Resistance is defined as R=UI. If Ohm's law holds, U(I) is a linear function and the slope of the curve is equal to the resistance R.
I realized only recently that if U(I) is a non-linear function, the slope of the function is no longer equal to the resistance as defined above. We then have two kinds of resistances:
the differential resistance r(I)=dUdI(I) (which is equal to the slope of the curve at the point I)
"ordinary" resistance R(I)=U(I)I.
My questions:
- Is the quotient R(I)=U(I)I used to describe devices with non-linear current-voltage characteristics at all? (I am aware of the fact that R isn't a property of the device in this case but it may still be a sensible concept)
- If both R(I) and r(I) are used, when do I use which one?
- What can we say about the relationship of the two quantities in general?
Example: Let's have a look at the current-voltage characteristic of a tunnel diode (see image below, taken from Wikipedia). I am not really familiar with how this device operates but it illustrates my question. For "ordinary resistance", we have R(i1)=v1i1≪R(i2)=v2i2 while for the differential resistance we have r(i1)=r(i2)=0 (/edit: As freecharly noted, this is wrong. Actually, we have r(i1)=r(i2)=∞)
So there's some justification to say that if we apply the constant voltage v2 that the resistance is bigger than the resistance if we apply the constant voltage v1, and there's also some justification to say that the resistance is zero infinity in both cases. How is the termonology actually used?
/edit: I edited the phrasing of the question and included an example in order to make things more clear.
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