3×n阶电阻网络等效电阻的研究  

Study on equivalent resistance of 3×n step network

作　　者：谭志中[1] 方靖淮[1] 

机构地区：[1]南通大学理学院,江苏南通226007

出　　处：《大学物理》2008年第9期7-10,共4页College Physics

摘　　要：研究了3×n阶电阻网络的等效电阻.应用矩阵变换方法求解了差分方程组,给出了3×n阶电阻网络等效电阻的一个简洁的普适规律,并计算出了无穷3×n阶电阻网络的等效电阻,发现无穷3×n阶电阻网络的等效电阻,是一个无理数.The basic structure of a 3 × n -network is studied and the equivalent resistance of the network is calculated. A set of differential equations is solved by using the matrix transform method and thus a general formula for the inlet resistance of 3 ×n -network is proposed. It is found the equivalent resistance of infinity resistance network is an irrational number.

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]