Capacitors Marked in CMs

[Radio Fixer]

First time I have seen this and it didnt register with me but did to a friend who has had the old radio hobby for about 7 decades

Its on the French Integra and I had sent him some chassis pics. Here are a coupla capacitor pics:

   
   

My friend even found a text book (Morecroft “Princuples of Radio
Communication”. ) and said "I think you will find a CM = capacitance of two 1 sq.centimetre plates one CM apart."

The book says to convert to pF divide by 0.9 (or roughly add on 10%).

Gary

[Nick]

Just thinking out loud here - my numbers may well be rubbish...

...My friend even found a text book (Morecroft “Princuples of Radio
Communication”. ) and said "I think you will find a CM = capacitance of two 1 sq.centimetre plates one CM apart."

The book says to convert to pF divide by 0.9 (or roughly add on 10%).

Two 1cm2 plates 1cm apart in air (or vacuum) is computed as K * ε0 * A / D where:

• A is the surface area of the plates in sq metres
  
• D is the distance the plates are apart in metres
  
• ε0 is the permittivity of free space, a constant = 8.854e-12 Farads/metre
  
• K is the dielectric constant (aka static relative permittivity, εr) of the insulator, 1 for a vacuum and very nearly that for air.
  

Plugging in the numbers for 2 x 1cm2 plates 1 cm apart in air, gives 8.85e-14 F, i.e. approx 0.09pF...

EDIT: Just found the following: http://www.radiomuseum.org/forum/old_cap...kings.html

cm was used until the 40ies of the last century: 1cm = 0.0885pF*4π ≈ 1.1pF

So, yes, it is indeed a pair 1cm2 plates 1cm apart, but why the "4π"? Four pi? I'm always for pie, especially tarte normande...

Thanks Heavens for SI units - at least they are consistent and make sense...

[Radio Fixer]

I'm always up for pie too Nick: my wife makes fantastic Bakewell Tart, not good for the waistline though

Thanks for the calc ... it lines up with an approximate formula in Moorcroft: C = KA / 4 * pie * d

where K is dielectic constant, A = area of ONE side of ONE plate in square centimetres, d = separation of plates in centimetres

Comes to 0.08

But why * 4 * pie to get to pF?

cheers Gary

[pwdrive]

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?

Lawrence.

[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

[pwdrive]

Ta.

Lawrence.

[Radio Fixer]

Um! thanks Nick ... I will have to give that some thought . Long time ago all those Units stuff

Gary

[pwdrive]

From the Radio & Television Engineers Reference Book, it's that 4*Pi again...

Lawrence.

[Nick]

From the Radio & Television Engineers Reference Book, it's that 4*Pi again...

Confusing, isn't it! I believe this comes from a subtlety in the way the above text is presented.

The confusion arises because there are at least 4 different variants of CGS units, normalised in different ways. I believe that the book is using CGS-Gaussian units - the 4pi bit comes from Maxwell's equations and the definition used for a unit of charge in the Gaussian CGS system which has a factor of 4pi in it - the Coulomb Constant (in SI), Kc, is 1 / (4 x pi x Eo), which when factored out is 10e-11 x c^2

So both methods are correct (for CGS-Gaussian at least) ! In my calculations I used 3.1e10 cm-2 as the speed of light and took the dielectric constant of air to be 1 (its a tiny bit more) which is why the results are a tiny bit different.

Unit systems are horrid - the CGS system was a nightmare - at least SI makes sense.

My head now hurts and I need coffee...

[pwdrive]

So the upshot is that a Pf is Pf and CM is times a multiplier to get a Pf.

Lawrence.