How to calculate the equivalent resistance using wye delta ?

[Julian102]

Homework Statement

https://z-1-scontent-sin1-1.xx.fbcdn.net/hphotos-xtf1/v/t34.0-12/12435980_942112312550457_1708451532_n.jpg?oh=b29a5e9b2ff96bbf0e11932d081eb25e&oe=568A9B79 [/B]

We need to find the equivalent resistance along A to B ie AB

Homework Equations

R=(1/R1 + 1/R2+...+1/Rn)^-1 , Y-Delta transformation , equation for parallel combination, equation for series combination.

The Attempt at a Solution

I tried wye-delta but my teacher says that I need not use wye-delta .How possible? I have two answer 1.43 ohms and 1.6 ohms .What is the actual equivalent resistance? Can you please solve these problems? [/B]

 

[Julian102]

Is there any other way?

 

[cnh1995]

Well, I believe wye-delta will give you the answer since there are a lot of wyes and deltas in the circuit, but I think there is other way(simpler, maybe). Consider the two 2Ω resistors in the middle, which are parallel to AB. Replace each of them by a parallel combination of two 4Ω resistors. Now cut the circuit into two halves along the horizontal symmetry, separating the 4Ω resistors.

 

[Julian102]

Well, I believe wye-delta will give you the answer since there are a lot of wyes and deltas in the circuit, but I think there is other way(simpler, maybe). Consider the two 2Ω resistors in the middle, which are parallel to AB. Replace each of them by a parallel combination of two 4Ω resistors. Now cut the circuit into two halves along the horizontal symmetry, separating the 4Ω resistors.

Then what will be the equivalent resistance?

 

[cnh1995]

Lets call the side along which we cut the circuit as CD Now, the equivalent resistance( between A and B )of the lower part and equivalent resistance of the upper part(between C and D) will be in parallel, which will give you net resistance between A and B. Out of that, equivalent resistance of the lower part is very easy to find, just by series-parallel combination. But for the upper part, I think you need to use wye-delta at least once(or twice). Seems that you can't get rid of wye-delta so easily! But I think the no of wye-delta conversions is reduced this way.

 

[cnh1995]

In the upper part, you only need to use wye-delta once. Then the upper part becomes a balanced Wheatstone's bridge and R_CDwill be easy to calculate.

 

[Julian102]

rating the 4Ω resis

In the upper part, you only need to use wye-delta once. Then the upper part becomes a balanced Wheatstone's bridge and R_CDwill be easy to calculate.

Can you calculate the equivalent resistance please .I am getting 1.43 ohms and 1.6 ohms as the answer in different cases. Can you tell me the answer, please :3

 

[cnh1995]

Well I'm afraid telling the final answer is not allowed here and if I did so, it will be removed immediately and I'll be warned! It will be helpful if you drew and posted the diagrams here. What answer have they provided? I just want to verify if my approach is right. Otherwise, it will waste your precious time.

 

[cnh1995]

Nope, this approach is not right. We are calculating the resistance between A and B. So, lower part resistance will be between A and B but upper resistance will be between C and D. They are not in parallel. I ran a quick simulation on my phone and verified it. That was a silly mistake! But I think there should be some other method since the configuration is symmetric. I'll try to work it out!

 

[epenguin]

Very likely you can simplify the problem by its top/bottom symmetry.
Here https://www.physicsforums.com/threads/how-to-find-the-equivalent-resistance.833345/#post-5235860 is an example, though your problem seems more difficult.

I am slowly getting it though. There are connections that might as well not be there - removing them simplifies the appearance of the problem and does not change flows or anything.

 

[cnh1995]

Well, the shortest way I got is delta-wye conversion itself. One on upper side and one on the lower side(viewed from AB).

 

[Julian102]

Well I'm afraid telling the final answer is not allowed here and if I did so, it will be removed immediately and I'll be warned! It will be helpful if you drew and posted the diagrams here. What answer have they provided? I just want to verify if my approach is right. Otherwise, it will waste your precious time.

Well, the shortest way I got is delta-wye conversion itself. One on upper side and one on the lower side(viewed from AB).

The shortest way is circuit symmetry which provides Equivalent Resistance= 11R/20 here R=2. hence equivalent R=1.1 ohm. This was so simple.

 

[Julian102]

The shortest way is circuit symmetry which provides Equivalent Resistance= 11R/20 here R=2. hence equivalent R=1.1 ohm. This was so simple.

But the critical part may be how you will find the final equation.But it is easy too.

 

[Julian102]

Y

Very likely you can simplify the problem by its top/bottom symmetry.
Here https://www.physicsforums.com/threads/how-to-find-the-equivalent-resistance.833345/#post-5235860 is an example, though your problem seems more difficult.

I am slowly getting it though. There are connections that might as well not be there - removing them simplifies the appearance of the problem and does not change flows or anything.

Yes.You are absolutely correct :) Thank you.

 

[cnh1995]

The shortest way is circuit symmetry which provides Equivalent Resistance= 11R/20 here R=2. hence equivalent R=1.1 ohm. This was so simple.

Yes. That's what I got using delta-wye transform. Good job!