# Y-Δ transform proof using superposition

In the Wikipedia page and in every book they prove the transformation by equaling the equivalent resistance between any pair of terminals while disconnecting the other node. https://en.wikipedia.org/wiki/Y-%CE%94_transform

Why this should make the two circuits equal? How can we apply superposition here? I have searched everywhere for this answer. Nowhere has anyone explained this. Please explain the principle or this way of proof.

• Is your question specifically about using superposition to prove Y-Δ transform, or are you questioning superposition in general? – brhans Oct 3 '18 at 19:07
• About using it to prove the transformation, They treat one node as not connected because of superposition.. I dont understand how. – Biker Oct 3 '18 at 19:11
• Are you looking for more of a straight-forward derivation from one to the other using nodal analysis? (Algebra, really.) Or are you looking to gain a geometric understanding, more qualitative and perhaps less algebra-heavy, where you can mentally move smoothly from one to the other in your mind? (There is a third concept which is neither the delta nor the Y that intercedes between these two and simplifies to one or the other, at each extreme.) – jonk Oct 4 '18 at 6:48
• Here's an animated GIF that illustrates the geometry of the conversion. If it turns out you'd like more explanation, I'll add it (including superposition algebra if you want it.) [I chose one direction to illustrate in that GIF. Of course, the reverse direction is also true.] – jonk Oct 4 '18 at 23:22
• I understood what the wikipedia article did now. It is actually brilliant. If there is more sure :) – Biker Oct 5 '18 at 11:20

Superposition problem with $$\\Delta\$$-Y conversion