Calculate Electrical Resistance for Material of Any Geometry

In summary: If you are just trying to find the voltage, then you could just use a vector field or something like that. If you are trying to find the current, then you would need to model the material itself and solve for the current.
  • #1
uq_civediv
26
0
lets say i have a block of material, measures a,b,c (length width height) and two wires running in from the top, both with circular cross section, radius r, distance d from the edges


Code:
    ____________________
   /  d            d   /|
  /<--->O       O<--->/ |
 /___________________/  |
 |                   |  |
 |                   |c |
 |                   | /
 |___________________|/ b
           a

if i were to let electrical current through the block, measure the current and voltage i could find its resistance. But how would i calculate it theoretically if i knew the specific resistance of the material? I have no idea how to do that because i can't imagine how the current would go through the block, i mean through what path.

Or, let's create a more general problem:
lets say i have a space filled with material, measurements infinite (fills up all the space), specific resistance known, and two wires (isolated from the material) (sames as before, circular cross section and radius r) running in from infinity with end points at distance L.

Code:
               <---------->
                     L
--------------|            |----------------------
--------------|            |----------------------

so what i need to know what the path of the current looks like (its diffuse of course but the further away from the shortest path the less current takes that path)


what I'm actually trying to understand is how electric current moves in human body if i would place electrodes on the skin and apply some voltage, but the geometry of this is nontrivial, which i have not seen before while solvin 'find the resistance of blah blah blah' kind of problems

thanks for any hints
 
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  • #2
Resistance = rho * L / A
rho is the resistivty of the material
L is the distance between the points
A is the cross section area
 
  • #3
Is it AC or DC current? Do the wires run through the whole bulk of the material or are they just probes on the surface?

If they are just probes, then I think you could probably estimate them as cylinders or points of potential and solve something like a Poisson's equation to find the voltage field. If you it is an AC current with wires that penetrate through then it could be easily estimated by solving for the fields of a simple twisted pair transmission line in a lossy medium (provided you estimate the bulk to be infinite).

I think it all depends on how you want to model this.
 

1. What is electrical resistance?

Electrical resistance is a measure of how much a material impedes the flow of electric current. It is typically measured in ohms (Ω).

2. How is electrical resistance calculated?

The electrical resistance of a material can be calculated using the formula R = ρ * (L/A), where R is the resistance, ρ is the resistivity of the material, L is the length of the material, and A is the cross-sectional area of the material.

3. What is the difference between resistivity and resistance?

Resistivity is an intrinsic property of a material that measures how well it resists the flow of electric current. Resistance, on the other hand, is a measure of the actual impediment to current flow in a specific object made of that material.

4. Can electrical resistance be calculated for any material?

Yes, the formula for calculating electrical resistance can be applied to any material as long as its resistivity is known and its geometry can be measured.

5. How does the geometry of a material affect its electrical resistance?

The geometry of a material, specifically its length and cross-sectional area, directly affects its electrical resistance. Longer materials and those with smaller cross-sectional areas have higher resistance, while shorter materials and those with larger cross-sectional areas have lower resistance.

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