# 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 Transformation

First eliminate the connection C considering it to by open circuit.For the star configuration this makes the resistance between A and B equal to R

_{A}+ R

_{B}.

For the delta configuration the resistance between A and B is equal to R

_{AB}in parallel with R

_{BC}+ R

_{AC}which is equal to R

_{AB}(R

_{BC}+ R

_{AC})/(R

_{AB}+ R

_{BC}+ R

_{AC}).

As these networks must always be equivalent: R

_{A}+ R

_{B}= R

_{AB}(R

_{BC}+ R

_{AC})/(R

_{AB}+ R

_{BC}+ R

_{AC}).

Similarly for B open circuit: R

_{A}+ R

_{C}= R

_{AC}(R

_{AB}+ R

_{BC})/(R

_{AB}+ R

_{BC}+ R

_{AC}).

Finally for A open circuit: R

_{B}+ R

_{C}= R

_{BC}(R

_{AB}+ R

_{AC})/(R

_{AB}+ R

_{BC}+ R

_{AC}).

From these three independent equations after some manipulation the following is obtained:

R

_{A}= R

_{AB}R

_{AC}/(R

_{AB}+ R

_{BC}+ R

_{AC})

R

_{B}= R

_{AB}R

_{BC}/(R

_{AB}+ R

_{BC}+ R

_{AC})

R

_{C}= R

_{BC}R

_{AC}/(R

_{AB}+ R

_{BC}+ R

_{AC})

## Star to Delta Transformation

R_{AB}= R

_{A}+ R

_{B}+ R

_{A}R

_{B}/R

_{C}

R

_{BC}= R

_{B}+ R

_{C}+ R

_{B}R

_{C}/R

_{A}

R

_{AC}= R

_{A}+ R

_{C}+ R

_{A}R

_{C}/R

_{B}