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Topic Title: Resistance of a Cube of Wire
Topic Summary: without using Google
Created On: 16 April 2018 08:38 PM
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 16 April 2018 08:38 PM
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Zs

Posts: 3849
Joined: 20 July 2006

Hello Friends,

Been a long time and I do have a story to which I have eluded in the past year. I'm ready to tell you that so that you or your children don't go through similar and I'll do that in the near future, it's about bad behaviour from new colleagues, maybe bullying, nearly resigning and all that kind of thing but this post isn't it. This is much more in keeping with how I want to be so a good point at which to come back. I've missed you.

My new team are as interesting as they are interested. I love them, and I do love a good nerd. We laugh together frequently, until we cry.

Last Friday an email came in from Rob. Rob is as round as he is Scottish. He has a lovely accent and is an absolute specialist in Pulsed Power (oh, that's where I am now, until I retire, but I'll tell that later). We both work late and quite often, in the quiet part of the day, he potters up the corridor to my desk and we talk about things like EMP and foil blankets (cloaks of invisibility).

So, I get this email called the Friday Quiz and I think of Zoomup! This is the first one.

I absolutely do not want to google this. He has taken the time to type it up and draw diagrams. So I have to make a disclaimer here - This is from the gut instinct. I wonder if you might tell me if I'm on the right track please? I also think if this is stretching one of us then you also might like to share.

He has sent me a picture of a cube. Imagine that it is made of wire and that each side of the cube (wire) has a resistor built into it.

There are three different puzzles - each has the incoming power at the point of the cube just in front of you at bottom left and each has a different point of departure. I am to reveal the resistance. The first point of departure is the far/ upper/ right hand corner.

So...Power in at one corner and immediately it splits up into three legs. Then it gets to another corner of each and splits some more, and so on... So, there are resistances in series and there are some in parallel (I think).

Each resistor is 12 ohms on the first question.

Well...I spent ages mucking my brain up thinking that I could not remember if there was a formula for combined resistances and then I went back to first principles. I'm going to tell you what I think is the way through this conundrum and I'm hoping you will tell me if I'm on the right track please.

I reckon...

1 Map out the paths through the cube and use different colours after each corner or vertex. See where the current flow changes path or character. Make a route to the point of departure as short as possible.

2 Smash the cube flat onto a piece of paper and end up with a 2D drawing of it. Sort of deconstruct the box so that it lays flat?

3 Anything in series? Add them up (in the way of resistors in series formula) and make all of the series resistors into one single resistor and one straight line.

4 See what you have left in parallel and treat the whole lot as a resistor in parallel calculation. That's the 1/R +1/R....1/N one I hope. I'm thinking that I am going to have to combine all the resistors in parallel as well, before going for the grand total.

That's as far as this bear of little brain has gotten so far. Care to offer your advice before my head explodes?

Love to all. The story of the disappearing Zs is to follow. I'm scared to write it down TBH, but I am still an electrical engineer and I am still here.

Zs
 16 April 2018 09:16 PM
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ebee

Posts: 6417
Joined: 02 December 2004

Welcome back Zs.
Hmm,
trying to get the gist but that diet coke I diluted with bacardi has kicked in.
A sketch might help

-------------------------
Regards,
Ebee (M I S P N)

Knotted cables cause Lumpy Lektrik
 16 April 2018 09:37 PM
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mapj1

Posts: 10269
Joined: 22 July 2004

Ah ha yes, this is the sort of question I used to set in another life. I know it already so I wont spoil it totally for you unless asked, but indeed the "always works" solution is to steam-roller it and treat as multiple series parallel branches with cross-links. The all resistors equal case has some simplifications.

In some of the cases of entry and exit point you can invoke rotational symmetry and only solve some part of the problem.

If I understand correctly you are looking at body diagonal first, and then one face diagonal, but you can also look at one edge, actually these are the only 3 cases as every other case is one of these rotated.
The face diagonal case is amenable to mirror symmetry, as is the side. Body diagonal needs drawing out, think like a star-delta circuit may help.

-------------------------
regards Mike
 16 April 2018 09:46 PM
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Legh

Posts: 4152
Joined: 17 December 2004

Nothing like a bit of electrical romance.......I wondered where you had disappeared to...

