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## Homework Statement

R1=28Ω, R2=30Ω, R3=15Ω, R4=55Ω, R5=11Ω, R6=25Ω, R7=35Ω, R8=20Ω, R9=40Ω, R10=75Ω, and R11=13Ω.

Determine the current through resistor R3.

Find the values of the unknown resistors needed for equivalence.

http://C:\Users\me\Desktop\deltawye.png http://C:\Users\me\Desktop\deltawye.png http://C:\Users\me\Desktop\deltawye.png

## Homework Equations

R

_{ab}= R

_{c}(R

_{a}+ R

_{b})/ (R

_{a}+R

_{b}+R

_{c}) = R

_{1}+ R

_{2}

## The Attempt at a Solution

I transformed the bottom delta in the first circuit in the attached image into a wye using the above equation to get the second circuit. However, I'm having trouble finding the values of R

_{12}and R

_{13}in the third image. I'm not sure how to tell what resistors are in series or in parallel with each other in the second circuit once a transformation is done. I thought that in the second circuit that R

_{11}, R

_{10}, R

_{b2}, R

_{b3}, R

_{8}, and R

_{5}were all in series with each other, so I added up the values of those resistors to get 143 ohms as the value of R

_{13}in the third circuit. However, I don't understand then, what the value of R

_{12}could be in that case. I'm also not sure how to tell what resistors are in series or in parallel when the transformed circuit looks like the second attached image. In that circuit, I had thought that the 10, 12.5, 40, and 37.5 ohm resistors were in series with each other, and that those were also in series with the 50 and 5 ohm resistors, but I know that doesn't make any sense. How would I be able to find the equivalent resistance in the circuits in those two images?

I would really appreciate any help on this. Thanks so much.