在线阅读 --自然科学版 2012年4期《三维□×n阶网络等效电阻的普适公式》
三维□×n阶网络等效电阻的普适公式--[在线阅读]
谭志中, 周玲, 李颂
南通大学理学院, 江苏 南通 226007
起止页码: 369--374页
DOI:
摘要
研究了一类三维□×n阶网络的等效电阻,采用网络分析构建差分方程组模型的方法,经过数学推导与计算,给出了三维□×n阶网络具有普适性的等效电阻公式.作为引申与应用,发现所得到结论同样适用于一类日×n阶电阻网络的等效电阻,由此得到了日×n阶电阻网络等效电阻的普适公式.同时给出了无穷三维网络的等效电阻公式,研究发现无穷三维网络的等效电阻是由无理数表示的有限常数.

A Universal Formula of the Equivalent Resistance for Three-dimensional □×n Resistance Networks
TAN Zhizhong, ZHOU Ling, LI Song
School of Sciences, Nantong University, Jiangsu Nantong 226007, China
Abstract:
The equivalent resistance for a type of three-dimensional □×n resistor networks is investigated.Difference equations of the model are established by mesh analysis.A perfect universal formula for the equivalent resistance is given through the strict derivation and calculation.As an extension and an application,it is found that the results are also suitable for a type of □×n resistance networks and a universal formula for such system is given.Taking a limit,the equivalent resistance formula are given for the 3D infinite resistance network is given and it is found that it is a finite constant expressed by irrational numbers.

收稿日期: 2012-3-6
基金项目: 江苏省高校自然科学基金(11KJB140006);南通大学自然科学基金(11Z054,10ZY001,11ZY022)

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