{"title":"Demonstration of the propagation of errors using resistors","authors":"K. Gan","doi":"10.1119/5.0145005","DOIUrl":null,"url":null,"abstract":"We present a simple experiment to demonstrate the concept of propagation of errors by measuring resistors on printed circuit boards (PCBs). We devise a method for connecting the resistors on a PCB that allows a relatively quick measurement of 200 resistor pairs to show that the distributions of the measurement of individual resistances, as well as the total resistance, are Gaussian-distributed, as expected from the central limit theorem. The measurement demonstrates how individual uncertainties propagate to the total uncertainty. The experiment is part of a laboratory course on statistics for physics students that emphasizes the application of statistics in data analysis.","PeriodicalId":7589,"journal":{"name":"American Journal of Physics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"American Journal of Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1119/5.0145005","RegionNum":4,"RegionCategory":"教育学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"EDUCATION, SCIENTIFIC DISCIPLINES","Score":null,"Total":0}
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Abstract
We present a simple experiment to demonstrate the concept of propagation of errors by measuring resistors on printed circuit boards (PCBs). We devise a method for connecting the resistors on a PCB that allows a relatively quick measurement of 200 resistor pairs to show that the distributions of the measurement of individual resistances, as well as the total resistance, are Gaussian-distributed, as expected from the central limit theorem. The measurement demonstrates how individual uncertainties propagate to the total uncertainty. The experiment is part of a laboratory course on statistics for physics students that emphasizes the application of statistics in data analysis.
期刊介绍：
The mission of the American Journal of Physics (AJP) is to publish articles on the educational and cultural aspects of physics that are useful, interesting, and accessible to a diverse audience of physics students, educators, and researchers. Our audience generally reads outside their specialties to broaden their understanding of physics and to expand and enhance their pedagogical toolkits at the undergraduate and graduate levels.
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