Y-delta transform

Tags: #theorem

Y-delta transform

Given an electrical network which contains something that looks like a Y inside can be switched for a Δ triangle shape without changing the effective resistance of the graph.

\usepackage{circuitikz}
\begin{document}
\begin{circuitikz}  
  
% --- Y (star) network ---  
\draw  
(-4,0) node[left]{$A$} to[R=$R_A$] (-2,0)  
(-2,0) to[R=$R_B$] (-1.2,1.4) node[above]{$B$}  
(-2,0) to[R=$R_C$] (-1.2,-1.4) node[below]{$C$};  
  
\node at (-2,-2.2) {Y (star)};  
  
% --- Delta network ---  
\draw  
(2,0) node[left]{$A$}  
to[R=$R_{AB}$] (4,1.5) node[above]{$B$}  
to[R=$R_{BC}$] (4,-1.5) node[below]{$C$}  
to[R=$R_{CA}$] (2,0);  
  
\node at (3,-2.2) {$\Delta$ (delta)};  
  
% Arrow indicating equivalence  
\draw[->, thick] (-0.2,0) -- (1.2,0) node[midway, above] {equivalent};  
  
\end{circuitikz}
\end{document}