Ah, I think I misinterpretted your post and thought you were saying that a zero resistance inductor would always have zero voltage across it because the resistance is zero.

But I see what you are getting at and, yes, there would be no shifting of current. But this is not the big quandry that it might seem. Consider a tank of water sitting on a table and we sit a second, empty tank next to it and then insert a tube the comes up out of one tank, goes over the rim, and down into the other tank. The total gravitational energy stored is more than if the two tanks had the same water level and there is even a path for water to travel. But if the tube wasn't filled with water when it was inserted, then there is an "activation" energy that must be overcome in order for an equilibration to happen. Without that impetus, the system will be happy sitting there with more than minimum energy.

There is no shifting of current in the circuit theory model, but each time I try to see what happens in any physical arrangement of conductors, I see current sharing. I'm not saying I am analysing it in enough detail to determine how much current flows, but I see mechanisms that cause currents to flow in the second inductor that are not predicted by the circuit theory model.

 

What are those mechanisms?

In a prior post I said that if you have two superconducting coils in parallel that there will be current shifts between them as a consequence of external influences in their magnetic environments. For instance, if a magnetic material is moved in their vicinity it will result in changes in the self-inductance and/or changes in the mutual inductance. These will results in voltages across the terminals which will result in changes in the currents in the coils. This is all completely consistent with E&M theory.

 

What are those mechanisms?

In a prior post I said that if you have two superconducting coils in parallel that there will be current shifts between them as a consequence of external influences in their magnetic environments. For instance, if a magnetic material is moved in their vicinity it will result in changes in the self-inductance and/or changes in the mutual inductance. These will results in voltages across the terminals which will result in changes in the currents in the coils. This is all completely consistent with E&M theory.

I did a long reply but managed to lose it in the current captcha trap. So here is a short one:

Firstly, there is no inconsistency with EM theory, rather it was the inherent inconsistency in the circuit theory answer that sent me looking to the physics. In circuit theory, if I have an ideal 1nH inductor carrying 1A, and I place a second inductor in parallel then there is no mechanism to cause the current to share, even though the stored magnetic energy would be minimised if it was.

I'm sure that the physics would show that the unbalanced current distribution is unstable, and would balance it. I was just looking for the mechanism that was missing from the circuit theory.

This applies only to ideal inductors. If I have ideal 1nH and 2nH inductors in parallel, then the lowest energy solution splits the current inversely proportional to the inductance. Put equal resistors (even 1μΩ or less) in series with each inductor and the current shares equally. (There are many cases in circuit theory where the limit as a resistor tends to zero gives different results to the r=0 case).

stopping to avoid captcha..

 

continued..

Now imagine a perfectly conducting cylinder carrying a steady current. This current flows on the outside of the cylinder. Now consider a short piece of the same conductor brought up to connect to the first. Place it just nearby. There will be a circulating current induced in the second inductor to cancel the magnetic field from the current carrying conductor.

When you connect the second conductor to the first, this results in at least some current being diverted into the second conductor.

If you draw a loop to attach to the first conductor, this mechanism will divert some of the current in the first conductor through the second.

 

I am not trying to promote any particular method, though I have no beef with MNA, it is a good method. Since you have introduced it there is no need for me to pursue it. Equally I have acknowledged further methods introduced by others, without trying to belittle any of them.

...

So this is not the thread or forum to promote particular circuit analysis methods.

Studiot, I'm not trying to be disruptive or rude, but I do find this strange and unhelpful.

This particular subthread started when you asserted:

The point I didn't make properly earlier is that as soon as you connect them with a zero impedance strap wire you change the circuit by converting two nodes into a single node.

A single node does not (should not) have a 'voltage' across it, that requires two nodes. All points on the wire are part of the same node.

and I pointed out that there were some circuit analysis techniques that allowed you to analyse circuits where separate nodes were connected with zero resistance branches. I gave an example of a circuit from another thread and showed how you could analyse it using MNA. You claimed:

So essentially you are calculating with a currents and a voltage constraint, I am calculating with voltages and a current constraint. These are mathematically duals and lead to the same answer.

so I'm thinking 'great, this guy knows something I don't, I'll ask him to explain it and maybe I'll learn a new trick', so I give you a circuit that I would find difficult to analyse with nodal analysis so I would like to see your dual technique, and you reply that you are not prepared to 'belittle' MNA by showing me how to do it! Please, belittle away, we are engineers, we need to see our tools humbled so we know when not to use them.

