3×n阶网络等效电阻的再研究  

Restudy on the Equivalent Resistance of 3×n Network

作　　者：谭志中[1] 罗达峰[1] 杨建华[1] 

机构地区：[1]南通大学理学院,江苏南通226007

出　　处：《南通大学学报（自然科学版）》2011年第2期67-72,共6页Journal of Nantong University(Natural Science Edition)　

基　　金：江苏省教育科学十一五规划立项课题(D/2009/01/127)

摘　　要：通过网络分析构建了三元差分方程组模型,提出了一种矩阵变换方法,得到了电阻网络中的电流分布规律.基于不同的边界条件,获得了3×n阶网络等效电阻的2个新的普适公式,该公式适用于网格数为一切自然数的情形,同时得到的无穷3×n阶网络的2个等效电阻是由无理数表示的常数.通过将所得结论与实际结果比较,说明了该公式的正确性.Whereas the equivalent resistance of 3 × n networks has not got a complete one as yet,the basic structure of a 3 × n resistance network is worth restudying.The distributing rules of the current can be obtained after the construction of the ternary difference equation model and matrix transform through network analysis.Based on the different marginal conditions of 3 × n network,two new general formulas are proposed for the inlet equivalent resistance of 3 × n network when the grid number is an arbitrary natural number.Meantime it proves that two inlet equivalent resistances of infinity 3 × n network are expressed as irrational number.Finally the result is compared with actual outcome.

关 键 词：3×n阶网络 差分方程模型 矩阵变换 等效电阻 

分 类 号：O441[理学—电磁学]