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# What is the Resistance of This Circuit, and How is it Calculated?

05/05/2019 11:22 AM

each resistor has a resistance of 6 ohms

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#1

### Re: what is the resistance of this circuit, and how is it calculated?

05/05/2019 12:16 PM

You could use Y-Δ formulas, but there's an easier way since all the resistors are the same. Current fed in from one corner splits equally 3 ways. At the end of each of these, it divides equally 2 ways, and two equal currents combine in each of three paths to the exit corner.

Suppose you feed 6 amps into the corner. Each 6 ohm resistor will have 2 amps for a drop of 12 volts. When the current splits two ways, each resistor will have 1 amp or 6 volt drop. Finally, there is a 12 volt drop to the final corner, a total of 30 volts for 6 amps or 5 ohms resistance between the corners.

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#2

### Re: what is the resistance of this circuit, and how is it calculated?

05/05/2019 1:39 PM

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#3

### Re: what is the resistance of this circuit, and how is it calculated?

05/05/2019 1:43 PM

Build it and measure it, or draw it into a circuit simulator (many free ones available). These are far more useful methods than calculating it manually.
this is probably a homework question anyway.
Del

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### Re: what is the resistance of this circuit, and how is it calculated?

05/05/2019 2:05 PM
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#5

### Re: what is the resistance of this circuit, and how is it calculated?

05/05/2019 3:43 PM

Ahh, this brings back memories.

https://www.electronics-tutorials.ws/resistor/res_5.html

Never had the need in my professional life to perform the calculation on a complex resistance bridge. The 3D nature of this question is a nice touch.

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### Re: what is the resistance of this circuit, and how is it calculated?

05/05/2019 6:50 PM

Here is a picture to clarify #1:

1. 6A current enters P1 splits 3 ways, 2A each

2. 2A enters P2, P3, P4, splits 2 ways, 1A each

3. 2 x 1A current merges at P5, P6, P7.

4. 3 x 2A current merges at P8.

5. Voltage at P8 = 0;

6. Voltage at P5, P6, P7 = 2A x 6Ω = 12v

7. Voltage at P2, P3, P4 = 12v + 1A x 6Ω = 12v + 6v = 18v

8. Voltage at P1 = 18v + 2A x 6Ω = 30v

9. Resistance = 30v / 6A = 5Ω

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### Re: what is the resistance of this circuit, and how is it calculated?

05/06/2019 12:07 AM

Nice way to do it! GA!

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#8

### Re: What is the Resistance of this Circuit, and How is it Calculated?

05/06/2019 9:50 AM

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#9
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### Re: What is the Resistance of this Circuit, and How is it Calculated?

05/06/2019 9:55 AM

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### Re: what is the resistance of this circuit, and how is it calculated?

05/06/2019 11:36 AM

Why don't you just go ahead and fax this to his teacher ....

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#11

### Re: What is the Resistance of this Circuit, and How is it Calculated?

05/06/2019 12:36 PM

What silly bu££er wired that up?��

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### Re: What is the Resistance of this Circuit, and How is it Calculated?

05/06/2019 2:16 PM

I think it was Picasso,or maybe Braque,or one of the other artists of that period.Anyway,the answer is 5/6 of the value of the resistors.

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#13
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### Re: what is the resistance of this circuit, and how is it calculated?

05/06/2019 5:34 PM

That's a good idea! Then, maybe the problem on the quiz won't have equal value resistors and the little symmetry trick won't work!

AP#1 probably ought to check out those Δ-Y and Y-Δ transform formulas just in case!

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#14
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### Re: What is the Resistance of this Circuit, and How is it Calculated?

05/07/2019 10:06 AM

Looks more like Escher.

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### Re: What is the Resistance of this Circuit, and How is it Calculated?

05/07/2019 2:56 PM

Would that be "Electro-Escher"?

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### Re: What is the Resistance of this Circuit, and How is it Calculated?

05/07/2019 3:20 PM

Actually, it's an art form that is a combination of resistance art and cubism.

https://www.tate.org.uk/art/art-terms/c/cubism

https://www.tate.org.uk/art/art-terms/r/resistance-art

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#17
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### Re: what is the resistance of this circuit, and how is it calculated?

