Apply the Delta Wye Transform to a Circuit

[rugerts]

Homework Statement

For the circuit of Figure 5, the resistors values are given as: R1=2.2k, R2=4.7k,
R3=3.3k, R4=4.7k, R5=2.2k, and R6=3.3k. Use Delta-Wye transform for terminals ac-b so that the network in Figure 5 is replaced by the network shown in Figure 6. Given that
Vin=12V determine:
a. The resistors values in Figure 6, Rx, Ry, and Rz. Show all work.
b. The total power generated by the voltage source.

Relevant Equations

Delta Wye transform equations.

I'm trying to get transform the larger circuit into the smaller one and then from there calculate power. My plan was to do the transform and then use kirchhoffs laws to find the current tofind the power.
My work so far:

Is the sequence of steps I used valid? I'm not focusing on the calculations just yet. I want to see first if this is even valid so that it can look like the circuit of figure 6. Essentially what I did in my work was apply the transform and then rotate the circuit so that it looks like the one I want it to look like.

THanks

 

[tnich]

It's a little confusing that you label the resistances in the transformed circuit with $R_1,R_2,R_3$, but assuming I am interpreting that correctly, you need to the voltage source $V_{in}$ in your transformed circuit.

 

[rugerts]

It's a little confusing that you label the resistances in the transformed circuit with $R_1,R_2,R_3$, but assuming I am interpreting that correctly, you need to the voltage source $V_{in}$ in your transformed circuit.

Yes it should be there but I'm focusing on just getting the resistive network down first. Do you have any advice?

 

[tnich]

Yes it should be there but I'm focusing on just getting the resistive network down first. Do you have any advice?

I don't think you will have the resistance network right until you put in $V_{in}$.

 

[rugerts]

I don't think you will have the resistance network right until you put in $V_{in}$.

What does Vin being in the picture have to do with the resistors being in the right configuration?

 

[tnich]

I think that if you put $V_{in}$ in the circuit, you will see what is wrong with your diagram.

 

[rugerts]

I think that if you put $V_{in}$ in the circuit, you will see what is wrong with your diagram.

Okay, I've redrawn now. I can't seem to see how to take the next step into making it look like the one with Rx, Ry, and Rz.

It looks like 2.2 k is in parallel with Rc. Ra in parallel with Rb.

 

[tnich]

I suggest that you redraw the circuit to make it obvious which resistors are in parallel and which are in series. In this case, the circuit will look something like this:

You need to figure out where to put the resistors. It might help if you label each end of each resistor with a potential, and use the same label for all of the points at the same potential. The resistor ends should have the same labels in the new drawing.
EDIT: I read over the problem again. I think you are meant to transform the delta at the top of the original diagram to a wye. Instead, you have transformed the wye at to the bottom to a delta.

 

[rugerts]

I suggest that you redraw the circuit to make it obvious which resistors are in parallel and which are in series. In this case, the circuit will look something like this:
View attachment 251144
You need to figure out where to put the resistors. It might help if you label each end of each resistor with a potential, and use the same label for all of the points at the same potential. The resistor ends should have the same labels in the new drawing.
EDIT: I read over the problem again. I think you are meant to transform the delta at the top of the original diagram to a wye. Instead, you have transformed the wye at to the bottom to a delta.

This is my updated work. Thanks for the advice. Is this correct?

 

[tnich]

It looks to me as though you have labeled the b and c endpoints of the wye incorrectly, so your final figure is incorrect. The labels need to match the labels of your original circuit, not the diagrams for converting Delta to Wye.

 

[rugerts]

It looks to me as though you have labeled the b and c endpoints of the wye incorrectly, so your final figure is incorrect. The labels need to match the labels of your original circuit, not the diagrams for converting Delta to Wye.

Hm, I thought I made an effort to match my original circuit. See the first delta I drew. It doesn't follow the diagram; it follows my circuit. If it followed the diagram, the "c" would be at the bottom of the delta. I have a "b" there.

 

[tnich]

In the last diagram, the nodes are not labeled. In the second-to-last they they seem to be labeled incorrectly, and you have extended the wrong wire with resistor $R_6$.

 

[rugerts]

In the last diagram, the nodes are not labeled. In the second-to-last they they seem to be labeled incorrectly, and you have extended the wrong wire with resistor $R_6$.

I think it's correct now.

but do you have any advice on how to keep track of the nodes and their labels? Cause I tried going back and keeping track and noticed that my b and c seemed switched. Do I just choose an order (say: a b c) and then the nodes in every subsequent diagram follow that order a b then c.

 

[tnich]

I looks to me like you copied the node labels from the Delat-Wye transformation template when you applied the transformation, which were different than your node labeling. One way to avoid that would be to use the same labeling in your initial diagram that the template uses.