Its a little more than basic series and parallel resistors. Consider two resistors in series with another two resistors in parallel then place a resistor across and between the four resistors at their mid point. As you might see in a bridge, well its a little more complex than that. You need a method beyond series and parallel resistors

Have a look at Thevenin's theory

-------------------------

http://www.leghrichardson.co.uk

de-avatared
 16 April 2018 09:57 PM
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mapj1

Posts: 10269
Joined: 22 July 2004

No its not necessary to do anything complex, because of the symmetry, so long as all resistors are equal, you may place non-current carrying bonds between the other ends of the 3 resistors where the injected current splits and re-draw it if you like. (because if you look down any one of the three resistors, you see the path to the end is the same, so all 3 resistors must be dropping the same voltage even though we don't know what it is yet we can draw a non-current carrying link in between equipotential places to aid the circuit drawing. )

-------------------------
regards Mike
 16 April 2018 10:27 PM
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rocknroll

Posts: 9589
Joined: 03 October 2005

Are you talking about what's commonly called the 'resistor cube', when flattened you end up with 3 resistors in parallel connected in series to 6 resistors in parallel connected to 3 resistors in parallel so the answer would be if using 1 ohm resistors 1/3 ohm plus 1/6 ohm plus 1/3 ohm the therefore 1/3 + 1/6 + 1/3 = 5/6 ohm, there are other methods using voltage and current to solve this equation but the resistance always ends up at 5/6 Ohm.

Using colours 3 red, 6 blue and 3 green.

Regards

-------------------------
"Take nothing but a picture,
leave nothing but footprints!"
-------------------------
"Oh! The drama of it all."
-------------------------
"You can throw all the philosophy you like at the problem, but at the end of the day it's just basic electrical theory!"
-------------------------
 16 April 2018 10:30 PM
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Zs

Posts: 3849
Joined: 20 July 2006

Thevewho? I'm all over it...

Anyway, I'm concerned by the complexity but yes, the first one is symmetrical. So I'll have a go at doing the sums and see if you agree with the answer.

Back in a while...cor, this is hard.

Zs

Mike, from your previous life...do you split the box forwards ( four sections joined together) with two side-cars so to speak?
 16 April 2018 10:34 PM
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John Peckham

Posts: 8847
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I started to draw it out and gave up.

I was going to get out the Weller and a box of resistors but I suspect RnR has provided the answer.

-------------------------
John Peckham

http://www.astutetechnicalservices.co.uk/
 16 April 2018 10:44 PM
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mapj1

Posts: 10269
Joined: 22 July 2004

Mike, from your previous life...do you split the box forwards ( four sections joined together) with two side-cars so to speak?

???? what ?
I'm sorry, I have failed to get the picture that is in your head into mine - can you try that again ?

If you mean this problem, then no, for the body diagonal problem, your visualisation needs to be to divide into triangles, not squares, though some triangles have unconnected sides that carry no current.
Actually R and R has just summarised the method I'm describing.

-------------------------
regards Mike
 16 April 2018 11:10 PM
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sparkingchip

Posts: 10472
Joined: 18 January 2003

Originally posted by: ebee

Welcome back Zs.

Hmm,

trying to get the gist but that diet coke I diluted with bacardi has kicked in.

A sketch might help


Tax dodger!
 16 April 2018 11:16 PM
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rocknroll

Posts: 9589
Joined: 03 October 2005

Ok draw a wire frame cube, connect a wire A to 1 node and a wire to the opposite node B, colour the three wires that connect to A (red), colour the three wires that connect to B (green) that will leave 6 wires colour them (blue), if you flatten them out you have three wires in parallel (red), which are in series with 6 wires in parallel (blue), which are in series with 3 wires in parallel, everything is symmetrical as Mike pointed out, you can also solve this using Kirchhoffs not Thevenins, use dotted lines for the diagonals.

P.S. I managed to find a site that should help you in understanding better than what we can input without diagrams on this forum.

Here

Regards

-------------------------
"Take nothing but a picture,
leave nothing but footprints!"
-------------------------
"Oh! The drama of it all."
-------------------------
"You can throw all the philosophy you like at the problem, but at the end of the day it's just basic electrical theory!"
-------------------------

Edited: 16 April 2018 at 11:58 PM by rocknroll
 16 April 2018 11:44 PM
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rocknroll

Posts: 9589
Joined: 03 October 2005

Just a tip for those who are going to progress, as the author pointed out if your aiming to get that plum job this is one of the questions that can crop up in interviews along with draw a diagram of a star/delta starter, you will be surprised how many people when presented with these problems have a blank look on their face.

Regards

-------------------------
"Take nothing but a picture,
leave nothing but footprints!"
-------------------------
"Oh! The drama of it all."
-------------------------
"You can throw all the philosophy you like at the problem, but at the end of the day it's just basic electrical theory!"
-------------------------
 16 April 2018 11:52 PM
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mapj1

Posts: 10269
Joined: 22 July 2004

and yet another use for the ever useful LT spice... certainly one I use a lot for power factors and so on.

