Resistance between two points on the surface of conducting spherical shells

[Thorr]

Hello,

I'm trying to find a calculator or an equation that would help me determine the total electrical resistance between two points (A and B) on the surface of several concentric conductive spherical shells.

The inputs for the calculation are the radii of the shells: r1, r2, r2, their specific resistivity rho1, rho2, rho3 and the separation angle between the two points on the surface of the shells.

As a first approximation I'd be happy simply knowing the total resistance between two points on opposite sides of the shell (alfa=180°).

I've been googling for a while but can't seem to find anything I can use directly. Any help would be greatly appreciated.

Cheers

 

[eljose79]

,Hello there,

Thank you for reaching out with your question about calculating total electrical resistance between two points on the surface of concentric conductive spherical shells. This is a common problem in electrical engineering and there are several ways to approach it.

One method is to use the concept of equivalent resistance, where you can replace multiple resistors with a single equivalent resistor that has the same resistance as the combination of the original resistors. In your case, you can consider each concentric shell as a resistor with a certain resistance value determined by its radius and specific resistivity.

To calculate the total resistance between two points (A and B) on the surface of these shells, you can use the following equation:

R = (rho1 * r1 + rho2 * r2 + rho3 * r3) / (r1 + r2 + r3)

Where R is the total resistance, rho is the specific resistivity, and r is the radius of each shell. This equation assumes that the shells are arranged in series, meaning the current flows through each shell in succession.

If you want to take into account the separation angle between the two points, you can use the formula for parallel resistors:

1/R = 1/R1 + 1/R2 + 1/R3

Where R1, R2, and R3 are the individual resistances of each shell. This equation assumes that the shells are arranged in parallel, meaning the current is divided between them.

I hope this helps you in your calculations. Please keep in mind that these are simplified equations and may not take into account all factors, such as the shape and thickness of the shells. It may be helpful to consult with a professional or use a more advanced software for more accurate results.

Best of luck with your research!