Engineering Confused about defining unique current loops when using the node voltage method

AI Thread Summary
In the discussion about defining unique current loops using the node voltage method, it is clarified that while multiple paths exist between nodes, only four independent loops are necessary to describe the circuit accurately. Each loop must include unique components not found in the others, ensuring all parts of the circuit are accounted for. Writing equations for redundant loops is discouraged as they do not contribute additional information. The choice of loop direction, preferably clockwise, is recommended to minimize errors in equation formulation. Ultimately, any selection of four independent loops will yield the same results for the circuit analysis.
Edy56
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Homework Statement
Write equations using node voltage method
Relevant Equations
none
Please only respond if you know the node voltage method.
I need to write equations for this circuit. My problem is that 1 has two paths towards 3, so when I write equations do I write both of those paths or only one.
U30(1(-jXc1)+1/(jXl1+R1)+1/(jXl2)-U10((1/(-jXc1)+1/(R1+jXl1))-U20.... (the rest is unimportant rn).
or
U30(1(-jXc1)+1/(jXl2)-U10((1/(-jXc1))-U20...
node.png
 
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There are 4 unique loops in that network. You are free to choose any set of 4 loops as long as you don't repeat any of them. All will yield the same result in the end.

PS: A fifth loop equation will be redundant. Not wrong but useless.
 
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Likes FactChecker and hutchphd
I would phrase that differently. There are always four distinct paths. There are many sets thereof: all will lead to the same result.
 
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As long as each loop has something unique that is not in the others, and all parts are included in some loop, it will work out. That means you will have 4 independent (not redundant) equations that describe the entire system. The solution will be the same.
 
Edy56 said:
Please only respond if you know the node voltage method.
One tip about using KVL is to always choose your loops in one direction (I prefer clockwise myself). It will help to avoid making errors when writing the equations.

It's similar when using KCL -- I always write my node equations with the current *leaving* the node.
 
hutchphd said:
I would phrase that differently. There are always four distinct paths. There are many sets thereof: all will lead to the same result.
Yes. The word unique is completely wrong. There are lots of unique loops, much more than four (10, I think). But only 4 (any 4) are independent.
 
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