According to the meaning of grounding resistance, grounding resistance is the ratio of grounding potential U and I when current I flows into the ground through the grounding body. Therefore, in order to measure the grounding resistance, a certain amount of current is first injected into the grounding body. As shown in Figure 1-1
To simplify the calculation, let the grounding body be a hemispherical shape, and the current density on the sphere at X from the center of the sphere is
J=1/2 π X2
In the formula, J - the current density on the sphere at X from the center of the sphere, A/m2 I - the current of the grounding body entering the ground X - distance from the center of the ball
Figure 1-1 Test Wiring for Measuring Grounding Resistance Using the Three Pole Method
We know that the electric field strength E=J ρ，ρ The potential difference between any two points in the electric field for soil resistivity is equal to the line integral of the electric field strength between the two points. Assuming that the potential at infinity is zero, the voltage at the distance x (x, rg) from the center of the grounded body is
U=∞ x - Edx=∞ x (- ρ／ 2 π x2) dx=（ ρι／ π x) ∞ x (15-9)
From equation (15-9), it can be seen that the potential difference between electrodes 1, 2, and is
U '=I ρ／ 2 π (1/rg-1/d12) (15-10)
Electrode 3 causes the potential difference between 1, 2, and to be
U "=I ρ／ 2 π (1/d23-1/d13) (15-11)
The total potential between electrodes 1 and 2 is equal to the sum of U 'and U ", i.e.
U=U'+U"=I ρ／ 2 π (1/rg-1/d12+1/d23-1/d13)
Therefore, the resistance Rg between poles 1 and 2 is
Rg=U/I= ρ／ 2 π (1/rg-1/d12+1/d23-1/d13) (15-13)
The actual value of the grounding resistance of grounding body 1 is
R= ρ／ 2 π rg (15-14)
In the formula, R - the actual resistance of the grounding body
rg - radius of the grounding body To make the measured grounding resistance Rg equal to the actual grounding resistance R of the grounding body, it is necessary to make equations (15-13) and (15-14) equal, that is,
1/d23-1/d12-1/d13=0
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