Circuits Question - Thevein & Norton Equivalents

GreenPrint

1. The problem statement, all variables and given/known data



Find the Thevenin and Norton equivalent of the circuit above between A and B using the node voltage method.

2. Relevant equations



3. The attempt at a solution

I place the ground reference at the node with where the two 10 ohm resistors, 30 volt supply, 40 ohm resistor, and 1 amp source meet in the upper right hand corner.

I'm confused by this problem. If I put a wire between A and B to find the short circuit current than the equivalent resistance between the 100 ohm resistor and the wire is zero ohms so I can just ignore this particular resistor. However I don't understand how any current is traveling though this part of the wire since it's just one giant node with one voltage so how can any current travel through it? Thanks for any help.

ehild

Currents flow through wires. The resistance of an ideal wire is zero, and multiplied by any current it gives zero voltage across. And you can make that wire short, even shrink it to a node, the same current flows through. But it is better to keep that wire between A and B and find the current through it.

The internal resistance both for Norton-equivalent or Thevenin-equivalent sources can be got also as the resistance of the circuit between A and B by replacing all voltage and current sources by their internal resistance (zero for ideal voltage source and infinite for an ideal current source).

ehild

GreenPrint

Ok so I built it in Circuit Lab to confirm that the node voltages I found where correct.



Node 9 = -61 Volts
Node 11 = 5 Volts
Node 12 = 128.75 Volts
Node 13 = -76.25 Volts

So agrees with what I calculated.

[itex]V_{Th} = V_{13} - V_{12} = -76.25 V - (-128.75 V) = 52.5 Volts[/itex]
[itex]V_{Th}[/itex] has an orientation of
A + - B
Where node 13 or A is more positive than node 12 or B

I than calculated [itex]R_{Th}[/itex] by the method below
I think that the answer I get in this post is wrong for the Thevenin equivalent resistance because I forgot to disable a current source.







As you can see I get [itex]R_{Th} = 76.19 Ω[/itex]. Below is what I get for the Thevenin and Norton equivalents of the circuit.




As you can see I get [itex]I_{Th} = 689.1 mA[/itex]. I think however that I'm doing something wrong but I'm not sure what.

GreenPrint

Oh I think I forgot to take out one current source.
So I think it should be
[itex]R_{Th} = 100 Ω[/itex]
[itex]I_{N} = .525 A[/itex]
[itex]V_{Th} = 52.5 V[/itex]

I still think I'm doing something wrong though.

gneill

Your Vth looks okay, but Rth is a problem. Check to make sure that you suppressed all the sources correctly.

GreenPrint

Shouldn't it just be the equivalent of this circuit?

gneill

Yup. That looks better. What's Rth then?

GreenPrint

I still get 100. Am I supposed to include the resistor between nodes A and B as part of the equivalent resistance?

gneill

Absolutely.

GreenPrint

So the answers I get for using the node voltage method is as follows:



The picture won't load but it's the same voltage already found with a 200 ohm resistor.

Now when I try to use source conversions I get a different answer. I'm really confused by source conversions and hate using this method. Any help would greatly appreciate me.



Here's my attempt













As you can see this answer is wrong as it dosen't match up.

Thanks for any help!

gneill

I don't know how you got from the second diagram in your attempt to the third. Looks like some rules were badly bent out of shape... like adding current sources that are not in parallel.

GreenPrint

Well like what can i do from the second one? I know that I can add that one set of parallel resistors. on the left but I don't see what else I can go from there.

gneill

Yes, definitely put those two resistors in parallel.

Something helpful to know: A resistor in series with a current source has no effect -- an ideal current source will produce its specified current no matter what its load is. What does that mean in practical terms? Since it doesn't matter what values those resistors have they might as well be zero! You can eliminate those resistors entirely, replacing them with wires. That should get you going.

GreenPrint

When I get down to here and covert the to a voltage source and a resistor in series I don't get the same answer =( is the above circuit above correct?

gneill

How did the 26.19Ω resistance evolve? It doesn't look right to me.

GreenPrint

Ok so it should be 50, this would give me the correct resistance, but that still dosen't give me equivalent voltage, it would give me 105 volts.

gneill

Yes, but 105 Volts spread across two 100Ω resistances....