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CHAPTER3
Mathematical
Principles of
Electrical Safety
Do not worry about your difficulties in
Mathematics.
I can assure you mine are still greater.
albert einstein (1879–1955)
3.1 Introduction
To prevent damage to persons, electrical equipment are manufactured
with “built-in” protective features (e.g., basic insulation, double insu-
lation, bonding provisions, etc.), and after their installation, more stan-
dard protective measures (PMs) against direct/indirect contact may
be added as per the electrical design (e.g., protective devices such as
circuit breakers, residual current devices, etc.).
This practice lowers the risk of electric shock below a specific
threshold considered acceptable by codes and standards.
Protective measures, like any other manufactured item, can fail,
though, and the electrical equipment may expose persons to the risk
of electric shock. As the failure of the PMs, like any other item, can be
statistically predicted, in this chapter we will examine the possibility
to quantify such a risk.
3.2 Mathematical Definition of Safety
The electrical safety of a piece of equipment against the appearance of
dangerous voltages on its enclosure is a parameter that can be thought
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