Abstract: Study of the equivalent resistance formulae for arbitrary m×n-order resistance network is a difficult problem. The equivalent resistance and capacitance of 7 ×n-rectangular network are investigated in this paper. We built a quaternion matrix equation and proposed the method of matrix transformations in terms of the network analysis. A brief equivalent resistance formula is proposed, meanwhile a equivalent resistance of infinite networks is gained. Using the inverse mapping relation between capacitance parameters and resistance parameters, the equivalent capacitance formula is given for the 7 ×n-rectangular capactitance 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 achieved before. Some new trigonometric identities are obtained when the result is compared with others.

Key words: 7 ×n-rectangular network, equivalent resistance and capacitance, matrix transformation, two conjectures, trigonometric identity