## Study on Equivalent Resistance of an Arbitrary m × n Cobweb Network

**MIAO Ziyi;LI Xiaolei;TAN Zhizhong;School of Sciences,Nantong University;**

This paper studied the equivalent resistance of an arbitrary m × n cobweb network by the recursion-transform(RT) method, where the main research methods include: firstly by network analysis a recursive matrix equation(includes the boundary condition equation) was established;next constructing matrix was transformed to obtain the eigenvalues and eigenvectors of matrices so as to obtain the general solution and particular solution of the equations;finally by matrix inversion the branch currents was obtained, thus the equivalent resistance between two nodes in the m×n cobweb network is obtained, and the obtained result is composed of characteristic root and single summation. As applications of the formulae, a number of results of equivalent resistance in special cases are given, which includes the equivalent resistance in the case of semi-infinite and infinite, and a new trigonometric identity is identified when two equivalence results were compared with different form.

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