Date of Submission
Spring 2015
Academic Programs and Concentrations
Mathematics
Project Advisor 1
James Belk
Abstract/Artist's Statement
We study the resistance of infinite electrical networks that contain a single source and a sink at infinity. We will be exploring the total resistance on the infinite binary tree, line, grid, and hyperbolic grid using two different methods. The two methods are discrete forms of Laplace’s equation and the heat equation. These two methods are used to find the potentials of nodes in the networks. By modeling the resistance of large subnetworks in Sage we are able to estimate the resistance of infinite networks. Using Laplace’s equation we were able to determine the resistance on the binary tree and line. Using the heat equation we were able to obtain a resistance for all four specified networks. These two methods may prove useful for more complicated infinite networks.
Open Access Agreement
On-Campus only
Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 License.
Recommended Citation
Maharaj, Sharma, "Resistance of Infinite Networks" (2015). Senior Projects Spring 2015. 278.
https://digitalcommons.bard.edu/senproj_s2015/278
This work is protected by a Creative Commons license. Any use not permitted under that license is prohibited.
Bard Off-campus DownloadBard College faculty, staff, and students can login from off-campus by clicking on the Off-campus Download button and entering their Bard username and password.