关键词: 蛛网模型, 网络分析, 矩阵变换, 等效电阻公式, 等效电阻和电容猜想

Abstract: A classic problem in electric circuit theory studied by numerous authors over 150 years is the computation of the resistance between two nodes in a resistor network, but some basic problems in polygon resistance network are still not solved. In this paper we intend to promote the polygonal network structure to cobweb structure, and study the equivalent resistance formula of 2×n cobweb model. We obtain a universal formula of the equivalent resistance by using the methods of network analysis and matrix transformation. It is found that the equivalent resist- ance value decreases along the growing of the order n, and the value is limitary. Putting forward a conjecture on the equivalent resistance formula, a conjecture on the equivalent capacitance formula of any m×n cobweb model accord- ing to the structure character of equivalent resistance formula is obtained. This offers a thought direction which to study the intricate cobweb network.

Key words: cobweb model, network analysis, matrix transformation, equivalent resistance formula, two con-jectures of the equivalent resistance and capacitance