Inductance of a double circuit line -- struggling with return the path

AI Thread Summary
The discussion revolves around understanding the inductance of a double circuit transmission line, specifically the self and mutual geometric mean distances. Participants express confusion about the return path of current in parallel conductors, questioning how currents in conductors labeled as a-a' and b-b' interact. Clarification is sought on whether these conductors carry currents in opposite directions or if they are truly in parallel, particularly in a three-phase system. The labeling of conductors as 'supply' and 'return' is noted to be potentially misleading, causing further confusion. The importance of addressing these ambiguities with instructors is emphasized to ensure accurate understanding.
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So for inductance of transmission line book says formula
H = 2 * 10 -7 Loge { [Ds]/[Dm] }
I'm struggling to understand self and mutual geometric mean distance.
Here is one solved example
upload_2017-12-26_11-3-26.png

and for this they've drawn
upload_2017-12-26_11-3-56.png

And they say that let a a' form one connection and let b b' form other connection.
I'm struggling to understand how are they in parallel.
Current will go from a and return from a' or return from b?
How can b and b' be return path? As per question two upper and two lower conductors are in parallel so it means a and b are in parallel. So current in a and current in b have to be same.

And in three phase there are conductors r - r', y - y', b - b' So does this mean r and r' are in parallel or is it like current goes from r and returns from r' at one instant.
 

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This 3-phase double circuit.
upload_2017-12-26_11-9-32.png

I don't understand what does a -a' mean. Are they in parallel or do they carry currents in opposite direction?
And here is double circuit another example.
upload_2017-12-26_11-12-1.png
 

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From the text description I get.

In the first image. You are looking at the ends of four wires. They extend into the page. It seems the current requirement is greater than is convenient for a single conductor to carry. To handle the extra current, two conductors are used, wired electrically in parallel. A set of two conductors would be A&B (call that pair the 'supply' side). For the 'return' side the set of two conductors is A'&B'.

That is certainly not the way I would prefer to label them, it makes it too confusing... perhaps that is the 'standard' way of labeling them, but it seems strange.

p.s. If you are graded as 'wrong', you may have to point out the ambiguous description to your instructor. Print this out if needed to show him.
 
Thanks. So according to you the top conductors carry current I and bottom conductors carry -I at a given instant of time?
 
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