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

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

Bob

 

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.

 

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

 

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

 

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.

 

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)?

 

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

 

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.

 

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

 

Sorry Chris, but that is not Ohm's Law.

Bob

 

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