I came across this interesting video on youtube. Here's the link.

I think I understand what he's saying but he loses me at the part where he says connected one voltmeter here and another one there.

Regardless of which "side" the wires go, as long as two voltmeters are connected to the exact same nodes(Polarities also same), they should give identical readings no?

Puzzling...

 

I think this has been discussed previously on AAC.

http://forum.allaboutcircuits.com/showthread.php?t=16150

 

As soon as he wrote

\(
E = 1V = \frac{I}{R_1+R+2}
\)

I was pounding my head on my palms because we KNOW it's wrong because the units don't work out.

Now, he didn't utilize the equation for the next step and did spot it and pointed it out. I know full well how easy it is to make all kinds of glaring errors when you are writing on a chalkboard, talking, and trying to keep your presentation on track. One thing I always did was give one point of extra credit (typically out of about a thousand points for the entire course) to the first person that could point out an error I had made on the board. I wanted them paying attention and getting in the habit of looking for errors and I also wanted my inevitable mistakes caught as early as possible to minimize the backtracking. It was, unfortunately, still the case that I caught the overwhelming majority of my errors before any student pointed them out. I once toyed with the idea of doubling the points each time a given student brought an error to my attention. So the eight error a person got would have gotten them more than half the total points in the course in extra credit. But I haven't given it a try yet.

He may have been talking about hypothetical voltmeters that somehow chose the path through which they were taking the measurement. Otherwise, I was expecting him to actually show the readings.

But, having said that, it is possible that he meant physical voltmeters; I would have to play with the math a bit to convince myself one way or the other. Notice that when the meter is on the right side of the circuit, the solenoid is inside the loop created by the meter and the 100Ω resistor but outside the loop created by the meter and the 900Ω resistor. When it is on the left side, the opposite is true.

 

they should give identical readings no?

Puzzling...

It is puzzling for sure, but the answer is no because the path of the leads matters when you have non-conservative fields.

As mentioned, this subject has come up a few times. I participated in the discussion referenced. I also was debating the subject at the physics forums, and because of the mis-information given there, I felt compelled to do my own experiments and analysis and document the results. I've attached a copy of the document I published there.

 

Steve,

In the earlier thread, you said in one post:

"He is basically playing a magic trick on us. He sets up a field problem and expects us to be surprised that circuit equations do not work. If you only know circuit equations, you are surprised and can't explain the result. If you know field theory but don't use it often, you are surprised at first, but will understand once he explains. If you do field theory all the time, you just say, "yeah, so what?"."

When I viewed the video, that last one was also my reaction--"Of course; tell me something I don't know."

 

This dragged on so long I gave up on his astounding discovery.

tl;dr