Can someone explain to me how the equations for the star-delta circuit
transformation are derived? (refer to
http://en.wikipedia.org/wiki/Y-delta_transform) I am interested in the
transform from the delta arragement to the star. Using the symbols
defined on the linked page, to derive R1, R2 and R3 in terms of Ra, Rb
and Rc I presume you have to consider the resistance between each of
the terminals in turn. Doing this I get:

Ra=R1+R3
Rb=R1+R2
Rc=R2+R3

Which, when solved, gives an equation for the resistors of:

R1=0.5(Ra+Rb-Rc)
R2=0.5(-Ra+Rb+Rc)
R3=0.5(Ra-Rb+Rc)

Which is incorrect. I guess there must be a fault in my logic at step
1! How do you correctly evaluate the resistances between points x, y
and z?

You are leaving out one of the paths current can follow in the delta
circuit.  Current can flow from x to z say through Ra, as you've
accounted for, but also the 'long way' through both Rb and Rc.  So
instead of

Ra = R1 + R3,

you need to calculate the actual impedence between x and z in the
delta circuit.  To do that:

1/Rxz = 1/Ra + 1/(Rb + Rc) = (Ra + Rb + Rc) / (Ra (Rb + Rc))

So:

Ra(Rb + Rc) / (Ra + Rb + Rc) = R1 + R3

You can derive similar equations for the impedences between the other
two pairs of points, and solve the system.

Bump! Thanks very much...

I must have been busy sleeping when I was trying to figure that one out!