利用对称性分析巧解电阻网络两点间的等效电阻

doi:10.14139/j.cnki.en22-228.2025.02.004

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摘要

分析了 4 种电阻网络的对称性，并据此绘制了相应的简化等效电路，明确了各电阻之间的串联与并联关系。基于串联和并联电阻的基本规律，计算出了网络中各节点之间的等效电阻值。在此基础上，利用电流叠加法，计算了其他非对称情况下的两点间等效电阻。进一步扩展讨论了某些不具备明显对称性的物理问题，通过构建适当的对称性来简化问题求解过程。这种方法不仅提升了计算的准确性和效率，还为解决复杂物理问题提供了一种新的思路。

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	翁祝林

关键词: 等效电阻对称性电流叠加物理教学

Abstract:

The symmetries of four kinds of resistance networks are analyzed, and the simplified equivalentcircuits are drawn according to the symmetries, and the series-parallel relationship between each resistor isdefined.Based on the basie law of series parallel resistanee, the equivalent resistanee values between networknodes are caleulated, On this basis, the equivalent resistanee between the other asymmetrical two points iscalculated by using the electric current superposition method.The extension shows how to solve some physicsproblems without symmetry by constructing symmetry. This method not only enhances the accuracy andefficieney of calculations but also provides a new approach for solving complex physical problems.

Key words: equivalent resistance symmetry electrie current superposition Physies teaching

出版日期: 2025-04-25 发布日期: 2025-04-25 整期出版日期: 2025-04-25

ZTFLH:

G 642.46

基金资助:

湖北民族大学 2023 年度教学研究与改革项目(2023JY014)

引用本文:

翁祝林 . 利用对称性分析巧解电阻网络两点间的等效电阻 [J]. 大学物理实验, 2025, 38(2): 16-24.
WENG Zhulin. Method of Equivalent Resistance Between Two Points ofResistance Networks Through Symmetry Analysis . Physical Experiment of College, 2025, 38(2): 16-24.

链接本文:

https://dawushiyan.jlict.edu.cn/CN/10.14139/j.cnki.en22-228.2025.02.004 或 https://dawushiyan.jlict.edu.cn/CN/Y2025/V38/I2/16

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