How is capacitor size related with frequency

A capacitor operating frequency range depends on frequency right?
but how?

lets say i have self made parallel plate capacitor,
which is round, with diameter 2.5cm, which yields an area of 4.9087x10-4 m2
the distance between plates are adjustable between 0.1mm to 1cm.

what is the good operating frequency for this setup?

It depends on your wiring. Remember the wiring will have inductance, so at some frequency this forms a resonant circuit with your capacitor. To get decent accuracy, you need to measure well below the resonant frequency.

I'll leave you to do the math. I don't remember the rules of thumb for nH per inch of straight wire or inductance for a given loop area etc.

Actually, it's probably easier to skip the math and do this by trial and error: Take a capacitance measurement at one frequency and another measurement at double the frequency. The answers should be similar. If they're wildly different, you're too close to the resonant frequency.

Depending on what equipment you have, it may be easy to find the resonant frequency e.g. by doing a sweep of impedance vs frequency.

In any case, it would be a good idea to minimize inductance - keep wires short and avoid loops.

when i do a sweep of impedance vs frequency, the resonant frequency is the part where the impedance is the lowest right?
so the capacitor can function well as long as less than the resonant frequency? correct?

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when i do a sweep of impedance vs frequency, the resonant frequency is the part where the impedance is the lowest right?
so the capacitor can function well as long as less than the resonant frequency? correct?

Yes.

Yes, but the test frequency should be much lower than the resonance frequency. e.g. If test frequency = 0.1 * resonant frequency, then error is only about 1%.

Hi Godfreyl, is there any reference that support the above statement?

Per the discussion above, I am wondering is there a easy software tool that can do such kind of simulation efficiently?

I was thinking that what you are actually measuring is the capacitor in series with some unwanted inductance. At resonance, the impedances of the capacitor and inductance are equal but opposite, so they cancel.

At one tenth of the resonant frequency, the impedance of the capacitor will be ten times higher than at resonance, while the impedance of the inductance will be ten times lower.

Thus, at that frequency, the impedance of the inductance will be 100 times smaller than that of the capacitor, and will cause an error in the measurement of about 1%.

Spreadsheets can be useful to help with the arithmetic, especially if you want to make graphs e.g. of impedance vs frequency. Most office software e.g. Microsoft Office or Open Office.org (which is free) can do complex arithmetic too, which is really useful for this sort of thing.

You might also like to try some circuit simulation software. I use SIMetrix SIMPLIS, which is free, easy to learn, and works well.