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# Cube resistance

Posted on 2006-06-05
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Consider a cube in which each side has a resistance "R"

What is the resistance between opposite corners?
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Question by:danielarbib

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Expert Comment

ID: 16832758
what do you understand by "resistance"?
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Author Comment

ID: 16832803
Resistance is the value of a voltage measured across each arm divided by the electric current flowing through  that arm
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Accepted Solution

ozo earned 100 total points
ID: 16833227
5R/6
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Expert Comment

ID: 16835456
That definition is arguably misleading.  This would be my definition

The combined Resistance between two corners is the value of a voltage measured across the two corners divided by the electric current flowing through all paths that connect these two corners.
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Assisted Solution

Harisha M G earned 100 total points
ID: 16835829
Hi, ozo is right... and here is how to do it:

http://mathforum.org/library/drmath/view/65234.html

---
Harish
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Expert Comment

ID: 16841247
can u call it as a puzzle??
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Expert Comment

ID: 16851950
A side of a cube is infintesimally thin and therefore has infinite resistance whatever the material with the possible exception of a superconducting layer being considered to be the surface. Therefore the question does not make sense.
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Author Comment

ID: 16854679
Bit pedantic.  Those who replied did fully undertood and provided a proper answer.  There are. of course. variations where consdideration should be gvien to either sheet resistivity or bulk resitiviiy  but the question was on wire frame resistivity

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Expert Comment

ID: 16855070
I agree with David_Fong. IMO the quesiton is improperly framed. Probably better to have phrased it as follows:

"There are 12 resistors each of resistance R along the sides of a cube and connected at the vertices. What is the effective resistance between opposite corners."

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Author Comment

ID: 16855184
Duly chastised

Here is another problem,  Consider two vertical walls and a and a flat horizontal plane betwwn them

A 30 foot ladder rests from one corner and rests against the opposite wall
Another 20 foot ladder rest from the oppsite corner to its opssite wall
The ladders cross 10 feet above the flat plane

How far apart are the walls?
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Expert Comment

ID: 16855199
It *was* a bit pedantic though, it couldn't be a solid cube like a block of graphite anyway since the entire current would have to pass through a single atom at the corner.
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Expert Comment

ID: 16855315
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Expert Comment

ID: 16896425
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Expert Comment

ID: 16902609
Going with the original description the answer shall be (3*squareroot(R))

or, going with the doraiswamy description the answer shall be (3*R)
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Author Comment

ID: 16907969
jkmyoung is absolutely correct.  Curiously this was set in my maths "0" level way back in 1951!  It is probably beyond the durrent generation GCSE students.  Or am I wrong?
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Expert Comment

ID: 16922562

http://www.experts-exchange.com/Q_21696019.html

Now it is turn to concentrate on the cube resistance.. :)
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Expert Comment

ID: 16926108
This question was answered correctly by ozo, but perhaps he should show us how he derived it before being awarded points?
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Expert Comment

ID: 17012024
This is a classic EE (Electrical Engineering) problem.
Without a picture it is hard to tell if "side" means a face or an edge of the cube.

A cube has six faces, eight vetices, and twelve edges.
Vertices that share an edge are connected by a resistance R.  There are twelve resistors.
What is resistance between diagonal vertices?

Put 1 Amp into a top vetex and take 1 Amp out the opposite bottom vetex.  Look at the symmetry.

The input and output vertices are connected to three resistor.
Symmetry requires that the current split evenly ==>   I_Rin = I_Rout =  1/3 A

The other six resistor are connected between and input and an output resistor.
The current also splits evenly here   ==>   I_Rmid = 1/6 A.

The voltage drop between the opposite vertices is       R*[I_Rin + I_Rmid + I_Rout] = R*[1/3 + 1/6 + 1/3] = R*5/6

Since the current is 1 A, the net resistance is also  R*5/6
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LVL 37

Expert Comment

ID: 17014177
> Without a picture it is hard to tell if "side" means a face or an edge of the cube.

How do you tell that the cube has somer resistance at each "side", if "side" means "face" ?
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Expert Comment

ID: 17115755
its correct ..
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Author Comment

ID: 17115950
Thank you all  Close this series?

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