# Compute Grounding Resistance for Sphere Electrode

• parsifal
In summary, the author is trying to compute the grounding resistance for a sphere electrode, but does not understand how to use the definition of grounding resistance or the relationship between conductivity and resistivity. He takes the area of the sphere around the electrode into account, which is confusing.
parsifal
I'm not sure of the proper term here, but I'd guess it is either earth, ground or grounding resistance.

The task is to compute this grounding resistance for a sphere electrode (radius a) in a ground (conductivity sigma). The definition given for grounding resistance "between the surface of the electrode and a distant point in the ground" is the ratio of voltage between these two points (let say a and b) and current to the electrode, U_ab / I.

But I don't really know how I should use the definition in this computation. All I can come up with is this:

sigma = 1/rho => rho = 1/sigma

$$\Large R=\frac{\rho L}{A},L=dr,A=2 \pi r^2$$

$$\Large dR = \frac {\rho dr} {2 \pi r^2}$$

$$\Large R=\int_a^b dR$$

But this gives the resistance of the whole sphere of ground, right?

So should I just compute using the first equation, where L=distance between a and b, A=pi*a^2 (cross section of an imaginary tube just big enough to swallow the electrode)? Doesn't make sense either.

Last edited:
I think you are on the right track, but the area of a sphere is $A=4 \pi r^2$. I would take the upper limit of integration to infinity. That is as distant as you can get.

Oh, of course. Many thanks.

However, I fail to understand the solution. Why is the area of the whole sphere around the electrode taken into the computation? I mean: if an electron tries to get from point a on the surface of the electrode to point b somewhere in the ground, what does this have to do with the part of the sphere that's on the opposite side of the electrode than b?

Like this:

(-b) ------------- (-a) --- (a) ------------- (b)

Q tries to get from (a) to (b), but in the integral the whole area is taken into account, also the area in (-b).

Imagine a few million electrons all trying to make their escape from the sphere at the same time. Their mutual repulsion would spread them uniformly around the sphere traveling in all directions. At a fundametal level, the resistance to the movement of a single charge is very complicated. It really only makes sense to talk about conductivity and resistivity in an average sense involving many charge carriers. That would be true even for a wire of uniform diameter. The simple conductivity relationship that is the basis for your caclulation is consistent with the observed average behavior when many charges are migrating through a conductor.

## What is the purpose of computing grounding resistance for sphere electrode?

The purpose of computing grounding resistance for sphere electrode is to determine the electrical resistance of the grounding system, which is important for ensuring the safety and performance of electrical equipment and preventing electrical hazards.

## How is grounding resistance for sphere electrode calculated?

Grounding resistance for sphere electrode is calculated using the formula R = ρ/2πa, where R is the resistance, ρ is the resistivity of the soil, and a is the radius of the sphere electrode. This formula takes into account the size and material of the electrode as well as the properties of the soil.

## What factors can affect the grounding resistance for sphere electrode?

Several factors can affect the grounding resistance for sphere electrode, including the type and moisture content of the soil, the size and material of the electrode, and the proximity of other conductive objects. These factors can change the resistivity of the soil and alter the effectiveness of the grounding system.

## Why is it important to regularly compute grounding resistance for sphere electrode?

It is important to regularly compute grounding resistance for sphere electrode because the resistivity of the soil and the effectiveness of the grounding system can change over time due to environmental factors or wear and tear. Regular calculation allows for maintenance and adjustments to be made to ensure the safety and performance of the grounding system.

## How can the computed grounding resistance for sphere electrode be improved?

The computed grounding resistance for sphere electrode can be improved by using a larger or more conductive electrode, improving the moisture content of the soil, or increasing the number of electrodes in the grounding system. It is also important to regularly maintain and monitor the grounding system to identify and address any issues that may affect the resistance.

• Introductory Physics Homework Help
Replies
6
Views
350
• Introductory Physics Homework Help
Replies
10
Views
395
• Introductory Physics Homework Help
Replies
28
Views
656
• Introductory Physics Homework Help
Replies
43
Views
2K
• Introductory Physics Homework Help
Replies
17
Views
1K
• Introductory Physics Homework Help
Replies
17
Views
645
• Introductory Physics Homework Help
Replies
2
Views
241
• Introductory Physics Homework Help
Replies
39
Views
2K
• Introductory Physics Homework Help
Replies
44
Views
2K
• Introductory Physics Homework Help
Replies
3
Views
2K