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arXiv · 2410.07261

On the Average Resistance of n-circuits

Mehdi Nikopour Deilami·Bohdan Zhelyabovskyy
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Abstract

$n$-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.

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Mehdi Nikopour Deilami, Bohdan Zhelyabovskyy. 2024-10-29. On the Average Resistance of n-circuits. https://arxiv.org/abs/2410.07261

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