标题： 纳米厚度6B石墨层的估算：在高等教育中研究欧姆定律的实验活动 显示英文标题

标题： Estimation of nanometer-thickness layer of 6B graphite: an experimental activity to study Ohm's law in higher education

摘要： 欧姆定律对于理解电气电路和导电材料至关重要。 由乔治·西蒙·欧姆在19世纪提出，它描述了欧姆导体中电电压和电流之间的正比关系。 尽管其看似简单，文献指出不同教育水平的学生在理解它时存在困难，特别是由于与电电压、电流和电阻概念相关的抽象性。 为了提供克服这种抽象性和相关学习困难的可能性，本研究提出了一项实验活动，将欧姆定律应用于确定沉积在描图纸上的6B石墨痕迹的纳米尺度厚度。 所采用的方法基于测量诸如电电压、电流和长度等物理量，并对收集的数据进行分析。 通过此方法确定的石墨痕迹的厚度也与使用扫描探针显微镜（SPM）获得的值进行了比较。 根据所提出的方法，痕迹的厚度确定为456.5(34)~nm，而SPM测量得到的平均厚度为440(50)~nm。 因此，结果表明在实验不确定范围内测量结果具有良好的一致性，验证了所建议方法的有效性，并表明该方法是高等教育电力课程的一个可行方案，经过调整后甚至适用于高中。 显示英文摘要

摘要： Ohm's law is crucial for understanding electrical circuits and conductive materials. Formulated by Georg Simon Ohm in the 19th century, it describes the direct proportional relationship between electric voltage and electric current in ohmic conductors. Despite its apparent simplicity, the literature has pointed out that students at different educational levels have difficulty understanding it, especially due to the abstraction associated with the concepts of electric voltage, electric current, and electrical resistance. In order to provide possibilities to overcome this abstraction and the associated learning difficulties, the present work proposes an experimental activity that applies Ohm's law to determine the nanometer-scale thickness of 6B graphite traces deposited on tracing paper. The employed methodology is based on measuring physical quantities such as electric voltage, electric current, and length, and on analyzing the collected data. The thickness of the graphite traces determined by this method was also compared with values obtained using a scanning probe microscope (SPM). Based on the proposed methodology, the thickness of the traces was determined to be 456.5(34)~nm, while SPM measurements yielded an average thickness of 440(50)~nm. Thus, the results show good agreement between the measurements within experimental uncertainties, validating the effectiveness of the suggested methodology and indicating that it is a viable proposal for electricity courses in higher education and, with adaptations, even for high school.