Current sources power balance, nodal analysis. Urgent!

Thread Starter

Abdelrahman123

Joined Nov 2, 2016
6
In nodal analysis, when I solve a problem using a supernode and I get two node voltages with the same voltage we assume that the current in the common branch has zero current if R has value since the voltage difference = 0 like in question 3.13 Ch 3 Fundamental of circuits Alexandar. The question is does this really happen if yes why?

Another question about current sources and power balance. How to know whether a current source is dissipating power or supplying power. Do we need to let their calculations at the end and assign their values with the net power due to voltage sources and load or can we know expect it's power state from the direction of currents?

Thanks in Advance.
 

RBR1317

Joined Nov 13, 2010
605
If you replace the branch between the two nodes of equal voltage with a wire, is the rest of the circuit affected in any way? If so, then how it is affected? Does the same current flow in the wire as did in the branch components it replaced?

What is a current source? Is it not just a voltage source with the unique property that it adjusts the voltage supplied to whatever value is necessary to drive the specified current through the circuit? If you analyze a circuit and find the voltage across the current source, can you then replace the current source with a voltage source supplying the calculated voltage? Will the same current flow through the voltage source?

So would the same power be supplied/dissipated in the current source as in its replacement voltage source?
 

WBahn

Joined Mar 31, 2012
26,398
Don't expect that people here have access to the exact textbook that you are using. If you want to refer people to a particular problem, then copy, scan, sketch, or take a picture of the problem and include it with your post.

If you have a voltage difference of zero across a resistor, then there will be no current flowing in it. As for why, well just ask yourself if there was a current flowing in the resistor, which direction would it be flowing? Symmetry says that the direction is indeterminate, so neither direction can be correct. Thus the only correct answer is that it is flowing in neither direction and that means that there isn't any current at all.

As for the net power of a current source, the answer is the same as for the net power of a voltage source or a resistor or any other two-terminal device. If the current is leaving the device via the more positive voltage terminal, then it is delivering power, otherwise it is absorbing power.
 

MrAl

Joined Jun 17, 2014
7,978
Hi,

A super node is not exactly explained properly in any text i have read so far. That is probably because most circuit theorists talk about a 'short' between nodes when there really is NO SUCH REAL SHORT THERE.
A short implies that we connect a zero resistance wire between two nodes that were not the same to begin with. But that confuses the issue of how a super node works because we dont really handle the equations as if there was a real short there. In the equations i2=i1, but v2-v1 equals some constant or function.

The better way to explain a super node is that we apply an anisotronic short which is a short that has different properties depending on how we measure it. The anisotronic short can have different voltages at both nodes yet have the same current flowing through it. This means that the current flowing through resistor networks on either side will have the same current even though the voltage at the two nodes is different. Note this is not the same as a direct short which makes the two voltages the same as well as the current flowing through it the same. That is why i think the super node causes some confusion, because a short makes the two voltages the same while with a super node that's not the case. In the equations this means the same as before, except it is better explained then when using a direct short because with a direct short we can not have two different voltages but with an anisotronic short we can. This means that both currents are the same (like a direct short) but the two voltages are NOT the same (not like a direct short) unless we feel like allowing them to be the same (an option we retain in theory).

As to the second question, when the two voltages ARE really the same too, then a direct short does not change anything. The catch though is that the two voltages have to be the same for ALL time and ALL temperatures, and in fact for any conditions the two voltages must always be the same.
A counter example is an op amp input, where the inverting input is sometimes treated as a 'virtual ground' when the non inverting terminal is connected to ground. This view is good for some calculations but not others. If we short the two inputs, the op amp no longer functions properly. That is because although the two can be treated as the same voltage for some calculations, they are not really the same for all time and must be allowed to work independently of one another. This is a good critical view of this concept because with infinite gain the two inputs are exactly the same, but in the physical world we can not short them together. This is a little bit of a theoretical conundrum.
 
