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

[Edy56]

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...

 

[DaveE]

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.

 

[DaveE]

Khan academy has some good tutorials about this stuff.
https://www.khanacademy.org/science...rcuit-analysis/a/ee-circuit-analysis-overview

 

[hutchphd]

I would phrase that differently. There are always four distinct paths. There are many sets thereof: all will lead to the same result.

 

[FactChecker]

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.

 

[berkeman]

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.

 

[DaveE]

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.