When I analyse a circuit by hand I start by looking for tricks, Thevenin equivalents, symmetries, odd/even modes etc.. If this fails then I'll usually go for nodal analysis, except for the circuit in the other thread, where had I not seen the Thevenin trick I may have meshed or done MNA. I don't have 'favourites' to promote, I do Thevenin type things first as I can do them in my sleep, and they often lead to some understanding as to what is happening, whereas writing down circuit equations requires more thought. Solving for mesh currents always seems somewhat magical and normally doesn't help me understand what is happening.

 

Divided by a common language?

How on earth did you get from

I have no beef with MNA, it is a good method.
Since you have introduced it there is no need for me to pursue it.
Equally I have acknowledged further methods introduced by others, without trying to belittle any of them.

To

so I would like to see your dual technique, and you reply that you are not prepared to 'belittle' MNA by showing me how to do it! Please

My three sentences shortened and paraphrased.

1) MNA is good.

2) You have already described it.

3) There are other good methods.

Backalong I also asked you what you understand by a node.

You didn't reply.

I will add to this what do you mean by mesh analysis?

If you are looking for new methods, I also mentioned Maxwell's Mesh Method. This uses fictitious currents, unlike the Kirchoff loop analysis which I think your equations pertain to, except using conductances instead of resistances.

Can you confirm this is your understanding of the derivation of your equations?

These are very interesting questions and raise some interesting points of mathematics about linear circuit analyis. Not least that you can reconfigure the equations to the most convenient form for solution by change of basis.

A discussion is two way, as I said before, I am trying to respond to all your points, please return the courtesy.

 

Backalong I also asked you what you understand by a node.

You didn't reply.

I will add to this what do you mean by mesh analysis?

If you are looking for new methods, I also mentioned Maxwell's Mesh Method. This uses fictitious currents, unlike the Kirchoff loop analysis which I think your equations pertain to, except using conductances instead of resistances.

Can you confirm this is your understanding of the derivation of your equations?

These are very interesting questions and raise some interesting points of mathematics about linear circuit analyis. Not least that you can reconfigure the equations to the most convenient form for solution by change of basis.

A discussion is two way, as I said before, I am trying to respond to all your points, please return the courtesy.

I don't see why it is relevant to quiz each other on definitions, but rather to exchange tricks, but as you insist..

My understanding of circuit analysis is based on graph theory. Each component is represented by an edge in a directed graph. You need to know about cutsets and loopsets to understand some of the general formulations, I'm a bit rusty. Kirchoff's current law is generalised to a statement that the current out of any cut is zero, and the voltage law is simply that the sum of voltages around any loop is zero.

Formulating circuit equations reduces to producing sets of independent voltage or current equations, IIRC there are things called basic loopset matrices and basic cutset matrices that give independent sets. Basic loopsets and basic cutsets are sort of duals of each other, I think from one you can generate some sort of dual of the other - but it's been a while.

You can produce sets of nodal equations from a basic cutset (each cut gives an equation), but with nodal equations you can only have sources that have an admittance representation (no perfect voltage sources). If solving manually, you can allow voltage sources by eliminating some independent variables (i.e. if a node has a voltage set by a source you don't need to find it), but this is hard to generalise. The fact that a short circuit has no admittance representation is why you can't use nodal analysis to directly find the current in a short circuit between nodes.

You can produce sets of mesh (loop) equations from a basic loopset, but with mesh equations you can only have sources that have an impedance representation (no ideal current sources). Again, if working manually, you can often circumvent this my eliminating some variables. Generating a basic loopset for a planar network is easy, and is what is normally taught in circuit theory 101. It is hard to generalise to a general non-planar network, but graph theoretic algorithms can find a suitable mesh. The fact that a short circuit has an impedance representation is why you can use mesh analysis to solve for short circuit currents.

Nodal analysis is simplest to perform from the circuit netlist, but it suffers from not being able to include elements without an admittance representation (short circuits, current controlled sources, ideal transformers..). MNA simply removes those elements, and adds an additional independent variable which is the current in that branch, and one equation is added which is the constitutive equation of the branch. So no, MNA is not based on loop analysis.

There are lots of other ways, tableau techniques come to mind, but I know relatively little about them.

Change of bases is occasionally useful, but apart from odd and even mode analysis for symmetrical structures, and DFTs for phased arrays I don't use it much. Do you have any useful examples?

1) MNA is good.
2) You have already described it.
3) There are other good methods.

All methods are good for some problems, to be good at circuit theory you have to learn what techniques are best to apply to what problems. From what I know, I would conclude that the best general technique for the circuit I showed with the CCCS is MNA. When you say 'there are other good methods' you piqued my interest, but I suspect you were simply generalizing.

 

So studiot, do you now see that you can have separate nodes connected by zero impedance connections? It's just about the way you formulate the equations.