How can I show that R and RL are equal in this Y/Delta circuit problem?

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The discussion focuses on demonstrating the equality of resistances R and RL in a Y/Delta circuit. The user has attempted circuit simplification but lacks direction on how to proceed. After converting the Y configuration to Delta, the new resistances are identified as 3R, 3R/4, and 3R. Further conversion back to Y yields resistances of R/3, R/3, and 4R/3, leading to the equation Rab = RL = R/3 + [4R/3*(R/3+RL)]/(R/3 + 4R/3 + RL). The user expresses gratitude for the assistance and seeks help with a subsequent part of the problem involving total current calculations.
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Homework Statement


[PLAIN]http://img38.imageshack.us/img38/1620/halpwd.jpg


Homework Equations


I've been simplifying the circuit but with no real objective or guidance. I just don't know how to even begin to show that R and RL are equal. Can someone please help me?


The Attempt at a Solution


This is my work so far. I've just tried simplifying it, but like I said I have no real idea what to do next.
http://img706.imageshack.us/img706/6398/imggc.jpg
 
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You have already converted Y to Δ.

After simplification, new Δ consists of 3R, 3R/4 and 3R.

Again convert Δ to Y. Three sections contain R/3, R/3 and 4R/3.

So Rab = RL = R/3 + [4R/3*(R/3+RL)]/(R/3 + 4R/3 + RL)

Simplify the equation.
 
Wow, thanks a lot!
 
Does anyone know how I can get part B?
 
Total current I = vi/R.

Current through c-d branch is

T2 = I*(4R/3)/2*4R/3 = I/2

vo = R*I/2 = vi/2
 

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