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Solution of Cable Problem By Laplace Transform

Published online by Cambridge University Press:  03 November 2016

N. W. McLachlan
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Extract

Most of the tractable problems pertaining to submarine cables and electrical transmission lines have been solved. However, no result seems to have been given for the current at any point of a very long “loaded” cable with a series capacitance between it and the sending battery. By aid of a general theorem published recently in the Mathematical Gazette, the required result may be obtained without difficulty.

Type
Research Article
Information
The Mathematical Gazette , Volume 30 , Issue 292 , December 1946 , pp. 291 - 292
Copyright
Copyright © Mathematical Association 1946

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References

page note 291 * 30, 85, 1946.

page note 291 † The permeability when the magnetising force H → 0.

page note 291 ‡ McLachlan, Complex Variable and Operational Calculus : (1) is the first term of (2) § 13.42. The sign ⊃ a means that the function of p on the r.h.s. is the L.T. of f(t) on the l.h.s.

page note 291 § loc, cit. (3), § 8.411.

page note 292 * loc, cit. (8), § 8.731.

page note 292 † loc, cit. (7), § 13.33, with b=0, since G=0.