任意n阶多边形电阻网络的电特性研究  

Study on the electrical properties of an arbitrary n-order polygonal resistor network

作　　者：黄建兰 谭志中[2] HUANG Jian-lan;TAN Zhi-zhong(Rugao Binjiang Junior Middle School,Rugao,Jiangsu 226534,China;Department of Physics,Nantong University,Nantong,Jiangsu 226019,China)

机构地区：[1]江苏省如皋市滨江初级中学,江苏如皋226534 [2]南通大学物理系,江苏南通226019

出　　处：《大学物理》2020年第2期21-25,共5页College Physics

基　　金：江苏省自然科学资金面上项目(No.BK20161278);国家级大学生创新创业训练计划项目(201810304025)

摘　　要：文章采用基尔霍夫定律通过建立差分方程模型的方法研究了一类任意n阶多边形电阻网络的电学性质(节点电压,支路电流,等效电阻).首先采用基尔霍夫节点电流定律建立差分方程模型,同时建立边界条件方程,以此研究差分方程组的通解和特解,进而获得各节点电压公式,并且基于电压结果导出支路电流公式及等效电阻公式.本文的研究工作对于促进基础物理创新教学具有很好的理论意义与教学实践价值.This paper uses Kirchhoff’s law to study the electrical properties(node voltage, branch current, equivalent resistance) of an arbitrary n-order polygonal resistor network by establishing a differential equation model. Firstly, the differential equation model is established by using the Kirchhoff current law, and the general and special solutions of the difference equation are also studied, then the voltage formula of each node is obtained. Based on the voltage results, the formulae of branch current and equivalent resistance are derived. The research in this paper is of great theoretical value and practical significance in promoting physical inquiry teaching and cultivating students’ ability of scientific inquiry.

关 键 词：多边形网络 基尔霍夫定律 差分方程 电学性质 

分 类 号：O441.1[理学—电磁学] TN711.3[理学—物理]