Research PapersNo Access

INFINITE NETWORKS OF IDENTICAL CAPACITORS

J. H. ASAD

Department of Physics, Tabuk University, P.O. Box 741, Tabuk 71491, Kingdom of Saudi Arabia

Corresponding author.

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R. S. HIJJAWI

Department of Physics, Mutah University, Jordan

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A. J. SAKAJI

Department of Basic Sciences, Ajman University, UAE

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, and

J. M. KHALIFEH

Department of Physics, University of Jordan, Amman 11942, Jordan

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https://doi.org/10.1142/S0217984910022767Cited by:8 (Source: Crossref)

Abstract

The capacitance between the origin and any other lattice site in an infinite square lattice of identical capacitors each of capacitance C is calculated. The method is generalized to infinite Simple Cubic (SC) lattice of identical capacitors each of capacitance C. We make use of the superposition principle and the symmetry of the infinite grid.

Keywords:

PACS: 61.50.Ah, 61.50.+f, 61.66.f, 84.37.+q, 05.50.+q, 04.60.Nc, 63.90.+t, 84.30.Bv, 02.90.+p

References

P. G. Doyle and J. L. Snell, Random Walks and Electric Networks, The Carus Mathematical Monograph (The Mathematical Association of America, USA, 1984) p. 83. Crossref, Google Scholar
L. Lovãsz, Combinatorics, Paul Erdós is Eighty 2, eds. D. Miklós, V. T. Sós and T. Szónyi (János Bolyai Mathematical Society, Budepest, 1996) pp. 353–398, http://research.microsoft.com~Lovãsz. Google Scholar
B. Van der Pol, Probability and Related Topics in Physical Sciences, Lectures in Applied Mathematics 1, ed. M. Kac (Interscience Publ., London, 1959) pp. 237–257. Google Scholar
S. Redner , A Guide to First-Passage Processes ( Cambridge Press , Cambridge, UK , 2001 ) . Crossref, Google Scholar
S. Katsura and T. Horiguchi, J. Math. Phys. 12(2), 230 (1971), DOI: 10.1063/1.1665581. Crossref, Web of Science, ADS, Google Scholar
G. Kirchhoff, Ann. Phys. und Chemie 72, 497 (1847). Google Scholar
B. Van der Pol and H. Bremmer , Operational Calculus Based on the Two-Sided Laplace Integral ( Cambridge University Press , England , 1955 ) . Google Scholar
F. J. Bartis, Am. J. Phys. 35, 354 (1967), DOI: 10.1119/1.1974081. Crossref, Web of Science, ADS, Google Scholar
G. Venezian, Am. J. Phys. 62, 1000 (1994), DOI: 10.1119/1.17696. Crossref, Web of Science, Google Scholar
D. Atkinson and F. J. Van Steenwijk, Am. J. Phys. 67, 486 (1999), DOI: 10.1119/1.19311. Crossref, Web of Science, ADS, Google Scholar
M. Jeng, Am. J. Phys. 68(1), 37 (2000), DOI: 10.1119/1.19370. Crossref, Web of Science, ADS, Google Scholar
J. Cserti, Am. J. Phys. 68, 896 (2000), DOI: 10.1119/1.1285881. Crossref, Web of Science, ADS, Google Scholar
J. Cserti, G. David and A. Piroth, Am. J. Phys. 70, 153 (2002), DOI: 10.1119/1.1419104. Crossref, Web of Science, ADS, Google Scholar
J. H. Asad, Ph.D Thesis, University of Jordan, 2004, unpublished . Google Scholar
J. H. Asadet al., Int. J. Theo. Phys. 43(11), 2223 (2004), DOI: 10.1023/B:IJTP.0000049021.94530.6e. Crossref, Web of Science, Google Scholar
J. H. Asad, A. Sakaji, R. S. Hijjawi and J. M. Khalifeh, On the resistance of an infinite square network of identical resistors — Theoretical and experimental comparison, 2005, to be published . Google Scholar
J. H. Asadet al., Int. J. Theo. Phys. 44(4), 471 (2005), DOI: 10.1007/s10773-005-3977-6. Crossref, Web of Science, Google Scholar
R. S. Hijjawiet al., Eur. Phys. J. — Appl. Phys. 41, 111 (2008), DOI: 10.1051/epjap:2008015. Crossref, Web of Science, ADS, Google Scholar
F. Y. Wu, J. Phys. A: Math. Gen. 37, 6653 (2004), DOI: 10.1088/0305-4470/37/26/004. Crossref, ADS, Google Scholar
S. J. Van Enk, Am. J. Phys. 68(9), 854 (2000), DOI: 10.1119/1.1302907. Crossref, Web of Science, ADS, Google Scholar
J. H. Asadet al., Int. J. Mod. Phys. B 19(24), 3713 (2005), DOI: 10.1142/S0217979205032401. Link, Web of Science, ADS, Google Scholar
J. H. Asadet al., Eur. Phys. J. — Appl. Phys. 32(3), 149 (2005), DOI: 10.1051/epjap:2005075. Crossref, Web of Science, ADS, Google Scholar
J. H. Asadet al., Eur. Phys. J. — Appl. Phys. 40(3), 257 (2007), DOI: 10.1051/epjap:2007160. Crossref, Web of Science, ADS, Google Scholar
R. S. Hijjawiet al., Int. J. Mod. Phys. B 21(2), 199 (2007), DOI: 10.1142/S0217979207035972. Link, Web of Science, ADS, Google Scholar
E. M. Purcell, Electricity and Magnetism, 1st edn. (McGraw-Hill, New York, 1965) p. 424. Google Scholar
E. M. Purcell, Electricity and Magnetism, 2nd edn. (McGraw-Hill, New York, 1985) pp. 167–168. Google Scholar
A. H. Zemanian, IEEE Trans. Circuits Syst. 35 (1988) 1346–1358; A. H. Zemanian, Transfiniteness for graphs, Electrical Networks and Random Walks (Birkhauser, Boston, 1966) . Google Scholar
J. H. Asad, Asian J. Appl. Sci. 2(3), 296 (2009), DOI: 10.3923/ajaps.2009.296.299. Crossref, Web of Science, Google Scholar