Resistor Theory and Technology

Resistors are passive components (unlike transistors, integrated circuits, etc.), characterized by the deposition of a resistive element on an appropriate substrate. This resistive element can be a wire, metallic layer, metal foil, etc. Its ohmic value is determined by means of the following formula:
where L(m) = length of deposit
R( ?) = resistance
p( ?) = resistivity of the material forming the deposit
S(m 2) = cross-section of the deposit
R is inversely proportional to the thickness of the resistive material, which, for obvious technical reasons, must be greater than zero (the diameter of wound wire is close to 10 ?m; the thickness of a metallic deposition layer is roughly a micrometer). This relationship becomes more significant as the desired power increases, limiting the range of ohmic values possible with these devices.
Nominal value is the desired ohmic value of the resistor. Standard preferred numbers of nominal values R n are obtained by rounding the theoretical value obtained:
where n is a positive or negative integer number
m can take the values 3, 6, 12, 24, 48, 96, or 192
The series obtained (E3 to E192) include between 3 and 192 values per decade. They are associated with increasingly closer tolerances (greater than 20% for the E3 series, 0.5% for the E192 series).
Table 1 lists, for n = 1, the nominal values and...