Given an "infinite" 2D square grid of resistors with resistance R, the equivalent resistance across the diagonal of one square is 2R/pi [1,2]. Working out this solution theoretically has sniped many a nerd. Furthermore, it is prohibitively laborious for an amateur to attempt to verify this experimentally -- until now. Using Bare Paint, I drew a square grid of resistors on a page of normal copy paper, and measured resistances with a multimeter. My wishful thinking was that, with a large enough array of resistors (14 x 14), I could approximate "infinity" sufficiently from the perspective of squares in the middle of the page. Drawing the resistors with the Bare Paint seemed easier than gathering and connecting 196 resistors. While one set of measurements yielded a value of pi as impressive (to me) as 3.38, overall I observed poor consistency of measurements among adjacent squares near the center of the page, and poor repeatability of measurements for the squares tested. Nevertheless, I hope that you, dear reader, will consider trying this experiment for yourself. I will tell you how I did it, and perhaps you will take more care than I to apply the paint accurately and precisely; otherwise, you will too observe a high variance of resistance among your resistors. Note also that the resistance of the Bare Paint decreases as it dries, so be sure to allow ample time for drying (tens of minutes) before measurements.
I used one tube of Bare Paint, a multimeter with leads (pictured in the intro section), and an 8 1/2" x 11" sheet of paper.
No comments:
Post a Comment