How do you figure that Vy = 0 just because the red node is 0 V relative to ground?Your result is not correct. Look at the circuit; the node you have colored red is connected to ground. Assuming the usual convention, the voltage at the reference node (ground) is taken to be zero volts. This means that Vy is zero, and your equation 6 is not correct. Since the dependent voltage source Vs1 has value 25*Vy, its output must also be zero; therefore Vb is also zero.
You may have other errors but I haven't tried to find any.
It looks to me like Vy IS the red node; it's grounded, is it not?. I don't think that the purple node is at 0 V relative to ground.How do you figure that Vy = 0 just because the red node is 0 V relative to ground?
This is a bit of a trick question to my mind. We already have a definition for the voltage across the is2 source, Ve.
Ve is NOT defined as the voltage across the is2 source, it is defined as the voltage, relative to the common reference node, at node e. That it is numerically equal (in magnitude) to the voltage across the is2 source is a coincidence on two counts -- first it is a coincidence of the topology in that the other side of the source happens to be connected to the red node and, second, it is a coincidence of the arbitrary assignment of the red node as being the common reference node.This is a bit of a trick question to my mind. We already have a definition for the voltage across the is2 source, Ve.
The behavior of any particular circuit is dependent on many coincidences of the topology. Because one end of is2 is connected to ground, defining the voltage across it to be equal to the voltage at Ve relative to ground (for the purpose of analysis of this circuit) is to use an equivalent definition, for this particular circuit, and it's this particular circuit with all the coincidences that accompany it that I'm concerned with. To say otherwise for this circuit, as the lawyers would say, is a distinction without a difference. For some other choice of reference node there would be a difference, but not for this circuit as presented, coincidences and all.Ve is NOT defined as the voltage across the is2 source, it is defined as the voltage, relative to the common reference node, at node e. That it is numerically equal (in magnitude) to the voltage across the is2 source is a coincidence on two counts -- first it is a coincidence of the topology in that the other side of the source happens to be connected to the red node and, second, it is a coincidence of the arbitrary assignment of the red node as being the common reference node.
If the green node were the reference node, and if it were wanted that the controlling voltage be the voltage across is2, then that controlling voltage would have to be specified in such a way that made that clear. An example of where an unambiguously specified controlling voltage is across a component without one end grounded is the voltage Vx here: https://forum.allaboutcircuits.com/threads/dc-circuit-help-with-dependent-current-source.36737/Surely you would agree that if someone happened to decide that the green node would make a better common reference node that the circuit's behavior will not change. But if we use Ve (or -Ve) as the controlling voltage for the vs1 dependent voltage source, it would change since Ve changes with a change in reference node.
I fully understand that you believe the Vy symbol would represent the voltage across is2 regardless of which node is chosen as the reference node. I've explained why I don't interpret Vy the same way you do. If the Vy symbol had been placed much closer to is2 I would agree, but it is closer to the red colored parts of the circuit than to is2.But vs1 is not controlled by the voltage at a node, it is controlled by the voltage difference between two nodes (which is virtually always the case with a voltage-controlled source), thus the circuit needs to define the controlling voltage as being the voltage difference between the correct two nodes and that definition is completely independent of which node we happen to call "ground".
Then let's consider this circuit as presented. You said that we already had a defined voltage, namely Ve. That's not the case. The circuit, as presented, does not define ANY node voltage -- I'm not even sure that it defines the common reference node as the ground symbol appears hand drawn -- note particularly that it does not connect to the node at the connection dot, that the line connecting it actually crosses the node line, and there is no connection dot where it does cross. But even if it is defined, none of the other node voltages are defined by the problem as presented -- those are all names assigned by the TS.The behavior of any particular circuit is dependent on many coincidences of the topology. Because one end of is2 is connected to ground, defining the voltage across it to be equal to the voltage at Ve relative to ground (for the purpose of analysis of this circuit) is to use an equivalent definition, for this particular circuit, and it's this particular circuit with all the coincidences that accompany it that I'm concerned with. To say otherwise for this circuit, as the lawyers would say, is a distinction without a difference. For some other choice of reference node there would be a difference, but not for this circuit as presented, coincidences and all.
Simple. As you say, those other textual descriptions are "their" descriptions -- they define and describe the source. Vy is NOT the textual description for a source -- it is merely the definition of the controlling signal for one of the sources. Since the controlling signals are almost never immediately adjacent to the source they control, it is hardly reasonable to draw a conclusion based on this one not being close to the source it is associated with (which, by the way, is vs1). This would be the same as drawing some conclusion based on ix, the controlling signal for is1, not being drawn immediately adjacent to some source.Why is it that the all of the other sources have their textual descriptions immediately adjacent to them?
The location of the label, as far as whether it is in the middle or closer to one node or the other, is irrelevant. The far more important information that trumps that is that it is located in line between the two polarity marks so as to associate them as a set. This is the preferred layout. Because of the limited horizontal extent of both nodes, there is no way to move them outward far enough to enable the label to be centered vertically while still being inline with the marks. So it either had to be above or below the outline of the source symbol and the usual convention when this is the case is to place it on the positive side of the definition.The Vy symbol is closer to the red colored parts than to the is2 source itself; why wasn't it placed immediately adjacent to is2 if it was intended to represent the voltage across is2? I don't think it's unreasonable to believe that Vy is a designator for the red colored node. That would make for a nice trick to ensnare the student.
That vertical line connects to the supernode definition. I can't make out what it says either. Looks like Σn, which is perhaps a shorthand used by the TS's professor for "sum of nodes" to indicate a supernode. But that IS pure speculation on my part. Since that label is never used anywhere in the analysis, I can't see that it matters.Maybe the TS redrew the circu ciit, and chose the ground node. Look just below the green node. There's a small vertical line, and something just below that line that I can't make out.
I don't believe I am, precisely because I am using information in the circuit, as presented, that you are steadfastly refusing to consider.There are also 5 little horizontal lines just above the existing ground symbol. Do those things indicate that the TS modified the drawing he was given? If some node other than the red node (let's say the green node) were the reference node, then the proximity of the Vy symbol to the red color would even more strongly convince me that Vy would be the designator for the red node, and not the voltage across is2. Then Vy would represent the voltage of the red node relative to the green node, and 25 Vy as the controlling voltage of vs1 would workable even though this would give a different result than the given problem, because then Vy would not be equal to -Ve.
Since you are not the author of this problem, you are speculating as much as I am.
It's fine if you aren't following all the details at this point. Let them simmer in the back of your mind and, as you work more problems, particularly ones in which you have to come up with the schematics because you are involved in designing the circuit, the more subtle points being discussed will invariable raise their ugly heads again and you will be better able to reflect, even if just subconsciously, on discussions like this and make better sense of what you are doing.I can't begin to understand what you guys are talking about. I've solved the problem and have gotten the same answer as my teacher (ix = -0.379[A]). If there is a mistake in one of my labelings or maths please refer specifically to them in my work and I will be the wiser for it. Otherwise thank you for all your help in the matter.
Thanks, Jony. I think that makes it pretty clear what Vy has to mean.I upload orginal question and circuit.
Here is the matrix you derived and its solution showing all of your variables, not just Ix. I checked the numbers in this matrix several times and I believe I'm using the same values shown on your work sheet.I can't begin to understand what you guys are talking about. I've solved the problem and have gotten the same answer as my teacher (ix = -0.379[A]). If there is a mistake in one of my labelings or maths please refer specifically to them in my work and I will be the wiser for it. Otherwise thank you for all your help in the matter.
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