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RBR1317

Joined Nov 13, 2010
605
A super node is not exactly explained properly in any text i have read so far. That is probably because most circuit theorists talk about a 'short' between nodes...
Since I was not familiar with the concept of a 'short' between nodes, I went back to my first textbook explaining supernodes (Linear Circuits, by R. E. Scott, 1960):

"The Kirchhoff current law can be written at any single node in a network, but it can be written as well for any subsection of the network. The sum of currents entering the subsection must be equal to the sum of the current leaving the subsection. Such a subsection of the network represents a collection of nodes, and is termed a supernode. Not all of the current law equations written for the nodes and supernodes in a network will be independent. Our principal problem will be to determine how many of these equations are independent, and to find an easy way to write a set of independent current law equations. Any one set of equations will be satisfactory because the others can be obtained from this set by addition and subtraction."
 

MrAl

Joined Jun 17, 2014
7,978
Since I was not familiar with the concept of a 'short' between nodes, I went back to my first textbook explaining supernodes (Linear Circuits, by R. E. Scott, 1960):

"The Kirchhoff current law can be written at any single node in a network, but it can be written as well for any subsection of the network. The sum of currents entering the subsection must be equal to the sum of the current leaving the subsection. Such a subsection of the network represents a collection of nodes, and is termed a supernode. Not all of the current law equations written for the nodes and supernodes in a network will be independent. Our principal problem will be to determine how many of these equations are independent, and to find an easy way to write a set of independent current law equations. Any one set of equations will be satisfactory because the others can be obtained from this set by addition and subtraction."
Hi,

First, thank you for that post. That's an interesting way to look at this.

I do feel that it is still a little too over complicated, but the author was probably reaching for concepts that extend beyond the simple concept of a supernode.

The way i see the description of a short as being used in explaining a supernode is similar (not exact though) to the way we might see a resistor used to explain a diode. Imagine a full wave bridge made up of resistors instead of diodes, and then the author in a side note explaining: "Each resistor only conducts in one direction".
Not that cool right? If they were diodes, we'd see that right away.
With the supernode 'short', if we knew it was a special kind of short to begin with, we'd know what to expect right away just by knowing the special properties of that special kind of 'short' which isnt really a short anyway.
The diode acts like two different values of resistor depending on some conditions, while the supernode 'short' acts like two values of resistor also: 1. Like a zero ohm resistor, and 2. like an infinite value resistor, where the choice depends on what equation we are writing or simply what view point we are talking about. So is is sort of like a diode except the conduction properties depend on what our intentions are for that 'short' at the moment rather than what the current or voltage actually is at the moment.
 
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The Electrician

Joined Oct 9, 2007
2,815
When a homework problem has "Urgent!" in the subject, I think that the homework is due very soon, so I would have expected that Abdelrahman123 would be long gone. But I see that he checked in after RBR1317's last post.

The TS asked about current in a branch that was part of a supernode. He wanted to know: if the two nodes have the same voltage, is the current in a resistor-containing branch between the two nodes zero? A circuit diagram appeared in post #4 and we see that the branch in question has not only a resistor, but also a voltage source. Solving the circuit, we find that the node voltages v1 and v2 are indeed equal, but the current in the 2 ohm resistor is not zero.

So, Abdelrahman123, did you notice that the current in the 2 ohm resistor is not zero, and do you understand why?
 

Thread Starter

Abdelrahman123

Joined Nov 2, 2016
6
The Electrician Yes, I noticed that really was my point of confusion but I explained it with the short circuit. Short circuits have current through them, but we assume that they have zero resistance like superconductors and therefore the voltage difference is zero. The thing is that now the 3 ohm resistance from one point of view has 0 current as V1 = V3 ( V3 is the virtual node between the voltage source and the 3 ohm resistor) , but actually this branch has current of V1 / 8 ohm. And I think the confusion here is due to some fallacy in our assumptions that short circuits has zero resistors which actually is not true except under certain conduction of superconductivity. There for the equal voltages of nodes is due to this assumption of zero resistance for short circuits and the voltage source is assumed to be a short. Therefore there was the compensation in over the 3 ohm resistor. What I found that's a common side effects of many like theories.

All in all, Thanks for all people that tried to help me. I really appreciate that!
 

The Electrician

Joined Oct 9, 2007
2,815
If V3 identifies the node between the 2 ohm resistor and the voltage source, I don't think that V1 = V3. If V1 is not equal to V3 then there is no confusion about short circuits.

How did you derive the voltage at V3?
 
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