Page 85 - Electrical Safety of Low Voltage Systems

68 Chapter Four

mutual ground resistance between the two feet, as calculated in Sec. 4.4, is
negligible. 17 Thus, we can consider a person’s feet as electrodes in parallel.
Q. Why it may not be economically convenient to add more electrodes to a
given grounding system, if this reduces their interdistance?
A. Connecting electrodes to a grounding system always lower its total earth
resistance. This reduction, though, may not follow the rule of the parallel of re-
sistances, if the electrodes mutually interfere. In layman terms: if by adding an
electrode to a grounding system we lower its earth resistance from 19 to 10 ,
by adding a second one we may not reduce the total resistance to 5 (i.e., the
result of the parallel) due to their mutual couplings. The total value may be
7 . Therefore, the second element is less economically effective than the first
with respect to the same cost.
Q. What is the difference between V ST and V T ?
A. V T is the potential difference actually experienced by a person standing
at point A on the earth surface, while in hand-contact with a faulty grounded
part B. V ST is the potential difference between the same two points A and B,
but in the absence of the person.

Endnotes
1. As further discussed, this also applies to ungrounded systems (IT systems).
2. An isotropic soil has physical properties that do not vary with direction.
3. To fix ideas, imagine that the hemispherical electrode acts as a colander to
water.
4. The symmetry of the electrode yields uniform current density in the ground;
therefore, the formula for the resistance of conductors is still applicable.
2
5. The lateral area of a sphere equals 4 r , and therefore the lateral area of a
hemisphere is half of that.
6. The general equation of a rectangular hyperbola is y = m/x.
7. The electric potential at a point P(x,y,z) is a scalar quantity, which is solely
a function of the coordinates (x,y,z) being considered, once a reference (e.g.,
infinity) has been established.
8. They are independent if, upon their alternate disconnection, a current im-
pressed through the first one does not appreciably change the earth potential
of the other one.
9. In the case of the hemispherical electrode, the ground potential for r = 0 equals
infinity.
10. As already discussed in previous chapters, the voltage exposure is present
during the time the protective device employs to disconnect the supply.
11. As further discussed in Chap. 5, at 50/60 Hz, the body can be considered
a resistance instead of impedance; R B depends, among other things, on the
current path through the body, and, in our calculations, we conventionally
consider the most critical one consisting of the pathway both hands-to-both
feet.