摘要
研究了一类n阶Fan电阻网络的电特性(任意节点的电压,等效电阻),取得了理论和方法上的创新.文章以节点电压为变量应用基尔霍夫定律建立二阶差分方程模型以及边界条件方程模型,通过研究差分方程的通解与特解,获得了n阶Fan网络任意节点的电压公式,同时获得了任意2节点间的等效电阻公式,并分析与讨论了结论的特殊情形.本课题的研究工作实现了教学与科研的协同相长.
The electrical properties（ including the voltage of any node,and equivalent resistance） of a class of n-step Fan resistor network are studied,and innovation in theory and method has been achieved. In this paper,the second-order difference equation model and the boundary condition equation model are established by using the node potential as the variable in terms of applying Kirchhoff＇s law. By studying the general solution and special solution of difference equation,the voltage formula of arbitrary node of n-order Fan network is obtained,at the same time,the equivalent resistance formula between any two nodes is obtained as well,and the special situation of the conclusion is analyzed and discussed. Our research work realizes the cooperation and mutual benefit between teaching and scientific research.
作者
谭志中
吴鹏
罗小廉
孔泽霖
TAN Zhi-zhong, WU Peng, LUO Xiao-lian, KONG Ze-lin(Department of physics, Nantong University, Nantong, Jiangsu 226019, China)
出处
《大学物理》
2018年第8期24-28,共5页
College Physics
基金
国家级大学生创新创业训练计划项目(20171304006)
江苏省自然科学资金面上项目(BK20161278)资助
关键词
Fan网络
电位公式
等效电阻
差分方程
教学科研相长
Fan network
voltage tormula
diiterence equation
equivalent resistance
mutual benefit between teaching and research
