3×n阶蛛网等效电阻猜想的证明  

THE PROOF OF THE SUSPECT OF 3×n ORDER COBWEB EQUIVALENT RESISTANCE

作　　者：汤华[1] 谭志中[2] 

机构地区：[1]运河高等师范学校,江苏邳州221300 [2]南通大学理学院,江苏南通226007

出　　处：《物理与工程》2015年第1期44-48,52,共6页Physics and Engineering

基　　金：江苏省"青蓝工程"资助

摘　　要：本文应用基尔霍夫节点电流定律和回路电压定律,建立了3元矩阵方程模型,构造了矩阵变换方法,经过一系列严格的推导与计算,较好地证明了3×n阶蛛网等效电阻猜想的正确性,同时给出了3×n阶蛛网等效电阻公式.通过比较分析进一步给出了3×n阶蛛网在无限情形时的等效电阻公式,并且探讨了3×n阶蛛网等效电阻的单调性质.Based on the application of Kirchhoff＇s current law of nodes and the voltage of cir- cuit, a three-degree matrix equation model was established, and the method of matrix trans- formation was constructed. Through a series of strict deduction and calculation, the suspect of 3 × n order cobweb equivalent resistance was proved well in this paper. Meanwhile, the equiva- lent resistanee formula of 3 × n order cobweb was given. Then the equivalent resistance formula of 3× n order cobweb in infinite condition was given through further comparative analysis, and the monotone property of 3 × n order cobweb equivalent resistance was discussed.

关 键 词：3×n阶蛛网 猜想证明 基尔霍夫定律 等效电阻 矩阵方程模型 

分 类 号：O441.1-4[理学—电磁学] G652[理学—物理]