# Delta-Y transformation of resistors

• franktherabbit
In summary, the Delta-Y resistor transformation work out the conductance transformation equation, but the equation they get is different than the equation they use for Y-Delta transformation. They must have used a logical move to get there.
franktherabbit

## Homework Statement

Starting from the expression of the Delta-Y resistor transformation work out the conductance transformation equation.

## Homework Equations

3. The Attempt at a Solution [/B]
I will just be using one equation as others are done analogically. My Δ has ##(R_{12},R_{23},R_{13})## and my
γ has ##(R_1,R_2,R_3)##.
The first equation of transformation goes:
##R_1=\frac{R_{12}*R_{31}}{R_{12}+R_{23}+R_{13}}##
When i use that ##R=\frac{1}{G}## i get that
##G_1=\frac{G_{12}+G_{23}+G_{31}}{G_{23}}## which is not what they get. They get the same equation you get for Y-Delta transformation except for R u write G. ow did they get to that? I used a logical move and it can't get that way. What am i missing?

franktherabbit said:
I used a logical move and it can't get that way. What am i missing?
Must be an algebra issue somewhere... but we can't tell you what's missing since it's almost all missing --- we can't check what we can't see

Can you show your work in detail?

Sure, :).
##R_1=\frac{R_{12}*R_{31}}{R_{12}+R_{23}+R_{31}}##
##G_1=\frac{1/G_{12}+1/G_{23}+1/G_{31}}{1/G_{12}*1/G_{31}}##
##G_1=\frac{(G_{12}+G_{23}+G_{31})/(G_{12}*G_{23}*G_{31})}{1/(G_{12}*G_{31})}##
##G_1=\frac{G_{12}+G_{23}+G_{31}}{G_{23}}##
See it? :)

I don't see how you went from your second line to your third. You haven't involved he denominator yet, so everything must be happening in the numerator. There you should end up with a sum of products divided by a product since all the terms are different.

franktherabbit
gneill said:
Must be an algebra issue somewhere... but we can't tell you what's missing since it's almost all missing --- we can't check what we can't see

Can you show your work in detail?

gneill said:
I don't see how you went from your second line to your third. You haven't involved he denominator yet, so everything must be happening in the numerator. There you should end up with a sum of products divided by a product since all the terms are different.
Ohhh, i see now, i had this all wrong. Turns out algebra is the killer here. Thanks man! :D

gneill

## What is a Delta-Y transformation of resistors?

A Delta-Y transformation, also known as a Pi-T transformation, is a method used to simplify a circuit with three resistors in a triangle configuration into a circuit with three resistors in a Y configuration. This can help make the circuit easier to analyze and calculate.

## Why is the Delta-Y transformation useful?

The Delta-Y transformation can simplify a complex circuit into a simpler one, making it easier to analyze and calculate. It can also help in finding the equivalent resistance of a circuit or determining the current and voltage across each resistor.

## How do you perform a Delta-Y transformation?

To perform a Delta-Y transformation, you need to first identify the three resistors in a triangle configuration. Then, label the top resistor as RAB, the bottom left resistor as RAC, and the bottom right resistor as RBC. Next, you can use the following equations to calculate the equivalent resistances of the Y configuration: RAB = RARB / (RA + RB + RC), RAC = RARC / (RA + RB + RC), and RBC = RBRC / (RA + RB + RC).

## What are the limitations of the Delta-Y transformation?

The Delta-Y transformation is only applicable to circuits with three resistors in a triangle configuration. It cannot be used for circuits with different configurations or a different number of resistors. Additionally, the transformation only works for resistors in a linear circuit and does not account for non-linear components.

## Are there any real-life applications of Delta-Y transformation?

The Delta-Y transformation is commonly used in power distribution systems, such as in electrical grids, to simplify and analyze complex circuits. It is also used in electronic circuits to calculate the equivalent resistance and determine the voltage and current flows through each resistor. Additionally, the transformation is helpful in solving problems in network analysis and electric network topologies.

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