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

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.