Farad

Physics books (e.g. my very favourite Serway) start with explaining the S.I. units and the orders of magnitude. Most students skip this part, finding it boring. Do we really need to define that length is measured in meters and that 0,001 of a meter is 1mm? Well yes, of course we do. And I'm not going to start analysing the History of Metrology nor the meaning of standardization in measurement to convience you.

Last year, I came across an interesting lab report on the Series LCR Circuit from 2nd Year Labs. Part of the experiment is to evaluate the total capacitance of the circuit. As seen below, the student after doing a linear regression to their data, finds that the total capacitance of their circuit was 59±7 F. Interesting indeed...

Wikipedia is not considered as a scientifically reliable source, nontheless by doing a simple first research, one finds that: "For most applications, the farad is an impractically large unit of capacitance. [...] The capacitance of the Earth's ionosphere with respect to the ground is calculated to be about 1 F."

courtesy of King's College London (2017)

Assuming that we don't expect an undergrad student to have memorised the definition of a farad or furthemore the Earth's capacitance. What we do expect is the student to realize that their reported result is not only invalid but actually is impossible. We do see noted that the value for C is quite wrong (define wrong - that's another topic) as the capacitors used in the lab were in the scale of nF. Nano Farads. 10^-9 Farads. That is 9 orders of magnitude off, in other words 1 billion times larger than what they should expect!

And here comes the worrying part. The student, instead of double checking their calculations and do a dimensional analysis on their equations, they are confident that such a huge difference can be caused by laboratory systematic errors. Has the student depreciated experimental work in such a degree? Have they failed to realize the metric prefixes? Or have they missed that in Physics what matters is not only the numerical calculations but the logical defence of a result?