Electrical Engineering

, Volume 96, Issue 3, pp 287–297

# Current density in two solid parallel conductors and their impedance

Original Paper

## Abstract

A method is proposed for the calculation of current density in a long loop of solid conductors of arbitrary cross section that does not change along the conductors. The essence of the proposed method consists in replacing a segment of the loop by $$N$$ circuits with lumped parameters. The calculation is analysed of current density in two conductors of rectangular cross section, which are supplied from a source of sinusoidal voltage in steady state. Based on the calculated current density, the impedance and Joule power of a loop segment are examined as well as the loop’s coherence with solitary conductor and the skin effect. Loops of thin strip conductors are dealt with.

### Keywords

Solid conductors Current density Impedance Joule power Skin effect

### References

1. 1.
Matsushima A, Sakamoto H (2002) Application of wire model to calculation of impedance of transmission lines with arbitrary cross sections. Electron Commun Jpn Part 2 85(7):1–9
2. 2.
Coufal O (2012) On inductance and resistance of solitary long solid conductor. Acta Technica 57:75–89. http://journal.it.cas.cz
3. 3.
Coufal O (2013) On resistance and inductance of solid conductors. J Eng 2013:1–14. doi:10.1155/2013/526072
4. 4.
IEC 60050–131:2002/A1:2008 International electrotechnical vocabulary—Part 131: circuit theoryGoogle Scholar
5. 5.
Reitz JR, Milford FJ, Christy RW (1993) Foundations of electromagnetic theory. Addison-Wesley Publishing Company Inc, New YorkGoogle Scholar
6. 6.
Mayergoyz ID, Lawson W (1996) Basic electric circuit theory. Academic Press An Imprint of Elsevier, New YorkGoogle Scholar
7. 7.
Tamm IE (1979) Fundamentals of the theory of electricity. Mir Publishers, MoscowGoogle Scholar
8. 8.
Coufal O (2007) Current density in a pair of solid coaxial conductors. Electromagnetics 27:299–320
9. 9.
Kellog OD (1929) Foundations of potential theory. In: Dover Publications Inc, New York, republication of the work originally published in 1929 by J. SpringerGoogle Scholar
10. 10.
Budak BM, Fomin SV (1967) Kratnye Integraly i ryady. Nauka Publishing House, MoscowGoogle Scholar
11. 11.
Lide DR (2007) CRC handbook of chemistry and physics, 88th edn. CRC Press, Boca RatonGoogle Scholar
12. 12.
Coufal O (2008) Current density in a long solitary tubular conductor. J Phys A Math Theor 41(145401):1–14
13. 13.
IEC 60050–121:1998 International electrotechnical vocabulary - Part 121: electromagnetismGoogle Scholar
14. 14.
Rektorys K, Vitásek E (eds) (1994) Survey of applicable mathematics. Kluwer, DordrechtGoogle Scholar
15. 15.
Feynman RP, Leighton RB, Sands M (2005) The Feynman lectures on physics. The definition edition, vol. 3, 2nd edn. Addison-Wesley, Reading, Mass, BostonGoogle Scholar
16. 16.
Ralston A, Rabinowitz P (2001) A first course in numerical analysis, 2nd edn. Dover Publications Inc, Mineola, New York
17. 17.
Simonyi K Foundations of electrical engineering, part III, in German (VEB Verlag, Berlin, 1956); in English (Pergamon, Oxford, 1963); in Russian (Mir Publishers, Moscow, 1964)Google Scholar
18. 18.
Matick RE (1995) Transmission lines for digital and communication networks. IEEE Press, New YorkGoogle Scholar
19. 19.
Vujević S, Boras V, Sarajcev P (2009) A novel algorithm for internal impedance computation of solid and tubular cylindrical conductors. Int Rev Electr Eng 4–B(6):1418–1425Google Scholar
20. 20.
Lovrić D, Boras V, Vujević S (2011) Accuracy of approximate formulas for internal impedance of tubular cylindrical conductors for large parameters. Prog Electromagn Res M 16:171–184Google Scholar
21. 21.
Mayer D (2012) Applied electromagnetism, in Czech. KOPP, České BudějoviceGoogle Scholar
22. 22.
Maxwell JC (1954) A treatise on electricity and magnetism, unabridged, vol II, 3rd edn. Dover Publications Inc., New York
23. 23.
Raven MS (2013) Maxwell vector potential method, transient currents and the skin effect. Acta Technica 58(3):337–350Google Scholar
24. 24.
Coufal O (2011) Comments on skin effect in solitary solid tubular conductor. Adv Math Phy 2011:1–13. doi:10.1155/2011/983678
25. 25.
Hanka L (1975) Electromagnetic theory, in Czech. SNTL, PragueGoogle Scholar