Abstract:

This paper uses Kirchhoff’s law to study the electrical properties (node voltage，branch current，

equivalent resistance)of an arbitrary n-order polygonal resistor network by establishing a differential equation model. Firstly，the differential equation model is established by using the Kirchhoff current law，and the general and special solutions of the difference equation are also studied，then the voltage formula of each node is obtained.Based on the voltage results，the formulae of branch current and equivalent resistance are derived. The research in this paper is of great theoretical value and practical significance in promoting physical inquiry teaching and cultivating students’ability of scientific inquiry.

Key words: polygonal network, Kirchhoff’s law, difference equation, electrical properties