By way of background, in section 29.5 on page 770 it remarks in passing that many conducting materials exhibit current proportional to voltage. So far so good.
Alas in section 32.2 on page 816 it emphatically generalizes this to «any element in an electric circuit». This is quite a rash generalization. It doesn't work for batteries, dynamos, motors, electroplating cells, et cetera. What's worse, the idea of «constant of proportionality» does not even work for light bulbs, which are the workhorse example used throughout chapter 31. Incandescent light bulbs are spectacularly non-Ohmic, as discussed in #37 and #56.
For light bulbs, it is not the least bit obvious how to define resistance; it could be the gross large-signal resistance V/I or it could be the small-signal resistance ∂V/∂I.
Tactical Suggestion:
It's not clear how to fix this, but one possibility would be to return to the language of chapter 29: It is observed that for many conducting materials the voltage is more-or-less proportional to the current. Such materials are called Ohmic. The coefficient of proportionality is the resistance, R.
Not all circuit elements are Ohmic, perhaps because they are not linear and/or not passive chunks of material. Non-Ohmic examples include incandescent light bulbs, diodes (including LEDs), batteries, dynamos, motors, electroplating cells, et cetera. Under _some_ conditions it _might_ make sense to calculate the ratio V/I even when it is not a constant. Under _some_ conditions it _might_ make sense to call this ratio the large-signal resistance, but you cannot count on this, and there is significant risk of confusion. A full treatment of non-Ohmic devices is beyond the scope of the course.
Strategic Suggestion:
In chapter 31, each light bulb is trying to perform two functions (resistor and indicator) and doing a lousy job of both. This is basketball on Pluto: naïve theory running roughshod over real-world physics.
Therefore, it might be better, throughout chapter 31, to replace nearly all of the light bulbs with something better. I'm thinking of a nice Ohmic resistor with a voltmeter in parallel and/or an ammeter in series.
It could be argued that many students are unfamiliar with such meters ... but in response I would say:
It's high time they learned about voltmeters and ammeters, and
On the other side of the same coin: Students are equally unfamiliar with the voltage-versus-current-versus-brightness behavior of light bulbs ... and a great deal of what is implied in chapter 31 is wrong. It's better to say true things about meters than untrue things about light bulbs.
By way of background, in section 29.5 on page 770 it remarks in passing that
many conducting materialsexhibit current proportional to voltage. So far so good.Alas in section 32.2 on page 816 it emphatically generalizes this to «any element in an electric circuit». This is quite a rash generalization. It doesn't work for batteries, dynamos, motors, electroplating cells, et cetera. What's worse, the idea of «constant of proportionality» does not even work for light bulbs, which are the workhorse example used throughout chapter 31. Incandescent light bulbs are spectacularly non-Ohmic, as discussed in #37 and #56.
For light bulbs, it is not the least bit obvious how to define resistance; it could be the gross large-signal resistance V/I or it could be the small-signal resistance ∂V/∂I.
Tactical Suggestion:
It's not clear how to fix this, but one possibility would be to return to the language of chapter 29: It is observed that for
many conducting materialsthe voltage is more-or-less proportional to the current. Such materials are called Ohmic. The coefficient of proportionality is the resistance, R.Not all circuit elements are Ohmic, perhaps because they are not linear and/or not passive chunks of material. Non-Ohmic examples include incandescent light bulbs, diodes (including LEDs), batteries, dynamos, motors, electroplating cells, et cetera. Under _some_ conditions it _might_ make sense to calculate the ratio V/I even when it is not a constant. Under _some_ conditions it _might_ make sense to call this ratio the large-signal resistance, but you cannot count on this, and there is significant risk of confusion. A full treatment of non-Ohmic devices is beyond the scope of the course.
Strategic Suggestion:
In chapter 31, each light bulb is trying to perform two functions (resistor and indicator) and doing a lousy job of both. This is basketball on Pluto: naïve theory running roughshod over real-world physics.
Therefore, it might be better, throughout chapter 31, to replace nearly all of the light bulbs with something better. I'm thinking of a nice Ohmic resistor with a voltmeter in parallel and/or an ammeter in series.
It could be argued that many students are unfamiliar with such meters ... but in response I would say: