2013/11/13 by Maciej Kasperski, Waldemar Kłobus · 1 voice
Mathematics · Physics and Astronomy · #Experimental and Theoretical Physics Studies #Mathematical and Theoretical Analysis
paper · doi:10.1088/0143-0807/35/1/015008
openalex publication_date 2013/11/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/06/11
We address the problem of constructing a network of unit resistors such that it enables the retrieval of an arbitrary value of equivalent resistance. In particular, we employ the notion of continued fractions to construct a ladder network by which we can easily obtain any fractional value resistance. In addition, since any irrational number is associated with an infinite continued fraction, we discuss the convergence of the equivalent resistance of an infinite resistive ladder and various aspects concerning the approximations of arbitrary numbers attained by adding additional resistors successively to the network. The presented methods can be easily implemented in an educational laboratory and offer an interesting addition to the topic of Ohm?s law.