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Need to derive unknown Capacitance for Cap Meter

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jonnybgood

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Hi,
Attached are the formulas which describe the operation of an Capacitance meter. They can be found here: **broken link removed**

There are three formulas based on the resonant frequency of a parallel LC circuit. I tried very hard to derive them to get the equation written at the end but it was useless. Although I managed to get an equation involving only Cu, Ccal and F's ... when I tried to match by inserting simple values I did not have success.

I am sure of the last formula because I tested it with strange values (C=5, Ccal=3, L=7 and Cu=9) and I got the correct Cu value.

Can anyone give me some hints how to get there? thanks- Formulas.png
 
Last edited:

Ratch said:
jonnybgood,

Look at the attached file.

Ratch

View attachment 72866
Click to expand...

Hi Ratch,

thanks a lot for your patience. I used some 5 A3 sheets and couldn't get there. I suspect it is a very special case of 'simultaneous equations' which I never met at school. This type look like it has only one method in order to get a good and simplified result. I was trying to solve it by first substituting (1) in (2) for C and then (1) in (2) for L -- get those two equations for L and C in terms of Ccal, Cu and F's .. and substitute these in (3) but it was in vain unfortunately. I am sure there weren't any mistakes. thanks again.

jonny
 

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