Capacitors Marked in CMs

[Nick]

Thanks for the pics and post, that's a new one on me, just goes to show how these things evolve over the years, did you ever sought out the 4*Pi bit?

Yes!. The "cm" measurement is indeed "centimetres"! In the Gaussian system of measurement (which is also metric like the SI system), everything was related to the "CGS" system - centimetre/gram/seconds... The CGS system was supplanted by the MKS (metre/kilogram/second) system which in turn was replaced by what we use now, the SI system (which has the same base units as the MKS system).

The definition of 1cm of capacitance is the capacitance between a metal sphere 1cm in diameter and infinity in a vacuum, not, as previously speculated, the capacitance of two 1cm squared plates 1cm apart in a vacuum...

You might think that as as 4 pi appears in both the surface area of a sphere (4*pi*r*r) and the volume (4/2 * pi * r*r*r) that it really is Pi that is important.

But it isn't.

CGS units and SI units have a form of equivalence. In the case of capacitance, the equivalence is

1 F = 1e-9 * c * c "cm"s, where "c" is the speed of light in centimetres per second, which is approximately 3.1e10 cm/sec (its in centimetres as the base unit for distance in the CGS system, the "C", is 1 centimetre). Look up CGS in Wikipedia and elsewhere for a derivation of this equivalence from first principles...

So, 1pF, or 1e-12Farads, is equivalent to 1e-12 * 1e-9 * 3.1e10 * 3.1e10 = 0.96 cm and 1 cm = 1.042pF

There you have it - it seems that the "4pi" was a red herring, or as the French would say, "c'est pour brouiller les pistes".

EDIT: Note that "equivalence" as used here is not the same as "equality", i.e. you cannot mix and match CGS & SI "equivalences" as their dimensions do not match. i.e., an expression has to be all SI or all CGS, not a mix, so you can't drop in the expression for a capacitance in cm into an SI equation - you must convert the CGS unit to its SI equivalent and use that. Odd, but that's the way it seems to be.

HTH