Actually Robin, you did say V=IR was wrong. You also said in your post "V is dependent on I and R is silly" which it is absolutely not. Students should learn that if you double the resistance for a given current the voltage will double. As others said, this is just Ohm's law in practice. I feel sorry for anyone you might teach. The basics need to be explained, but the triangle diagram I mentioned and nicely illustrated by GopherT is one way those I have taught remember how to use the terms.

No one's arguing here that Ohms law is algebraically incorrect. The fundamental problem is simply that, stated as is, it can easily lead to wrong assumptions. Let's take the example from your post to illustrate the issue:

...if you double the resistance for a given current the voltage will double.

So student replaces a 1 ohm resistor with a 1M resistor in their 1A, 1V circuit and now expects to measure 1000000 volts across the terminals!

A very slight reformulation of Ohms law, which is both algebraically sound and conveys the implications more concisely might be something like this:

\(RI - V = 0\), or even: \(RI^2 - \frac{V^2}{R} = 0\)

From the above equations it should be absolutely clear that the overall power (energy) within a system is always conserved. Now there is no confusion because the student can readily see that, all things being equal, an increase in resistance for a given current must necessarily lead to a decrease in voltage.

 

No one's arguing here that Ohms law is algebraically incorrect. The fundamental problem is simply that, stated as is, it can easily lead to wrong assumptions. Let's take the example from your post to illustrate the issue:



So student replaces a 1 ohm resistor with a 1M resistor in their 1A, 1V circuit and now expects to measure 1000000 volts across the terminals!

A very slight reformulation of Ohms law, which is both algebraically sound and conveys the implications more concisely might be something like this:

\(RI - V = 0\), or even: \(RI^2 - \frac{V^2}{R} = 0\)

From the above equations it should be absolutely clear that the overall power (energy) within a system is always conserved. Now there is no confusion because the student can readily see that, all things being equal, an increase in resistance for a given current must necessarily lead to a decrease in voltage.

It can easily lead to the same confusion.

RI - V = 0

So now they increase the resistance by a factor of 10 and they then expect the voltage to go up by a factor of ten as a result.

If someone doesn't understand the fundamentals, then they will always be able to improperly apply any equation that describes the system.

Ohm's Law is simply the constitutive equation describing the relationship between voltage and current in a particular class of device. Nothing more and nothing less. It is the direct analog to Q = CV (which can be expressed as i = C·dv/dt) for a capacitor for v = L·di/dt for an inductor. No matter how you rewrite any of them, they describe exactly the same thing -- the relationship between voltage and current in that particular class of device.

In my view, the "natural" way to express all of these is to recognize that they describe the dominant parameter for that class of device. Hence that parameter should be on the left hand side as the starting point.

A resistor is a device that can be adequately parameterized by R = v(t)/i(t).

A capacitor is a device that can be adequately parameterized by C = i(t)/(dv(t)/dt).

An inductor is a device that can be adequately parameterized by L = v(t)/(di(t)/dt).

 

It can easily lead to the same confusion.

So now they increase the resistance by a factor of 10 and they then expect the voltage to go up by a factor of ten as a result.

If someone doesn't understand the fundamentals, then they will always be able to improperly apply any equation that describes the system.

Right, but also remember that Ohms law is generally taught at the very beginning. It's so intrinsically fundamental that not many concepts come before it. In my opinion placing zero on the right-hand side makes things much clearer, but another way which would perhaps be even better:

\(\frac{V}{IR} = 1\)

In any case, the bottom line is that the student should be taught at the same time that an interdependence is involved.

In my view, the "natural" way to express all of these is to recognize that they describe the dominant parameter for that class of device. Hence that parameter should be on the left hand side as the starting point.

A resistor is a device that can be adequately parameterized by R = v(t)/i(t).

A capacitor is a device that can be adequately parameterized by C = i(t)/(dv(t)/dt).

An inductor is a device that can be adequately parameterized by L = v(t)/(di(t)/dt).

I agree, that conveys the core concepts quite nicely.

 

Right, but also remember that Ohms law is generally taught at the very beginning. It's so intrinsically fundamental that not many concepts come before it.

I don't know that it is taught so early because it is so fundamental, as just that it is one of the easiest topics to work with. Arguably, capacitance and inductance are more fundamental -- and in fact many (most?) Physics II courses teach capacitance and inductance from first principles before they ever mention resistors or circuits.

But I agree that, in non-physics classes at least, it is presented first and students work with it quite a bit before they learn about any other kind of device. The result is that they tend to overgeneralize and think that Ohm's Law is somehow universal and applies to anything anywhere. There is certainly a tendency on many students part to grab the first V they see and the first R they see and throw them at Ohm's Law and come up with a current, even if the V and the R and the I in question have nothing to do with each other. Part of this is completely on the student, but part of it is also on how the material is presented -- especially since the fact that students have this tendency is so well known.

Back when I was teaching Linear Systems I, I tried to head this off -- with some success -- by stressing the first day that we were going to be looking at circuits involving three kinds of passive devices: resistors, capacitors, and inductors. That each had a constitutive equation that describe the relationship between the current through THAT device and the voltage across THAT device. I presented all three equations (which should have been review of stuff covered in Physics II) and then said that for the next several weeks we were going to focus on purely resistive networks only because we want to keep the math simple as we develop several key analysis techniques. Then we will add in capacitors and inductors and discover that they throw us into the realm of having to deal with differential equations, so we will then figure out some tricks that will allow us to use slightly more complicated versions of the same analysis techniques that we developed for purely resistive circuits.

 

Back when I was teaching Linear Systems I, I tried to head this off -- with some success -- by stressing the first day that we were going to be looking at circuits involving three kinds of passive devices: resistors, capacitors, and inductors. That each had a constitutive equation that describe the relationship between the current through THAT device and the voltage across THAT device. I presented all three equations (which should have been review of stuff covered in Physics II) and then said that for the next several weeks we were going to focus on purely resistive networks only because we want to keep the math simple as we develop several key analysis techniques. Then we will add in capacitors and inductors and discover that they throw us into the realm of having to deal with differential equations, so we will then figure out some tricks that will allow us to use slightly more complicated versions of the same analysis techniques that we developed for purely resistive circuits.

Hat's off to you man. Too bad so many instructors don't make such an effort to present things clearly. Makes you think they should really include a "Teaching 101" prerequisite credit for those wanting to be teachers in the first place.

 

Hat's off to you man. Too bad so many instructors don't make such an effort to present things clearly. Makes you think they should really include a "Teaching 101" prerequisite credit for those wanting to be teachers in the first place.

Some places (I'm talking about colleges, not K-12) have something in place, but unfortunately the notion of "academic freedom" is placed on such an absurdly high pedestal that anything smacking of telling someone how or what to teach is considered in unforgivable infringement at many places.

 

What's wrong with the Wiki information other than the fact it's true in this case?

Of course all is good.

You've really gone off the deep end now with ether theories and other tripe. What next? Links to perpetual motion using static magnetic fields and electrons.

It is up to you.