Simplifying a Circuit Using a Y-to-Δ Transformation

[Drakkith]

Homework Statement

[/B]
A.) Simplify the circuit (Figure 1) by using a Y-to-Δ transformation involving the resistors R2, R3, and R5 as shown in (Figure 2) . Determine the resistances of the equivalent Δ.

B.) Determine the equivalent resistance R_ab in the circuit.

Hopefully these two figures show up. If not, just say so and I'll try to fix them.

Figure 1.

Figure 2.

Homework Equations

The Attempt at a Solution

I've simplified the circuit and found:
R_a = 154 Ω
R_b = 92.4 Ω
R_c = 18 Ω 118 Ω

I know these values are correct. My problem is with part B. Now that I've got the resistance of the 3 new resistors, I'm unsure about how to find the equivalent resistance between terminals a and b. What about this Y-to-Δ transformation makes this circuit easier to work with?

 

[magoo]

It looks like Ra and R1 are in parallel. R4 is in parallel with Rc.

Does that help?

 

[Drakkith]

It looks like Ra and R1 are in parallel. R4 is in parallel with Rc.

Does that help?

R1 looks like it is in parallel with Ra and Rb+Rc, which wouldn't be a problem except that there's a node connecting Rb to the other side of R4, which is in series with R1.

 

[cnh1995]

What about this Y-to-Δ transformation makes this circuit easier to

As magoo showed, you can see it converts the network into a simplified circuit (series or parallel resistances).

R1 looks like it is in parallel with Ra and Rb+Rc, which wouldn't be a problem except that there's a node connecting Rb to the other side of R4, which is in series with R1.

No two (individual) resistances are in series in this network.

 

[Drakkith]

As magoo showed, you can see it converts the network into a simplified circuit (series or parallel resistances).

Oh I see it now. I see that R1 and Ra are in parallel, and it looks like R4 and Rc are in parallel too, as Magoo said.

No two (individual) resistances are in series in this network.

Ah, that's right.

 

[cnh1995]

Oh I see it now. I see that R1 and Ra are in parallel, and it looks like R4 and Rc are in parallel too, as Magoo said.

If you have time, you can try solving the same problem using
i)wye-delta transform on R1, R3 and R4
ii) delta-wye transform on R1, R2 and R3.
You'll see how they simplify the network.

 

[The Electrician]

Homework Statement

[/B]
A.) Simplify the circuit (Figure 1) by using a Y-to-Δ transformation involving the resistors R2, R3, and R5 as shown in (Figure 2) . Determine the resistances of the equivalent Δ.

B.) Determine the equivalent resistance R_ab in the circuit.

Hopefully these two figures show up. If not, just say so and I'll try to fix them.

Figure 1.
View attachment 211331

Figure 2.
View attachment 211332

Homework Equations

The Attempt at a Solution

I've simplified the circuit and found:
R_a = 154 Ω
R_b = 92.4 Ω
R_c = 18 Ω

I know these values are correct. My problem is with part B. Now that I've got the resistance of the 3 new resistors, I'm unsure about how to find the equivalent resistance between terminals a and b. What about this Y-to-Δ transformation makes this circuit easier to work with?

I don't think your 3 values for Ra, Rb and Rc are corrrect. One can work backwards with a delta to wye transformation and get the original R2, R3 and R5. If I do this I get:

53.82
10.48
6.29

Since you didn't give a value for R2 in post #1 we can't compare one of the three to it, but two of the three just calculated should equal 50 and 30 (R3 and R5); they don't. How do you know your values are correct?

 

[Drakkith]

Since you didn't give a value for R2 in post #1 we can't compare one of the three to it

My apologies, I had forgotten that they don't give us the value of R2 in the figure, but in the previous question. I assume it changes for every student and they didn't want to make a different figure for each person.

For this question R2 = 39 Ω.

Also, it appears I made a typo in my original post. R_c = 118 Ω, not 18.

How do you know your values are correct?

The online program we're using for class had me find those values prior to this question and it says they are correct. I just didn't double-check my post closely enough to make sure I hadn't made any typos.

 

[Drakkith]

Alright, I finally got the right answer.

R1 in parallel with R_a: R_1a= 37.745 Ω
R4 in parallel with R_c: R_4c= 17.101 Ω

R_1a4c in parallel with R_b: R_1a4cb = 34.417 Ω

R_eq between terminals a and b: R_eq = 34.417 + 7 + 13 = 54.417 Ω

Thanks all. Sorry for the confusion.