012
4,960
That's news to me. Tell me how an inductor is governed by Ohm's law.

Bob

I may be wrong because some things come across in print quite differently than they were intended but I can't help but read a sense of disdain in your post. So, before I answer your question please answer this.. Is this a challenge? I'm sure that your prostate is in much better shape than mine but if you're itching for a p!ssing contest I'll be more than glad to oblige you.

Chris

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#### BobK

Jan 5, 2010
7,682
Yes, as a matter of fact it is a challenge. You cannot characterize an inductor, or a capacitor, or a diode, or a BJT or a MOSFET, or a JFET, or a neon light, or a DIAC or TRIAC or an SCR or any integrated circuit via Ohm's law. If something obeys Ohms law, it can be only one type of component: a resistor. Your statement is ridiculous.

Hint: In V = I R, R is a constant.

Bob

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#### CDRIVE

##### Hauling 10' pipe on a Trek Shift3
May 8, 2012
4,960
I suspect this may be a long bloody battle. So out of respect for Eli I request that the mods snip this where it started and move this to its own thread. Then the games can begin.

Chris

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,505
I'd welcome comments from Steve on this point, too.

I was going to make a comment along the lines of "Assume a complex impedance Z..." but that only applies to some components that behave linearly after you perform mathematics. I then considered semiconductor junctions, so my reply would have to then talk about a small signal model (where even then it is an approximation).

Whilst I also agree that it is true that if you measure an instantaneous value of V across. and I through something, you can come up with an R describing the current state, you can't be sure that this will be time invariant or predictive for other values of V and/or I.

In any case, Chris was really talking about the load resistor, and that does behave like a resistor (when it's a resistor).

On balance, I thought I would remain silent.

#### Solidus

Jun 19, 2011
349
I suspect this may be a long bloody battle. So out of respect for Eli I request that the mods snip this where it started and move this to its own thread. Then the games can begin.

Chris

Chris, I am more than happy to watch you go at this battle and oblige him!

I'll root for you from the sidelines.

Eli

#### KrisBlueNZ

##### Sadly passed away in 2015
Nov 28, 2011
8,393
Whilst I also agree that it is true that if you measure an instantaneous value of V across. and I through something, you can come up with an R describing the current state, you can't be sure that this will be time invariant or predictive for other values of V and/or I.

I think that's the important issue. It's certainly true that whenever you have a voltage across and a current through any component or circuit, you can calculate a "resistance" value, but this value is only really useful and meaningful for an ohmic component or circuit, where voltage and current are proportional to each other.

In the case of a semiconductor, voltage and current are not proportional. Another way of looking at this is to say that the resistance depends on the voltage (or current), but this doesn't usually help you understand what's happening, and the idea of resistance is a bit of a red herring.

In the case of reactive components, the ratio between voltage and current varies in real time, so trying to characterise it as "resistance" is not helpful. That's what reactance is for.

#### Harald Kapp

##### Moderator
Moderator
Nov 17, 2011
12,770
May I join the battle?

In the case of a semiconductor, voltage and current are not proportional. Another way of looking at this is to say that the resistance depends on the voltage (or current), but this doesn't usually help you understand what's happening, and the idea of resistance is a bit of a red herring.
Right, and that's where small signal models come into play, as Steve mentioned. By approximating the nonlinear characteristiv by a linear one at the operating point of he circuit the math becomes much simpler.
But that doesn't mean that the small signal "resistance" is a true resistance. It is just a mathematical approximation.

Also you can, for certain considerations, treat the complex impedance of an inductor or capacitor as a resistance - at least mathematically. An example is the use of a capacitor as a current limiting element in an AC circuit for driving an LED. One has to be aware of the limitation, e.g. that a phase shift between voltage and curent is not taken into consideration.

#### Laplace

Apr 4, 2010
1,252
Hint: In V = I R, R is a constant.

Bob

Suppose that R is a non-linear function of the voltage or current. Does that invalidate Ohm's Law? The usual method for analyzing non-linear circuits is to treat them as piecemeal linear and use the dynamic resistance as constant over each linear segment. Ohm's law applies to that.

Resistance is measured in ohms. E/I=R Reactance is also measured in ohms. E/I=X Reactance obeys Ohm's Law. So why would reactance be measured in ohms if capacitors & inductors didn't obey Ohm's Law (in the frequency domain, of course)?

#### (*steve*)

##### ¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
Moderator
Jan 21, 2010
25,505
I just typed a huge message, and lost it.

I'm not going to type it again, but the general gist of it is that Ohms Law is a nice approximation in just the same way as F=ma is a nice (and inaccurate under certain circumstances) approximation.

