3×n阶网络等效电阻的另一个普适规律  

Another general formula of equivalent resistance of 3×n step network

作　　者：谭志中[1] 李颂[1] 

机构地区：[1]南通大学理学院,江苏南通226007

出　　处：《大学物理》2009年第4期23-25,28,共4页College Physics

摘　　要：再次研究了3×n阶电阻网络的等效电阻,通过网络分析构建差分方程组模型,应用矩阵变换方法巧解差分方程组,给出了3×n阶电阻网络等效电阻的另外一个优美、简洁的普适规律,同时给出了无穷3×n阶电阻网络的等效电阻,并在最后对特殊情形的相关结果进行了比较与验证.The equivalent resistance of 3 × n-step network is studied again. By means of virtual current method, the 3 × n-network is analyzed and a model of two-variable difference equation is proposed. The matrix transform is constructed by artifice. Based on different marginal conditions, a general formula for the inlet resistance of 3 × n-network as well as an utmost rule for the equivalent resistance of 3 ×n-network are presented. It is proved that the utmost equivalent resistance of infinity resistance network is equal to a constant.

关 键 词：3×n阶网络 矩阵变换 差分方程模型 等效电阻 普适规律 

分 类 号：O441[理学—电磁学]