教学讨论

一类n 阶电桥电路网络的等效电阻研究

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  • 1. 南通大学物理系,江苏南通226019; 2.南通大学电子信息学院,江苏南通226019
李伟( 1996—) ,山西屯留人,南通大学硕士研究生,主要从事物理教学论研究及物理创新方法研究.

收稿日期: 2018-10-10

  修回日期: 2019-03-09

  网络出版日期: 2019-10-16

基金资助

国家级大学生创新创业训练计划项目( 201810304025) ; 江苏省自然科学资金面上项目( BK20161278) 资助.

Study of equivalent resistance of a n-step bridge network of resistors

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  • 1. Department of Physics,Nantong University,Nantong, Jiangsu 226019,China; 2. School of Electronics and Information,Nantong University,Nantong, Jiangsu 226019,China

Received date: 2018-10-10

  Revised date: 2019-03-09

  Online published: 2019-10-16

摘要

电阻网络模型的结构复杂多样,被应用于自然科学的许多领域.本文研究了一类n 阶电桥电路网络模型,这是一个没有解决的新问题.研究表明该网络模型容纳了多个不同的电阻网络类型.文章主要采用建立简化的等效模型以及应用基尔霍夫定律建立非线性差分方程模型解决此问题,研究得到了一个简洁的分数阶等效电阻公式,同时给出了数个有趣的特殊结论,其中阐明了该网络称为电桥电路网络的缘由.

本文引用格式

李伟, 谭震, 王明君, 谭志中 . 一类n 阶电桥电路网络的等效电阻研究[J]. 大学物理, 2019 , 38(9) : 19 . DOI: 10.16854 /j.cnki.1000-0712.180557

Abstract

The structure of resistor network model is complex and diverse,which is applied in many fields of natural science.This paper researches a kind of n-step bridge network model,which has not been solved before.The investigations show that the network model contains multiple different network types.In this paper,a simplified equivalent model is adopted and a non-linear difference equation model is established by using Kirchhoff's law to solve this problem.A concise formula of fractional equivalent resistance is obtained and several interesting special conclusions are given,where we explain the reason why this network is called bridge circuit network.
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