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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.

mike65535
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Biker
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  • Is your question specifically about using superposition to prove Y-Δ transform, or are you questioning superposition in general? – brhans Oct 03 '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 03 '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 04 '18 at 06:48
  • Here's an [animated GIF](https://i.stack.imgur.com/af5i8.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 04 '18 at 23:22
  • I understood what the wikipedia article did now. It is actually brilliant. If there is more sure :) – Biker Oct 05 '18 at 11:20
  • @Biker So the animated GIF helped you? If so, I'm glad. Sometimes, just doing a little geometric exercise can open eyes where a series of mind-numbing algebra expressions cannot. I enjoy the process of seeing things visually or, more especially, in thinking about the "fundamental shape" of problems -- an area of which is Clifford algebra or geometric algebra. If you get a chance and the inclination, you will gain a lot from that area alone. – jonk Oct 05 '18 at 21:12

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Please take a look at this:

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

I think it might be helpful.

Dr. Strange
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