# Resistance between the terminals of a star configuration?

The derivation of the delta-star transformation rules is based on the fact that the resistance between terminals 1,3 is R1+R3 I can't see how we can consider R1,R3 just two resistances connected in series between terminals 1 and 3 with R2 having no significance in this arrangement. Can someone enlighten on this?

In the derivation you refer to, you start by getting some equations that must be true if the two circuits are to be equivalent. Once you get enough independent equations, you can isolate the parameter of interests (either $[R_1,R_2,R_3]$ or $[R_{12},R_{23},R_{31}]$) using usual algebraic methods.
Hence $R_1 + R_3 = R_{31} \parallel (R_{12} + R_{23})$. This gets you an equation. Repeating the same reasoning with terminals 1 and 3 open, gets you another two similar (but independent) equations. With a total of three independent equations you can isolate any 3 variables, hence you can express the parameters of the delta circuit using those of the star circuit or vice-versa.
If you don't understand why the presence of $R_2$ is irrelevant when terminal 2 is disconnected, keep in mind that in this case there is no current flowing in $R_2$. Hence the KCL equation at the junction between $R_1$, $R_2$, and $R_3$ is the same as if $R_2$ weren't there! Therefore, even if $R_1$ and $R_3$ are not topologically in series, they behave as if they were in series, because the equations you would write with or without $R_2$ would be equivalent.