How to find a hollow cuboid's resistance

Thread Starter

Sumit Aich

Joined Dec 3, 2016
100
how to find a hollow cuboid's resistance between two points on same face but not lying on the edges. the line joining 2 points is parallel to the length of the cuboid.
resistivity is uniform
another related doubt - will resistance between those same points change if the cuboid is deformed (the box is crumbled)
edit:contact points arent "dimensionless ", i mean copper wires are connected to cuboid at A and B
 
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Thread Starter

Sumit Aich

Joined Dec 3, 2016
100
If the point has "no size" the resistance will be infinite.
and if it has got some size?
i wonder if the cuboid can be replaced by a hollow sphere of same surface area (think cuboid deformed into sphere)
such that distance (along surface) between A and B remains same
will resistance remain same (for simplification of problem)?
 
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wayneh

Joined Sep 9, 2010
17,496
Box crumpling wouldn't make much difference so long as no walls touch and no major distortion occurs - no thinning or thickening of the surface.

This is not a physics problem so much as a math problem. I think it's a topology problem.
 

Thread Starter

Sumit Aich

Joined Dec 3, 2016
100
Box crumpling wouldn't make much difference so long as no walls touch and no major distortion occurs - no thinning or thickening of the surface.
If so, then--
i wonder if the cuboid can be replaced by a hollow sphere of same surface area (think cuboid deformed into sphere)
distance (along surface) between A and B remains same
will resistance remain same (for simplification of problem)?
 

wayneh

Joined Sep 9, 2010
17,496
Well, can you pressurize a cube and blow it into a sphere? I don't think so. The faces round but you can't make a sphere without stretching. I think. You know you want the same surface area for both shapes. The sphere will have a little more volume.
 

Thread Starter

Sumit Aich

Joined Dec 3, 2016
100
Well, can you pressurize a cube and blow it into a sphere? I don't think so. The faces round but you can't make a sphere without stretching. I think. You know you want the same surface area for both shapes. The sphere will have a little more volume.
right, so itll work only in theory?
 

Thread Starter

Sumit Aich

Joined Dec 3, 2016
100
If you carefully read the link I provided, which I actually spent some of MY time searching for you would have the answer regarding the point question. But it appears you want the answer served up to you on a plate with as little effort as required on your behalf.
but in post #1 i didnt mean "dimensionless points", i meant copper wires are connected to cuboid at 2 points A and B
 

MrAl

Joined Jun 17, 2014
11,389
Hi,

Yes when you say contact points we can assume you mean that they make perfect contact and so do not introduce any extra resistance at the two nodes, and these two contact points are assumed to be two nodes which in theory do not have any electrical resistance themselves. This is in stark contrast to a real life measurement which would include the mating surface areas when the contact surface area resistance is known to be comparable to the material resistance.

This might be related to sheet resistance or resistance per square.

One finite element model would look like a lot of resistors connected to form a grid of small squares such that the cuboid 'box' would look almost like a fishing net of the same shape. The small resistors size could be reduced to zero or near zero and in the limit the final result would emerge.
You could start with a single flat sheet and go from there once you get the calculation procedure. It should be on the web somewhere.
 
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MrAl

Joined Jun 17, 2014
11,389
contact points arent "dimensionless ", i mean copper wires are connected to cuboid at A and B
That was addressed in post #10 which outlines the difference between two theoretical contacts and two real life contacts. If you mean two real life contacts then you must specify the contact areas.

Also, this would be related to Laplace's Equation.
 

wayneh

Joined Sep 9, 2010
17,496
I think the assumption in a problem like this is that the contact area is big enough that it can be ignored. The focus is on the rest of the cube. Or conversely it's about the contact surface area only and you ignore the rest of the cube. But there's not enough information given to approach it that way.
 

AnalogKid

Joined Aug 1, 2013
10,986
If you carefully read the link I provided, which I actually spent some of MY time searching for you would have the answer regarding the point question. But it appears you want the answer served up to you on a plate with as little effort as required on your behalf.
It appears that you actually volunteered your time without being asked. Volunteering time and effort is the engine that runs this place, so I don't understand why you brought it up.

ak
 

kubeek

Joined Sep 20, 2005
5,794
While on the other hand, people who can´t be bothered to read and do the effort to understand are the bane of a lot of threads that are on this forum, and if not the bane, then the cause of the 100+ futile replies that lead to nothing more than misunderstanding and frustration on all sides.
 

russ_hensel

Joined Jan 11, 2009
825
Without thinking very hard I think this requires a surface for the contact, and the solution to a differential equation that relates current density ( as a vector ) to the electric field or potential. I expect the math is hard. It might be best to approach as a numerical model. Where does this question come from?
 
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