We consider the problem of two-point resistance in a resistor network previously studied by one of us (Wu 2004 J. Phys. A: Math. Gen. 37 6653). By formulating the problem differently, we obtain a new expression for the two-point resistance between two arbitrary nodes which is simpler and can be easier to use in practice. We apply the new formulation to the cobweb resistor network to obtain the resistance between two nodes in the network. Particularly, our results prove a recently proposed conjecture on the resistance between the center node and a node on the network boundary. Our analysis also solves the spanning tree problem on the cobweb network.
|Journal||Journal of Physics A: Mathematical and Theoretical|
|Publication status||Published - 24 Jan 2014|
- mathematical physics
- electronics and devices
- instrumentation and measurement