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

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Homework Help Overview

The discussion revolves around a Y/Delta circuit problem, specifically focusing on demonstrating the equality of R and RL. Participants are engaged in simplifying the circuit and exploring the relationships between the resistances.

Discussion Character

  • Exploratory, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to simplify the circuit but expresses uncertainty about how to proceed in showing the equality of R and RL. Some participants provide insights into converting between Y and Delta configurations and suggest simplifications that lead to equations involving R and RL.

Discussion Status

Participants are actively discussing the problem, with some offering guidance on circuit simplifications and conversions. There is no explicit consensus yet, as the conversation includes various interpretations and approaches to the problem.

Contextual Notes

The original poster indicates a lack of clear objectives or guidance in their attempts, which may reflect constraints in the problem setup or understanding. Additionally, there is a mention of a subsequent part of the problem that remains unaddressed.

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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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