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What is the best way of solving the circuit?

(*steve*)

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What ways have you tried?
 

pyler

Sep 19, 2012
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What ways have you tried?

Nodal analysis and mesh analysis
I was thinking of doing a source transformation for the left resistor and current pair on the left and right of the network but was not sure.


With nodal analysis, I used the middle node and defined ground to be at the lower right corner of the network but didn't get anywhere with that. I had two equations with three unknowns and I couldn't find a useful way of writing one of the variables in terms of the other(s) so I abandoned nodal analysis. I tried solving the currents and voltages using the the left and right nodes but didn't get far...
 

(*steve*)

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For nodal analysis, maybe you could try using the centre point as your defined ground. That should simplify the equations.

Then try solving for each independent voltage and current source, one at a time, then sum the solutions.
 

Laplace

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The equations for nodal analysis are the easiest to write, and least likely to make mistakes. Using a symbolic algebra program allows for a minimum busy work solution. See attached analysis.

The node equations are written for each of the identified nodes: V1, V2, V3, & V4 with currents I1 & I2. I like the convention that current leaving a node is positive while current entering a node is considered negative. That way the equation for any node always begins (V,node - V,othernode). Note that here V1=100 and I1 is a multiple of (V1-V2)/6 so there are 4 equations and 4 unknowns (V2,V3,V4,I2). Once the initial equations are written, MathCAD makes it easy to solve the system of 4 equations by repeated copying and pasting of substitutions. Algebra manipulations are handled automatically by the 'solve' command. Calculations are done in place and intermediate results are not shown, otherwise the size of the pdf file would exceed the limit for posting here.
 
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(*steve*)

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Looks a bit like a solution Laplace?

I've unapproved your attachment at the moment. Did you go too far?
 

Laplace

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Did you go too far?

Possibly. But the OP didn't seem to have sufficient grounding in nodal analysis to be able to know what to do with cryptic hints. The OP seemed to need an example to demonstrate that nodal analysis was possible and even the best way to analyse this circuit. Perhaps I should have constructed the example with slightly different component values in order to demonstrate the method without providing the exact solution. See attached nodal analysis for a modified circuit that illustrates the technique.
 

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  • Mathcad - Nodal-Analysis.pdf
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CocaCola

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Possibly. But the OP didn't seem to have sufficient grounding in nodal analysis to be able to know what to do with cryptic hints.

Or laziness... This isn't just a model he/she whipped up in paint one day for the heck of it, I'll place money on it being a copy out of a homework assignment...

Thus doing the homework and giving the answer does not provide (in your words) the 'sufficient grounding in nodal analysis' that the exercise was supposed to teach or test for...

The OP seemed to need an example to demonstrate that nodal analysis was possible and even the best way to analyse this circuit. Perhaps I should have constructed the example with slightly different component values in order to demonstrate the method without providing the exact solution. I'll do that next time.

I agree using different values and even a slightly different model would be a better choice, make the student work the noodle vs cut and paste the answer on his homework... With the advent of the Internet it scares me how many students are getting degrees in stuff that they have little to no understanding of because they cheated there way to answers on the Internet... It's bad enough there are mathematical programs that do all the work for equations and the students likely never learn any advanced math, but giving them the answer flat out only furthers the problem...
 

CocaCola

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The OP posted this on at least 2 other forums, and got a solution on one of them right away.

And IMO that is sad, a bunch of inept graduates with degrees that they obtained by cheating due to Internet do-gooders that willingly did their homework for them...
 

(*steve*)

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What would be really funny is if we could somehow find that the OP was attending the University of Massachusetts.

Since pyler hasn't deemed it appropriate to return, we could email someone there, say Prof. Hollot, and see if he could put us in contact with him.

Of course, we only have a couple of IP Addresses and times, but since at least some of these were from the University network, I'm sure their admins could assist in getting the message back to pyler.

Like I said, it would be funny. But I'm only joking of course. How would we know any of that? (Incidentally, I couldn't find their undergraduate honor code, so I have emailed the person above to ask for a copy to post here)
 

pyler

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And IMO that is sad, a bunch of inept graduates with degrees that they obtained by cheating due to Internet do-gooders that willingly did their homework for them...

This, therefore because of this, that....
need I say more?
 
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pyler

Sep 19, 2012
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The equations for nodal analysis are the easiest to write, and least likely to make mistakes. Using a symbolic algebra program allows for a minimum busy work solution. See attached analysis.

The node equations are written for each of the identified nodes: V1, V2, V3, & V4 with currents I1 & I2. I like the convention that current leaving a node is positive while current entering a node is considered negative. That way the equation for any node always begins (V,node - V,othernode). Note that here V1=100 and I1 is a multiple of (V1-V2)/6 so there are 4 equations and 4 unknowns (V2,V3,V4,I2). Once the initial equations are written, MathCAD makes it easy to solve the system of 4 equations by repeated copying and pasting of substitutions. Algebra manipulations are handled automatically by the 'solve' command. Calculations are done in place and intermediate results are not shown, otherwise the size of the pdf file would exceed the limit for posting here.

Thanks. There must be an efficient method for solving this though.
 

The Electrician

Jul 6, 2012
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Thanks. There must be an efficient method for solving this though.

If by efficient, you mean less work to find a solution, letting a computer do most of the work is about as efficient as it gets.

If you don't care about the current through the 100 volt source, you could use a nodal formulation of 3 equations in 3 unknowns, since the voltage at the node where the 100 volt source is connected is known.

Otherwise, you've got 4 unknowns however you formulate it.

If, on the other hand, you mean compactness of appearance of the solution, the best you can do is to formulate as a matrix solution.

Since Laplace has already done a nodal formulation, go back to the other forum where you were given a mesh solution:

http://forum.allaboutcircuits.com/showthread.php?t=75500

Formulating as a matrix solution, you have what I've shown in the attachment. The only work you, the human, has to do is to set up the problem; the computer does the algebra for you. I don't know how you can get any more efficient that that.
 

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  • MeshFormulation.png
    MeshFormulation.png
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CocaCola

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This, therefore because of this, that....
need I say more?

You did originally before you edited the post, with some excuse about how you just whipped up this problem for the heck of it... You must have realized how silly that sounded since it's been pointed out you cross posted the thread to multiple forms seeking an answer rather than actually interacting to discover and discuss said answer and how to go about solving it :rolleyes:
 

(*steve*)

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This, therefore because of this, that....
need I say more?

I wrote more, but it boils down to: "A perception of dishonesty will act against you".
 

pyler

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You did originally before you edited the post, with some excuse about how you just whipped up this problem for the heck of it... You must have realized how silly that sounded since it's been pointed out you cross posted the thread to multiple forms seeking an answer rather than actually interacting to discover and discuss said answer and how to go about solving it :rolleyes:

This, therefore because of this, that....
 

(*steve*)

¡sǝpodᴉʇuɐ ǝɥʇ ɹɐǝɥd
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You did originally before you edited the pos

Do you mean when he said this?

Hahahahaha

.....actually this was a practice problem that I was trying to do but didn't know where to start. I've solved a number circuits using nodal analysis,mesh analysis and KVL/KCL on networks with fewer elements but that became boring so I decided to try some hard ones and....

On that note I usually do all my work and rarely ask for help except for when I attempt to move from a basic or intermediate understanding of something to an advanced understanding.

And incidentally, whilst I composed and saved an email to the university concerned at the time, I did not send it. I have reconsidered that and I am now awaiting a response.
 
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