Perhaps we can now see our way to the generalisation to any polygon of order 2N, where N is an integer; and then either by induction or integration across segments, to the limiting case of a conduction between the poles of a sphere with a uniform resistive shell. Tommorow's lite reading..
[l]http://www.lajpe.org/dec13/16-LAJPE_850_Fabio_Fajardo-1_pag.pdf[/l]

-------------------------
regards Mike
 17 April 2018 05:17 AM
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ebee

Posts: 6417
Joined: 02 December 2004

Hah,
now I see it.
The penny has dropped.
Nice one.

Years ago (Centuries ago!) I thought of something not totally dissimilar.
Imagine a wheatstone bridge.
Replace the meter with another resistor.
Use different resistors to calculate voltages at the points and current flow thru the arms, note the effects of different resistances.

After reams and reams of calculations I programmed computer to run for days giving me a shed load of results (OK ZS SPECTRUM in BASIC nothing heavy!).

I eventuallly came to the conclusion that if the resistor replacing the meter is small in comparison than treat it as almost a dead short and if it is large treat it as infinite gives a rough approximation.

Why I didn`t realise this in the first 5 seconds I`ll never know. Nerd!

I did , years later, work out the Monty Hall conundrum though.
After weeks of not thinking about it.

-------------------------
Regards,
Ebee (M I S P N)

Knotted cables cause Lumpy Lektrik
 17 April 2018 07:59 AM
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mapj1

Posts: 10269
Joined: 22 July 2004

I hope you were not awake until 5.17 thinking about it.
The Monty Hall problem is clearer if you consider say ten doors, you pick one, with a chance of 1 in ten of the prize, and the game host opens 9, and then offers you the chance to swap, but now the chances are 1 in 2 - the opening of the doors that were not the prize has added information you did not have at the beginning.

-------------------------
regards Mike
 17 April 2018 08:33 AM
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ebee

Posts: 6417
Joined: 02 December 2004

No Mapj I wasn`t awake till 05:17 thinking about it.
LOL.

The Monty hall lost me sleepless nights so I forgot about it.
2 or 3 weeks later I looked in the mirror whilst shaving and I had a road to Damascus experience. It became clear and I wasn`t even thinking about it.
A Eurika moment

-------------------------
Regards,
Ebee (M I S P N)

Knotted cables cause Lumpy Lektrik
 17 April 2018 08:34 AM
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ebee

Posts: 6417
Joined: 02 December 2004

Anyway that cube`s a good un. I like it Zs

-------------------------
Regards,
Ebee (M I S P N)

Knotted cables cause Lumpy Lektrik
 17 April 2018 08:54 AM
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Jaymack

Posts: 5448
Joined: 07 April 2004

Originally posted by: Zs
I absolutely do not want to google this. He has taken the time to type it up and draw diagrams.

Why waste time on trivial pursuits, where did Jock get it from?. Somebody probably passed it on or he got it from t'net.

Mr. Ohm probably took a long time to figure out the basic law. Rather put minds to solving the plastic problem.

Regards
 17 April 2018 11:34 AM
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mapj1

Posts: 10269
Joined: 22 July 2004

Not sure I agree - for the same reasons kittens play ,and before the internet, children used to play games with balls and things- it is all harmless practice, and unlike being forced into doing something odd for the first time on a real job all of a panic, there is the leisure to think about it as much or as little as you like, turning the concepts over in your head and seeing parallels with other odd snippets you have picked up on the way, and come back next week and go 'aaahha!'

The result is that should the panic job one day come in, you are better equipped to catch the ball, hit the tarmac running or whatever is required, because you have thought about something rather like it already, and are, as it were, mentally toned up.
If this was not true, revising for exams would not work.

I guess it depends on the type of job you like doing, I like the unknown and I last learnt something I had no idea about at ~ 4pm yesterday, and that is quite typical for me. (Youla Waves anyone - no physical significance, but allow some radio type problems to be solved using matrix maths.)

-------------------------
regards Mike
 17 April 2018 06:36 PM
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Zoomup

Posts: 3785
Joined: 20 February 2014

Welcome back Zs. I was wondering where you had gone. You certainly got me thinking with your puzzle, but having had a hard day I had to leave it to others to solve. Anyway it is nice to hear from you again, and please don't leave it so long next time. Are you still playing your guitar?

Bye,

Z.
IET » Wiring and the regulations » Resistance of a Cube of Wire

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