Equivalent circuits

[Richardcavell]

Hi.

I designed a circuit, on the left.  I then decided to redesign it, and you see the result on the right.

Are these circuits "equivalent" to each other?  Are they the same circuit?

The only difference that I can think of is that the one on the left, you can put an ammeter into the horizontal wire in the middle to detect whether there's current flowing.

Richard

[retiredfeline]

They are equivalent. You haven't redesigned it, you've just redrawn the graph a different way. Why are the battery symbols slightly different though?

[Richardcavell]

The battery symbols are slightly different because I didn't pay attention when laying this out on the web program that I used.  I don't intend for there to be any meaningful difference.

So if I build this circuit, am I allowed to place the wires wherever is convenient for me?  If I am the builder, not the engineer, do I have to ask the engineer for permission?

[retiredfeline]

In theory, the circuits are equivalent because all the connected junctions collapse to a single vertex in the graph. In the real world, wires have resistance and inductance. So I wouldn't make one of the wires 1 km long and expect the same result. But you get the idea.

Not sure why you think you need permission to build such a simple circuit.

[tooki]

Hi.

I designed a circuit, on the left.  I then decided to redesign it, and you see the result on the right.

Are these circuits "equivalent" to each other?  Are they the same circuit?

They're the same circuit. The thing to remember is that a schematic is not a wiring diagram. A node is a singular thing, no matter how you draw it. There is no "horizontal wire" -- in the schematic, it's all a singular node. You can redraw it in countless ways. (And indeed, a key skill in analyzing circuits is to redraw them into familiar forms that make it easy to identify and analyze.)

The only difference that I can think of is that the one on the left, you can put an ammeter into the horizontal wire in the middle to detect whether there's current flowing.

Now, if you want to model how it behaves if you were to insert a physical wire there, then you have to actually insert the wire as a component. For modeling (e.g. in LTspice), you might insert a resistor with a very low resistance (e.g. 0.01 ohms) so you can see how current balancing works in it. If the point is to give assembly hints, you might use a jumper component instead.

It's good that you are thinking about things like this. Just remember that the schematic is nothing more than a graphical representation of nodes, not a wiring diagram.

[golden_labels]

From mathematical perspective, the model in both cases looks this way:

Yes, the way we draw circuits is a kind of counter-intuitive: because what we draw as lines are graph nodes, while “fat” elements are in fact edges. Blame history.

And, in fact, note what happens if you want to calculate the resistances. Your first step will be treating each pair of 100Ω/200Ω resistors as parallel — the same as your second picture.

Of course, as tooki noted, in real circuits wires don’t have zero resistance. But in a model those lines are not wires: they mark a single node with a single voltage on it.

[Zero999]

They're the same circuit.

Note that most simulator programs will not work with that circuit, because you didn't provide a 0V reference node. There are some simulators which will guess, but it's always better to put a 0V/ground symbol somewhere, so the voltages are predictable.

[Terry Bites]

Learn a bit about topolgy in maths.
Its not "math" because there's more than one of them.

[ledtester]

Its not "math" because there's more than one of them.

And it's "sports" not "sport" because there's more than one of them.

[tooki]

Its not "math" because there's more than one of them.

In North America we say “math”, because in our usage, it is an abbreviation of the already-plural “mathematics”. It’s every bit as correct as the British pluralization of an abbreviation of a singular. (If anything, the North American usage is more logical, since English doesn’t have a singular noun “mathematic”.)

[golden_labels]

Topology doesn’t help, if you don’t know the underlying mathematical structure. OP apparently didn’t know the model, so why would they be “learning a bit about topology”?

If you know the model, seeing it is sufficient to understand. Most EE never learned topology and somehow they have no trouble grasping equivalence of both diagrams. And knowing topology doesn’t provide any insight deeper than that.

So what’s the point of telling OP to learn topology?

I don’t get lecturing about “maths” vs “math” too, given nobody used either in this thread. Even worse, in that single sentence you are wrong on so many levels.

[EEVblog]

As others have said, the two circuits are identical.
Unless there are specific requirements (like say a star ground), as a general rule you aren't going to draw your schematic the same as how you lay it out on the PCB.
So you saying "you can put an ammeter into the horizontal wire in the middle to detect whether there's current flowing" is based on how you physically lay the circuit out on the PCB and do the traces.

A simple resistor circuit like this has no electrical requirements that dictate that it needs a specific physical PCB layout.
In this case you could have your circuit on the left but the PCB designer could have phsyically laid it out like the circuit on the right, and that would be normal practice.

[boB]

The battery symbols are slightly different because I didn't pay attention when laying this out on the web program that I used.  I don't intend for there to be any meaningful difference.

Yes !  What you have made is a schematic symbol of a battery with a couple of shorted cells !

It is a new circuit element ! 

 

So if I build this circuit, am I allowed to place the wires wherever is convenient for me?  If I am the builder, not the engineer, do I have to ask the engineer for permission?

[MrAl]

Hi.

I designed a circuit, on the left.  I then decided to redesign it, and you see the result on the right.

Are these circuits "equivalent" to each other?  Are they the same circuit?

The only difference that I can think of is that the one on the left, you can put an ammeter into the horizontal wire in the middle to detect whether there's current flowing.

Richard

Hi there,

Because you have drawn the circuits differently and also in addition to that asked the question about asking the designer of the circuit for permission to change it, the implication is that your intention is to wire it differently than what was normally expected.  The short answer then is, "Yes", you do have to ask permission to wire it differently.

That's because there are subtle yet important differences in the way some things are wired.  It depends what kind of circuit it is of course as an RF circuit would be different than a pure DC circuit and different than a Power circuit or Control circuit, but in most cases you have to pay attention to how long the wires are and where they are placed and things like that.  This is involved in the transition from schematic to a real-life product.  Other issues come up such as parasitics.

Most of the time the schematic does not show the wiring details, but sometimes it DOES.  This is to put an emphasis on the way the circuit should be wired, even though it is not in great detail.
For one example, if that short center 'wire' in your right-hand side schematic was drawn as a thicker line than the others, that would indicate that that wire should be of larger diameter (heavier gauge wire).  This technique would be found in various Power circuit like power supply circuits and the like.
For another example, sometimes you will find several wires that come in at various angles and form a single 'point' where they all connect.  That is to put emphasis on the fact that there should be a single point in the real-life layout where all those wires are ONLY connected at that single physical point.  This would also be found in Power circuits such as power supplies.  The intention circuit wise is to control current flow through the various wires so that the current in one wire does not affect the current in another wire by altering the voltage at some node other than that one single point.  Schematic wise, the intent is to put emphasis on the need for this kind of attention to the wiring detail.
Those kinds of drawings are usually also accompanied by a note explaining the importance of such a wiring scheme.
It's interesting to note that a simulator may not show any difference, but if you substitute the parasitic values in for the wires you then can see a huge difference in circuits involving higher currents especially if they are constantly changing.
You can see the difference if in your right-hand side schematic you substitute some arbitrary resistance values in for each wire.  The node voltages will change.  If they change a lot it could be a big problem.  This is a very significant issue in power circuits like in power supplies.

This as all why the short answer I gave was "Yes", you have to ask if the change will be acceptable.  Sometimes there are notes that specify how the wiring is to be laid out too though so you don't have to ask any questions.  A long time ago when wire wrapped prototype circuits were still being used, we had to lay out the entire wiring plan so the assemblers would be sure to get all the wires (every one of them) in the right place.  This was to manage current flows and also noise issues and EMI.  That required a completely separate diagram though.