Equivalent Resistance and Capacitance of 8×n-rectangular Network and Two Conjectures of m×n-rectangular Network
Tan Zhi-zhon · Journal of Hebei Normal University · 2013
A quaternion matrix equation and the method of matrix transformations in terms of the network analysis were built.A brief equivalent resistance formula is proposed.Meanwhile,a equivalent resistance of infinite networks is given.Considering the inverse mapping relation between capacitance and resistance parameters,the equivalent capacitance formula is given for the 8×n-rectangular capacitance network.Two conjectures of the equivalent resistance and capacitance formulas for the random m×n-rectangular network are proposed according to the architectural feature of a series of formulas of equivalent resistance which have been achieved before.By comparison in this paper,a new trigonometric identity is obtained.