In order to compare the resistance of various pencils, the nature of this resistance, ohmic or otherwise, was first tested by graphing the voltage over current (Refer to Figure 5). The R2 values of the trend lines, which were close to 1, confirm that the pencils’ resistance is linear. As the graphs are linear, they can be said to be ohmic resistors. It was also noted that the trends became less accurate, indicated by lowered R2 values, as the resistance declined. This is because as the voltages and currents recorded became smaller, the uncertainty involved in the experiment became more influential, resulting in less accurate trends.
Figure 5: Ohmic resistance of pencils
The equations for the linear trend lines were ascertained, with the gradient denoting the resistance of the pencil. These trend lines were plotted with a set intercept at the origin given that theoretically when there is no current, there cannot be voltage. As all pencils were ohmic resistors, it was then possible to analyse the influence of carbon percentage by plotting this against the gradient resistances (Refer to Table 2 and Figure 6).
Table 2: Resistance compared to carbon concentration
| Physics (2007): Sample assessment instrument and student response - Extended experimental investigation: Electrical
conductivity of graphite Sample student assessment and responses
systematic analysis of primary data to identify relationships between patterns
discriminating selection, use and presentation of scientific data and ideas to make meaning accessible to intended audiences through innovative use of graphs
Figure 6: Effect of carbon concentration on resistance
The relationship between the resistance and carbon proportion was expected to be a decreasing function, as carbon is a more effective conductor than clay, given the assumption that clay acts as an insulator. Thus an increase in carbon would lead to a decrease in resistance. Given this relationship, it would be expected that as the concentration of carbon approached zero, the resistance would approach infinity. Similarly, it was expected that as the percentage of carbon increased, the resistance would approach zero, levelling out at the resistance of pure graphite. Thus, it was expected that the model would most closely model an inverse function,