Find the current through a complicated circuit

[DaveE]

Way to let the OP do his own work

Yes, I get that. I thought the thread had moved beyond the OP's solution. So I was more in the mode of "train the trainers". Showing how EEs use schematics and circuit analysis to focus on the nature of lumped element networks. It truly doesn't matter at all what the physical shape of the circuit is once you've defined the lumped elements; it could be a sphere or a square, whatever. It's a network problem, not a mechanical one. This is one of the key things that many physicists don't get about circuits, they are highly contextualized to allow you to focus on tools like KVL/KCL etc.

Step 1: strip out all of the irrelevant information. Step 2: speak to other EEs in a language we all are comfortable with. This avoids the confusion you saw at the beginning with other EEs not understanding about "fading resistors" and such.

I confess that I get tired of HW problems that are trying to trick the students instead of focusing on the key analytical issues.

 

[Orodruin]

This is one of the key things that many physicists don't get about circuits, they are highly contextualized to allow you to focus on tools like KVL/KCL etc.

I don’t think this video supports the claim that many physicists don’t understand KVL application to circuits. It shows that Walter Lewin may not understand it (and possibly anyone he taught). In fact, Lewin himself says everybody else is wrong.

It truly doesn't matter at all what the physical shape of the circuit is once you've defined the lumped elements; it could be a sphere or a square, whatever. It's a network problem, not a mechanical one.

While true, drawing it one way or the other can certainly help in guiding your mind in identifying good ways of analysing a circuit.

Ultimately, the image in the OP does not seem as much a circuit diagram to me as an attempt to illustrate the construction (which was perfectly well defined in terms of descriptive text).

 

[DaveE]

Walter Lewin may not understand it

Yes there's no doubt that he knows EM. What he doesn't know is this: "Kirchhoff's circuit laws are two equalities that deal with the current and potential difference (commonly known as voltage) in the lumped element model of electrical circuits." -- the first line of Wikipedia on Kirchhoff's laws.

Ultimately, the image in the OP does not seem as much a circuit diagram to me as an attempt to illustrate the construction (which was perfectly well defined in terms of descriptive text).

OK, but then they shouldn't have used the lumped element resistor symbol. When I see that, I assume that all of the interconnections are assumed to have zero resistance (and no induced voltage). That symbol tells me it's a network problem, not a mechanical one and thus shape doesn't matter.

It's not the concepts, physicists don't understand, it's the language.

PS: Plus Dr. Lewin doesn't know much about oscilloscope probes, but that's a different issue.

 

[Orodruin]

OK, but then they shouldn't have used the lumped element resistor symbol. When I see that, I assume that all of the interconnections are assumed to have zero resistance (and no induced voltage). That symbol tells me it's a network problem, not a mechanical one and thus shape doesn't matter.

That’s more of a language problem based on where you are coming from I think. I personally had no problems understanding what was implied from neither text nor image, but I have a different background and do not make the same assumptions. Similar to how people speaking dialects of the same language sometimes not understanding exactly what the other means. That doesn’t mean either is correct or wrong, just that they will be misunderstood in some situations when surrounded by people from the other place.

 

[DaveE]

That’s more of a language problem based on where you are coming from I think. I personally had no problems understanding what was implied from neither text nor image, but I have a different background and do not make the same assumptions. Similar to how people speaking dialects of the same language sometimes not understanding exactly what the other means. That doesn’t mean either is correct or wrong, just that they will be misunderstood in some situations when surrounded by people from the other place.

Yes, exactly. The issue is, do you know which language you are speaking? Does the listener? This is precisely Lewin's problem with induced voltages and KVL.

 

[SammyS]

Nice, but can you give the answer you got for completeness of this thread?

Highly doubtful.

OP has a (bad) habit of not giving feedback on his/her final solutions.

 

[bob012345]

The OP's trick solves this as does solving the set of current-voltage equations but is there any other way to solve for the net resistance between any two nodes without assuming anything about currents?

 

[DaveE]

The OP's trick solves this as does solving the set of current-voltage equations but is there any other way to solve for the net resistance between any two nodes without assuming anything about currents?

You mean Kirchhoff's laws? Your spice simulator does it that way.

 

[bob012345]

You mean Kirchhoff's laws? Your spice simulator does it that way.

I used Kirchhoff's laws to get equations for the currents but I meant rules like adding resistors in series and parallel. Are there special rules if they are mixed series and parallel? I suspect not.

 

[DaveE]

Are there special rules if they are mixed series and parallel?

No, the rules are simple. Either they are in series or not, either they are in parallel or not. Sometimes it's sort of an iterative process. Other times it just can't be simplified down to one resistor (like T and π sections).