John A. Roebling's Sons Company, Trenton, N. J. Standard Underground Cable Company, Perth. Amboy, N. J. Heddernheimer. Kupferwerk und Suddeutsche.
THE TEMPERATURE COEFFICIENT OF RESISTANCE OF COPPER By
H. Dellinger
J.
CONTENTS Page I.
II.
Introduction
Former Values
Use
72
2.
Necessity for the Present Investigation
73
in
Experimental Data
73
74
3.
The Resistance Measurements The Temperature Coefficient Measurements The Sources of Material Represented
4.
Effect of Chemical Differences of Samples
78
5.
Effect of Physical Differences of Samples
6.
Hardening Copper Samples that had never been Melted
79 80
1.
2.
7.
III.
72
1
74 77
Effect of Local
81
Conclusions
83
1.
Proportionality of Temperature Coefficient and Conductivity
83
2.
The Resistivity-Temperature Constant
84
3.
Temperature Standard
Correction
Measurements
against
a
Copper 84
Hardening, Impurities, and Distortion on the Tem-
4.
Effect
5.
The Temperature
of
for
perature Coefficient
Measurement
of Conductivity".
,
.
Odd Shapes
b.
c.
86
Short Samples Wires that have been Distorted and Bent d. The Estimation of Chemical Purity Explanation of Disagreements of Previous Observers
87
Values Suggested for Annealed and Hard-Drawn Copper IV. The Mathematical Expression of the Temperature Coefficient 1. On General Functions of Temperature 2. Calculation of Linear Temperature Coefficient from Observations. 3. Effect of Thermal Expansion in the Expression of the Linear 7.
.
Temperature V. Summary VI. Appendix.
85 86
86 86
a.
6.
Coefficient as a
Coefficient
—Reichsanstalt
87 88
88 88 92 93 96
Results
97 71
Bulletin of the
72
Bureau
of
Standards
[Vol. 7,
No. I
INTRODUCTION FORMER VALUES IN USE I.
1.
temperature coefficient Some of those which have been much
Widely varying values are of resistance of copper.
in use for the
used are given in the following table, in which aQ and respectively by the equations:
^^20
are given
= Ro (i+^oO Rt -R20 (i+«'2o[^-2o]) i^< = resistance respectively at 0° C, at 20° C, and Rt
Rq,
i?20J
t = any temperature
at t°.
centigrade ^0
^20
0.00398
0.00369
Laboratoire Central d'Electricite
.00400
.00370
Kennelly and Fessenden, 1890
.00406
.00375
.00420
.00387
Verband Deutscher Elektrotechniker
.00426
.00392
(British) Institution of Electrical Engineers
.00428
.00394
Lagarde, 1893
.00445
.00409
Matthiessen's temperature coeflBcient,
American
0° C
to
20°
C
Institute of Electrical Engineers
Matthiessen's formula is: X«==Xo (i— 0.0038701 /+0.000009009 conductivity, or reciprocal of resistance, at t° and 0° C, respectively.
t"^).
X
and one other temperature, t. The "differential at^'' is the temperature coefficient obtained when a copper sample is measured against another in the same bath and thus undergoing the same variations of temperature. It is simply the difference of the temperature coeffi*^