Information

A. The Electrical Resistance and its Temperature Coefficient
Resistivity
In accordance with the equation
q
l
R
t
t
⋅
=
ρ
the electrical resistance of a
conductor at temperature t is
proportional to its length and
inversely proportional to its cross-
sectional area on the condition that
there is a constant cross-section
over the whole test length.
R
t
= Resistance in Ω at
Temperature t
l = Length in m
q = Cross-Sectional area in mm²
ρ
t
= Resistivity in Ω · mm²· m
-1
at
temperature t
In order to calculate
l
q
R
tt
⋅= ρ
R
t
, q and l are determined. If
q = 1 mm² and
l = 1 m
are given, one calculates the
resistivity in Ω · mm² · m
-1
, i.e. the
resistance of a conductor of 1m
length and 1 mm² cross-sectional
area.
page 2
The resistivity can also be defined
as to be the electrical resistance of
a cube with 1cm edge length; then it
is expressed in units of Ω · cm.
Since for base metals and alloys the
resistance of such a cube is very
low, the resistance values are
expressed in µΩ · cm, i. e. in
millionths of an Ω · cm.
The values for e.g. ISOTAN
®
would
then be either
0.49 Ω · mm² · m
-1
or
49 µΩ · cm.
The practical determination of the
resistivity can be difficult, since
determination of the cross-sectional
area of e.g. wires with non-circular
cross-section or very thin wires is
difficult. In such cases, the cross-
sectional area is determined on the
basis of weight and length.
The resistivity of a wire can then be
determined in accordance with the
equation:
²
1
l
gR
t
t
⋅
⋅
=
γ
ρ
R
t
= Resistance in Ω at
Temperature t
ρ
t
= Resistivity in Ω · mm²· m
-1
at
temperature t
g = Weight in g
γ
= Density in
γ
/cm³
l = Length in m
For countries using a different
system of meaurement the
resistivity is expressed in units
which must be converted when
changing over from one system to
another (see Annex “Conversion
Values”):
Resistance per Meter
The resistance per meter of a
conductor is determined by the
quotient of its resistivity and cross-
sectional values.
The Temperature Coefficient (α)
of Resistivity
Metals and their alloys exhibit a
dependence of the resistivity on
temperature. In general the
resistivity increases with
temperature dependence of
resistivity can be expressed by the
equotion:
R
t
= R
o
[1 + α (t - t
o
)]
This equation applies only if
resistance and temperature expose
a linear relationship in the test
temperature expose a linear
relationship in the test temperature
range from t
o
to t. For most alloys
and metals this is not the case,
especially as regards large
temperature intervals. In order to
deliver an exact description of the
temperature dependence of the
resistivity, complicated equations
are required.
In spite of this temperature
coefficient is defined from the
equation above as being:
()
[]
1−
−
−
= K
ttR
RR
oo
ot
α
Resistance per Meter =
Resistivity (Ω · mm² . m
-1
) = Ω · m
-1
Cross-sectional area (mm²)