Theory on resistance of mxn cobweb network and its application

A basic theorem of equivalent resistance between two arbitrary nodes in an mxn cobweb network in both finite and infinite conditions is discovered, and two conjectures on the equivalent resistance are proved in terms of the basic theorem. We built a tridiagonal matrix equation by means of network analysis and made a diagonalization method of matrix transformation and work out its explicit expressions. The new formulae obtained here can be effectively applied in complex impedance network, especially the formulation leads to the occurrence of resonances and a series of novel results in RLC (denote resistor, inductance and capacitance) network. These curious results suggest the possibility of practical applications to resonant circuits. Copyright (c) 2014 John Wiley & Sons, Ltd.