There are various rabbit holes we can go down, Johnson noise is one, wavelengths shorter than the scale of our measurements is another, and so on.

Whilst we may decide to differ on whether we are applying Ohms law when we talk about complex impedances or whether we are applying something of a similar (and more complex) form, the practical fact is that there are points where it does break down if we operate outside of certain constraints.

#### BobK

Jan 5, 2010
7,682
The reactance model only works at a constant frequency, so even there it is not a universal law, it cannot be applied at all to changing, non-repetetive waveform. Ohm's law is universal law that states the dependence of voltage and current in an ideal resistor. To call anything else Ohm's law is to redefine Ohm's law.

You cannot use Ohm's law to tell me what current is going through a capacitor or inductor given the voltage across it, other factors must be brought into the equation, and thus, the equation is no longer Ohm's law, which is simply V = I R with R being a constant.

KrisNZ mentioned something about and inductor obeying Ohm's law for DC currents. I can imangine the following conversation:

Kris: But officer you can't give me a ticket I obey the law!
Officer: What? I caught you going 90 in a 70 zone.
Kris: But I do obey the speed limit when I am stopped!

A more accurate statement about Ohm's law would be "No real component obeys Ohm's Law" Even resistors have inductance and capacitance that come into play at higher frequencies.

Bob

#### KrisBlueNZ

##### Sadly passed away in 2015
Nov 28, 2011
8,393
KrisNZ mentioned something about and inductor obeying Ohm's law for DC currents. I can imangine the following conversation:

Kris: But officer you can't give me a ticket I obey the law!
Officer: What? I caught you going 90 in a 70 zone.
Kris: But I do obey the speed limit when I am stopped!

Cute. And I WAS trying to be a smart-arse.

But Ohm's law IS actually applicable to the DC resistance of inductors, and can be usefully applied - for example when you're calculating the average DC voltage dropped by a filter inductor in an SMPS at a particular load current. But this is only a secondary (pun intended) characteristic of inductors, and Ohm's law doesn't help with understanding an inductor's behaviour at f>0.

#### Laplace

Apr 4, 2010
1,252
The reactance model only works at a constant frequency, so even there it is not a universal law, it cannot be applied at all to changing, non-repetetive waveform.

That is not a true statement. Ohm's Law applies to reactive components in both the steady-state AC domain and the complex frequency domain. Complex frequency is normally represented by the 's' variable and the Laplace Transform is used to shift the analysis between the frequency domain and the time domain. It should be noted that non-repetitive waveforms in the time domain can be shifted to the complex frequency domain where Ohm's Law does apply to reactive components.

#### BobK

Jan 5, 2010
7,682
That is not a true statement. Ohm's Law applies to reactive components in both the steady-state AC domain and the complex frequency domain. Complex frequency is normally represented by the 's' variable and the Laplace Transform is used to shift the analysis between the frequency domain and the time domain. It should be noted that non-repetitive waveforms in the time domain can be shifted to the complex frequency domain where Ohm's Law does apply to reactive components.
What you are saying is that there is a analog to Ohm's law that applies, not the V = IR applies.

Bob

#### CDRIVE

##### Hauling 10' pipe on a Trek Shift3
May 8, 2012
4,960
That's news to me. Tell me how an inductor is governed by Ohm's law.

Bob

Before I fire my opening shot I have something to say to the forum. I asked Bob if the tone in his first post was disdainful toward me. He didn't deny it at all. In fact, he escalated his contemptuous tone. So if I seem combative it's not your imagination. I don't turn the other cheek! Before we're done here and the ground is soaked with Bob's blood, I fully intend to validate the relativity and application of Ohms Law to every component I mentioned.

Bob, number one on your list. Inductors and Ohms Law.

Perhaps you slept through this part of your course studies?

Chris

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#### BobK

Jan 5, 2010
7,682
Sorry Chris, but that is not Ohm's Law.

Bob

#### CDRIVE

##### Hauling 10' pipe on a Trek Shift3
May 8, 2012
4,960
What you are saying is that there is a analog to Ohm's law that applies, not the V = IR applies.

Bob

You must be a damn lawyer or politician! This is just BS spin!

Chris

#### BobK

Jan 5, 2010
7,682
Chris,

Please look up Ohm's law on Widipedia or somewhere. It is this equation:

V = I R

Where R is a constant.

Inductive and capacitive reactance are not constants, they are frequency dependent. And the reactance analog of Ohm's law can only be stated in complex numbers. The simple equation above does not apply.

Take a capacitor with a voltage across it. What is the constant R that tells me what the current is?

1. In the open circuit case
2. In the shorted case.

Remember, R has to be a constant.

Bob

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