Abstract

There are several examples of infinite networks of resistors; it is always assumed that a unique current exists as a consequence of Kirchhoff's laws. Actually, unlike the situation in finite networks, these laws are insufficient to determine a unique current. A plausible set of network laws are formulated and two main theorems are proved. 1) In an infinite network consisting of nonnegative resistors (with no short circuits) and a finite number of sources, there exists a unique current flow. 2) This current flow is the limit of the unique current flows in finite, subnetworks that approximate the whole network. Methods of algebraic topology and Hilbert space theory are used in the formulations and proofs.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.