# Computation of resistance with arbitrary local resistivity rho(x,y,z)

• pierebean
In summary, the individual is seeking to calculate the net electrical resistance of a given geometry with a shape similar to a parallelepiped flanked by two trapezoids. They have a data table with coordinates and corresponding resistivities that vary depending on position. Due to the preferential flow of electrical current, the standard resistance formula cannot be used and instead, they are looking for an algorithm to solve J=sigma*E for each point, where sigma is equal to 1/rho and rho is a tensor.

#### pierebean

Bonjour,

I need to numerically compute the net electrical resistance of a given geometry.

I know the shape of my object, it is relatively simple. It's close to this: http://2.imimg.com/data2/QX/UC/IMFCP-3019296/i-shape-big-1-250x250.jpg
Actually my shape is even simpler because it's a parallelepiped flanked by two trapezoids.

As data, I have many points coordinates x,y,z and the corresponding resistivity which is unusually dependant of the position.

my data table looks like that:

x1 y1 z1 rho1
x2 y2 z2 rho2
x3 y3 z3 rho3
x4 y4 z4 rho4
...
ect...
...
xn yn zn rhon

n is my number of point in my geometry.

Naturally, since the electrical current will preferentially go to the low resistivity domain. I cannot use the R=rho*l/S formula.

I probably have to solve J=sigma*E for every point with sigma(x,y,z)=1/rho(x,y,z)

Does someone have any idea of algorithm that can compute the resistance?

Thank you very much

Pierre

I forgot to mention that my resistivity was a tensor and not a mere scalar.

## 1. What is the concept of local resistivity and how does it affect resistance calculations?

Local resistivity refers to the resistance of a material at a specific point or location. It can vary based on factors such as temperature, impurities, and material composition. In the computation of resistance with arbitrary local resistivity, the resistance is calculated by taking into account the varying resistivity at different points in the material.

## 2. How is the resistance calculated with arbitrary local resistivity?

The resistance is calculated by dividing the voltage (V) by the current (I) according to Ohm's law (R = V/I). However, in the case of arbitrary local resistivity, the resistance is not constant and varies at different points. Therefore, the voltage and current must be integrated over the entire material to account for the varying resistivity, resulting in a more complex calculation.

## 3. Can the computation of resistance with arbitrary local resistivity be applied to any material?

Yes, the computation of resistance with arbitrary local resistivity can be applied to any material as long as the resistivity values at different points are known. This technique is commonly used in the analysis of electronic circuits and materials with non-uniform resistivity distributions.

## 4. What are the limitations of using arbitrary local resistivity in resistance calculations?

The main limitation is the complexity of the calculation. It requires knowledge of the resistivity values at different points in the material and integration over the entire material, which can be time-consuming and difficult for complex materials. Additionally, it may not accurately reflect real-world conditions as the resistivity values used are assumed to be constant at each point.

## 5. How does the computation of resistance with arbitrary local resistivity compare to other methods of resistance calculation?

Compared to other methods, such as the use of a constant resistivity value, the computation of resistance with arbitrary local resistivity provides more accurate results for materials with non-uniform resistivity distributions. However, it is more complex and time-consuming, making it less practical for certain applications. The method used should be chosen based on the specific needs and limitations of the situation.