含反馈电路的n阶电阻网络的新理论  

A new theory of n-order resistor network with feedback circuits

作　　者：刘雅慧 陈芸 檀钰 王慧莹 孙雯雯 谭志中[1,2] LIU Ya-hui;CHEN yun;TAN Yu;WANG Hui-ying;SUN Weng-weng;TAN Zhi-zhong(School of Science,Nantong University,Nantong,Jiangsu 226019,China;Xinglin College,Nantong University,Nantong,Jiangsu 226236,China)

机构地区：[1]南通大学理学院,江苏南通226019 [2]南通大学杏林学院,江苏南通226236

出　　处：《大学物理》2024年第6期63-67,共5页College Physics

基　　金：2022年江苏省大学生创新创业训练计划项目(202210304076Y);2022教育部产学合作协同育人项目(22067069245638);2021年度江苏省高等教育学会评估委员会课题(2021-C122)资助。

摘　　要：研究了一类含有外接电阻的n阶电阻网络模型,给出了一个任意2节点间的等效电阻解析式,解决了一个电阻网络难题.文章研究所采用的方法主要是利用支路电流建立差分方程模型以及边界条件约束方程模型,然后求解差分方程组,由此导出等效电阻解析式.文章最后讨论了一些特殊情形的问题,并且将特殊情形的结论与其他相关结果进行了比较与验证.本文的研究工作对物理教育工作者开展实践创新研究具有比较好的示范作用.A class of n-order resistor network model with external resistor is studied,and an analytical expression for the equivalent resistance between any two nodes is given to solve a resistor network problem.The method used in the research of the article mainly uses the branch current to establish a difference equation model and a boundary condition constraint equation model,and then solves the difference equation system to derive the equivalent resistance analytical formula.At the end of the article,some special case issues are discussed,and the conclusions of the special case are compared and validated with other relevant results.The research work of this article has a good demonstration role for physics educators to carry out practical and innovative research.

关 键 词：反馈电路 n阶网络 差分方程 等效电阻 约束条件 

分 类 号：O441.1[理学—电磁学] TN711.3[理学—物理]