A mathematical model and microcontroller-based method for measuring dielectric permittivity and discharge characteristics with Arduino ATmega 328: a case study in a physics laboratory

Abstract

A microcontroller-based measuring instrument and a new mathematical model are used to investigate capacitor permittivity and dielectric materials' charge-discharge characteristics. In this study, a prototype capacitive permittivity measurement apparatus for dielectric materials was carefully developed using an Arduino microcontroller, a resistor, and a capacitor. The experimental setup comprises a capacitor-resistor circuit, wherein a 5-volt power supply sourced from the microcontroller interfaces with a computer. During the charging process, a comprehensive evaluation of model-data alignment was performed, yielding values of 0.54252156, 0.9951, and 111.2508701 for the sum of squares error (SSE), the coefficient of determination (R-squared), and the sum of squares total (SST), respectively. Similarly, the analysis extended to the discharging process, unveiling values of 5.10174756, 0.962805684, and 137.1647082 for SSE, R-squared, and SST, respectively. These findings confirm the accuracy of the microcontroller that was programmed by incorporating a model in precisely measuring the relative permittivity of dielectric materials and capacitance values, with an R-squared value above 0.95 following capacitor literature benchmarks. The novelty of this study is that this configuration enabled the precise assessment of both permittivity and the charge-discharge characteristics of the dielectric materials within the capacitor. This methodology made it possible to accurately measure the permittivity and charge-discharge characteristics of dielectric materials within a capacitor. The scientific significance of this research lies in its ability to provide a carefully developed instrument capable of investigating the permittivity of dielectric materials and capacitor capacitance measurements. Scholars, international engineering communities, and academics can use this technological breakthrough to advance research into dielectric material properties and capacitor characteristics.