An integration method of deriving the alternating current resistance and inductance of conductors . - .41 - . - .03 - .05 . The first term of (79) is the inductance of two tubes. Hencethis term may be considered as the inductance caused by themagnetic field external to the conductor. The second term,identical with the last term of (23), gives the inductance causedby the field inside a single conductor. Hence the sum of termsone and two gives the inductance of the circuit, assuming thatthe current distribution is the same as for infinite spacing. Theother terms s
An integration method of deriving the alternating current resistance and inductance of conductors . - .41 - . - .03 - .05 . The first term of (79) is the inductance of two tubes. Hencethis term may be considered as the inductance caused by themagnetic field external to the conductor. The second term,identical with the last term of (23), gives the inductance causedby the field inside a single conductor. Hence the sum of termsone and two gives the inductance of the circuit, assuming thatthe current distribution is the same as for infinite spacing. Theother terms show the effect on the inductance of the change incurrent distribution caused by the field of the adjacent wire. I20 Scientific Papers of the Bureau of Standards [Vol. i6 In Fig. 4 the relative decrease of inductance with increasingfrequency is shown. The inductance, Lq, at zero frequency isalways greater than the inductance, L, at any other frequency, so that function —j—- is in all cases negative. As the spacing is decreased, the relative inductance decreases rapidly. FREQUENCY 2000- 3W»-. Fig. 4. —Curves showing the effect of frequency on the inductance of a return circuit I have received valuable suggestions from a number of mycolleagues at the Bureau of Standards. Also, Dr. F. W. Grover,of Colby College, has read the manuscript with care and correctedseveral errors in the numerical coefficients. Dr. T. J. I , of Cambridge University, England, has suggestedmethods for simplifying the integration in certain cases. Curtis] A. C. Resistance and Inductance 121 VI. APPENDIX.—EVALUATION OF INTEGRALS AND DEVEL-OPMENT OF SERIES In this appendix are given the evaluation of some of the integrals and the expan-sion of some of the series which are necessary for the development of the formulasof this paper. In each case the nomenclature is that used in the body of the those formulas which are not readily found in text-books of mathematics areincluded. 1
Size: 1766px × 1414px
Photo credit: © The Reading Room / Alamy / Afripics
License: Licensed
Model Released: No
Keywords: ., bookcentury1900, bookdecade1920, bookpublishernatio, bookyear1920
