Star and Delta Configurations
The Star network is also known as the T or Y configuration and the Delta network is also known as the triangle (Δ) or pi (Π) configuration.
Delta to Star TransformationFirst eliminate the connection C considering it to by open circuit.
For the star configuration this makes the resistance between A and B equal to RA + RB.
For the delta configuration the resistance between A and B is equal to RAB in parallel with RBC + RAC which is equal to RAB(RBC + RAC)/(RAB + RBC + RAC).
As these networks must always be equivalent: RA + RB = RAB(RBC + RAC)/(RAB + RBC + RAC).
Similarly for B open circuit: RA + RC = RAC(RAB + RBC)/(RAB + RBC + RAC).
Finally for A open circuit: RB + RC = RBC(RAB + RAC)/(RAB + RBC + RAC).
From these three independent equations after some manipulation the following is obtained:
RA = RABRAC/(RAB + RBC + RAC)
RB = RABRBC/(RAB + RBC + RAC)
RC = RBCRAC/(RAB + RBC + RAC)
Star to Delta TransformationRAB = RA + RB + RARB/RC
RBC = RB + RC + RBRC/RA
RAC = RA + RC + RARC/RB