05/08/2019 9:22 AM

Sure, it's a good answer, but I'm baffled: Why would you trouble yourself to do it?

I look at a problem like that with the attitude of my pet cat: It could do this trick or that trick if it wanted to, but it just can't be bothered.

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#18
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### Re: what is the resistance of this circuit, and how is it calculated?

05/08/2019 9:58 AM

I suspect Rixter was helping a cat that couldn't figure how to open the can of tuna. Answer given, but the good bit is helping the cat to communicate it's problem.

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#19
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### Re: what is the resistance of this circuit, and how is it calculated?

05/08/2019 11:03 AM

Why would you trouble yourself to do it?

But it's no trouble, it's a puzzle.

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#20

### Re: What is the Resistance of This Circuit, and How is it Calculated?

05/08/2019 11:05 AM

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### Re: what is the resistance of this circuit, and how is it calculated?

05/08/2019 11:33 AM

Nice answer. I'd chance my arm that most people here like solving a puzzle, even if it has no evident practical use. A bit of brain exercis is just as valuable as physical exercise. Kudos for such a clear explanation, it would never have occured to me.

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### Re: what is the resistance of this circuit, and how is it calculated?

05/08/2019 2:44 PM

I understand. Yesterday, in the ophthalmologist's waiting room, I passed the time solving some spatial relationship puzzles in a magazine. I threw it aside when I was called.

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### Re: what is the resistance of this circuit, and how is it calculated?

05/08/2019 7:02 PM

Interesting points. From my own childhood, I moved frequently (almost yearly). At one point I moved to another new school. Whilst trying to fit in, I found that I had a better knowledge on certain subjects. I frequently began to keep my arm down with open questions to class because I wanted to fit in and not appear as a know it all. That did cause me a few problems, but becoming an old goat I have learned otherwise.

Basic point is that I don't think anybody here is out to put an apple on teachers table. A number of Admin could testify to that. I've no idea how they have tolerated me !

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#24

### Re: What is the Resistance of This Circuit, and How is it Calculated?

05/09/2019 4:19 AM

I have an other idea. Let’s number the currents as per attached polyhedron[fig1].

Let's write the sum of currents in each of 8 corners and take another 5 voltage drops on different ways from A to B and put VAB=120 V. We shall get 13 equations of 13 unknowns[Fig.no.2].

The general determinant will be[Fig.no 3-the result 48] :

and the IA determinant [Fig.no.4-result 960]

So IA=960/48=20 A

Then the equivalent resistance from A to B will be R=120/20=6 ohm.

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### Re: what is the resistance of this circuit, and how is it calculated?

05/09/2019 12:36 PM

"Basic point is that I don't think anybody here is out to put an apple on the teacher's table."

Speak for yourself. One of my recurring dreams (nightmares?) is that I'm back in Grade 5, a full grown adult, sitting cramped on one of those little chairs, at a little desk, surrounded by kids half my size. Miss Mayberry, the teacher, is very cross with me, but I try my best to please her, and dutifully attend to my lessons as I try to learn the things I missed the first time around.

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#26
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### Re: What is the Resistance of This Circuit, and How is it Calculated?

05/09/2019 1:34 PM

I have only the vaguest memory of determinants from college over 50 years ago, and have never used them since, so I have no idea how you constructed or used them here.

On the other hand, I'm virtually certain that Rixter's methods are correct, giving a value of 5Ω, and that value was confirmed by at least one other poster, so I suspect that you have an error somewhere.

Since all the resistors have the same 6Ω value, the unit is symmetrical, so the voltages at the non-supply ends of R1, R2, and R3 must be equal. If those three voltages are identical, then those three points can be connected together, and nothing will change. Once you make that connection, you have R1, R2, and R3 connected in parallel, and thus equivalent to a single 2Ω resistor.

Do the same with R10, R11, and R12 and you have another 2Ω resistor. What's left is 6-6Ω resistors in parallel, which is of course equal to a single 1Ω resistor

Now you have a series of a 2Ω, a 1Ω, and another 2Ω resistor, which of course add to . Having done that, I'm now confident to remove the word 'virtually' from paragraph 2 of this post.

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#27
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### Re: What is the Resistance of This Circuit, and How is it Calculated?

