Introduction:
The Y-Δ transform, also written wye-delta and also known by many other names, is a mathematical technique to simplify the analysis of an electrical network. The name derives from the shapes of the circuit diagrams, which look respectively like the letter Y and the Greek capital letter Δ. This circuit transformation theory was published by Arthur Edwin Kennelly in 1899.

Equations for the transformation from Δ to Y

The general idea is to compute the impedance  at a terminal node of the Y circuit with impedances ,  to adjacent node in the Δ circuit by

where  are all impedances in the Δ circuit. This yields the specific formulae

Equations for the transformation from Y to Δ

The general idea is to compute an impedance  in the Δ circuit by

Example:

Find the resistance shown by the meter !

Let's convert the R₁, R₂, R₃ wye network to a delta network. This conversion is the best choice for simplifying this network

Solution by TINA's Interpreter

First, we do the wye to delta conversion, then we notice the instances of paralleled resistors in the simplified circuit.

{wye to delta conversion for R1, R2, R3 }

Gy:=1/R1+1/R2+1/R3;

Gy=[95m]

RA:=R1*R2*Gy;

RB:=R1*R3*Gy;

RC:=R2*R3*Gy;

Req:=Replus(Replus(R6,RB),(Replus(R4,RA)+Replus(R5,RC)));

RA=[76]

RB=[95]

RC=[190]

Req=[35]

.

With Dennis James Matildo.