Y-Δ transform proof using superposition

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The discussion centers on the Y-Δ transform proof, specifically questioning the application of superposition in demonstrating the equivalence of two circuits. Participants highlight that traditional proofs involve equating equivalent resistances while isolating nodes, but clarity on how superposition applies is lacking. The principle of superposition is acknowledged as applicable to linear equations, yet the specific conditions for each situation in the proof remain unclear to some. The original poster seeks a detailed explanation of these conditions and how to sum them effectively. Overall, the conversation emphasizes the need for a clearer understanding of the superposition principle in the context of the Y-Δ transformation.
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In the wikipedia page and on every book they proof the transformation by equaling the the equivalent resistance between any pair of terminals while disconnecting the other node.https://en.wikipedia.org/wiki/Y-Δ_transform

Why this should make the two circuits equal? How can we apply superposition here? I have searched everywhere for this answer, In no where anyone explained this. Please explain the principle or this way of proof
 
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In general, when equations are linear you can apply superposition.
 
anorlunda said:
In general, when equations are linear you can apply superposition.
Yes I know that but I am asking how you can do that? Like what codition do you put in each situation then sum it up?

In wikipedia they put some conditions on the current in 3 situation but I didnt understand how ?
 
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