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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.07261 |
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Table of Contents:
- $n$-circuits are series-parallel networks composed of exactly $n$ unit resistors. This paper is focused on evaluating the mean resistance of all $n$-circuits, $M_n$, establishing that it lies between $1$ and $4.3954$ for all $n$. We ultimately conjecture that $M_n$ converges to $1.25$ as $n$ grows, based on computational analysis and other intuitive arguments. Although the number of $n$-circuits has been explored quite thoroughly, this paper also provides complete proofs of some important results.