Y-Δ transform proof using superposition

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SUMMARY

The forum discussion centers on the Y-Δ (Wye-Delta) transform proof using superposition, specifically addressing the conditions under which the equivalent resistance between terminals is established. Participants highlight that the transformation is validated by disconnecting one node and equating resistances, as outlined in the Wikipedia article on Y-Δ transforms. The application of superposition is emphasized, particularly in linear equations, but clarity on the specific conditions for each scenario remains a point of confusion among users.

PREREQUISITES
  • Understanding of Y-Δ transform principles
  • Familiarity with superposition theorem in linear circuits
  • Basic knowledge of equivalent resistance calculations
  • Experience with circuit analysis techniques
NEXT STEPS
  • Study the mathematical derivation of the Y-Δ transform
  • Learn about the superposition theorem in electrical engineering
  • Review examples of equivalent resistance calculations in circuit analysis
  • Explore advanced circuit analysis techniques using linear equations
USEFUL FOR

Electrical engineering students, circuit designers, and anyone involved in circuit analysis or studying linear electrical systems will benefit from this discussion.

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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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