05/09/2019 2:51 PM

Thank you for your remarks dkwarner. I learned my self about determinants 60 year ago in my college, too. However, I used them very seldom, indeed. But Microsoft Excel presents a very easy way to use it. So I found the currents in the corners are not equal. For instance, if we shall take the IA=6 [as Mrs.Rixter] I1=I3=1 but I2=4 A. I really appreciate very much Mrs. Richter’s activity. But nobody is perfect and this time he could be wrong.

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### Re: What is the Resistance of This Circuit, and How is it Calculated?

05/09/2019 3:01 PM

"So I found the currents in the corners are not equal. For instance, if we shall take the IA=6 [as Mrs.Rixter] I1=I3=1 but I2=4 A."

This is a totally symmetrical circuit. How can the three A corner currents be different?

Please show how you obtained those values.

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### Re: What is the Resistance of This Circuit, and How is it Calculated?

05/09/2019 5:49 PM

For symmetry reasons, the three entering and exiting currents must be the same. How could one be different? If you turn the cube 120 degrees about an axis through the two corners, the cube looks exactly the same.

- Mr. Rixter

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#30

### Re: What is the Resistance of This Circuit, and How is it Calculated?

05/09/2019 11:42 PM

Checking carefully the paralelipiped of resistors I also concluded that it is symmetrical.
It is possible that I was wrong somewhere and I apologize.

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#31

### Re: What is the Resistance of This Circuit, and How is it Calculated?

05/10/2019 12:10 AM

It seems like a good idea is not enough. At my age it is not a good idea to compute in such late hours. I apologize again for the letter 's' too. It was not intended. I forgot how to write “ Mister” in English.

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#32

### Re: What is the Resistance of This Circuit, and How is it Calculated?

05/10/2019 10:46 AM

When I retired - 16 years ago - everyone told me I would have a lot of free time. It's totally wrong. Now I have a lot less free time. Any work that takes longer is delayed or not done. I have a list of 40 urgently delayed things.

However, it is interesting why my way to solve the problem failed.

First, it seems I have a lot of recurrences. Usually excel announces whether there is any recurrence and stops calculating. But, it does not seem, for determinant's case. You’ll get a result but it is wrong.

The problem is how to eliminate recurring equations

Then, I reduced number of unknowns from 13 to 7 [ I kept only the first node current and I increase the number of voltage drop equations to 6] Now the current is 6 A for 30 VAB .

The currents are now as per attached image.

I again ask my apologies for the inconvenience

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#33
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### Re: What is the Resistance of This Circuit, and How is it Calculated?

05/10/2019 10:59 AM

It's all cool. I just didn't want any of my crudeness to reflect badly on the fairer sex.

Your English looks pretty good to me.

Being basically lazy, I usually try to find the easiest way to solve a problem, but the easiest way usually depends on special conditions such as equal resistors and regular polyhedra as in this case. Your method (loop equations) is general and should work in the general case. I suspect that that is how computer programs solve the problem, but I usually make an error someplace when there are 13x13 matrices involved (even sparse matrices).

I looked at your diagram and equations and the current directions are consistent.

However, in your matrix, for equations 5, 6, and 7, I believe the coefficient for I6, I8, and I9 should be negative because these terms are on the left side of the equation. I don't know if there are any other errors, that's as far as I got.

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#34

### Re: What is the Resistance of This Circuit, and How is it Calculated?

05/10/2019 2:14 PM

Alright, I've been sucked into this. Because all of the resistances are equal, here is another method that works, and uses only the value of the resistors, without introducing current flow or voltage drop into the calculation. I use Rixter's drawing (post #6) because it visually clarifies the problem.

From P1 and P8 the two tri-branched resistor arrays are resistors in parallel, so the total of each array is 2 ohms (1/Rt = 1/6 + 1/6 + 1/6).

Consider those two arrays now as two equally resistive plates between which the remaining 6 resistors are connected in parallel. Their total resistance is 1 ohm (1/Rt = 1/6 + 1/6 + 1/6 + 1/6 + 1/6 + 1/6).

Therefore the circuit is equivalent to two 2 ohm resistors and one 1 ohm resistor in series, for a total of 5 ohms, which agrees with Rixter's result.

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