Delta to Star/Y Conversions and vice versa in Electric Ciruits We all know the basic rules for conversion of $"Delta"$ circuits to $"Star"$ circuits and vice versa. We also know that this is needed for simplification of circuits in complex cases. Can anyone please explain HOW the concept of such conversions came about?
To be clearer, can anyone show the derivation of the Conversions? for both Capacitors and Resistors?
 A: The concept is a special case of a more general topological notion of graph theoretic duality: see the Wikipedia page for Dual Graph. 
Graph theoretic duality is "compatible" with the Kirchoff voltage law (voltages around a loop sum to nought) and charge conservation (currents into a node sum to nought) insofar that nodes in a graph map to loops in a graph theoretic dual, so that we get a meaningful electric circuit for the dual if we swap the roles of voltage and current - the two laws (Kirchoff voltage and charge conservation also swap places). The impedances naturally transform too.
So, with graph-theoretic duality and electrical duality combined, we get the procedure written up in the Dual Impedance Wiki Page. The relationships between the star and its topological dual delta are specifically worked through as an example on this page. 
As in Alfred's comment, which references:
http://www.engineersblogsite.com/delta-to-wye-and-wye-to-delta-conversion.html
he says the rules work for any impedance, not simply resistances. The topological reasons given above show why.
