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Many multimeters have the ability to measure capacitance along with the ability to measure AC voltage, DC voltage, current, resistance ... The only equations I am aware of that determine capacitance at least for parallel plate capacitors are:

\begin{equation} C=\frac{Q}{V} \;\; \& \;\; C=\frac{\epsilon A}{d} \end{equation}

The only method I can think of is that the meter somehow measures the charge in the plate and then subsequently measures the potential difference. If anyone knows of a more detailed explanation I would be happy to hear it.

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  • $\begingroup$ You are basically right. The meter feeds a known current into the capacitor for a known length of time (i.e.it puts a known amount of charge into the cap) and then measures the voltage across the plates. In practice, it charges and discharges the capacitor repeatedly, rather than just making a single measurement. There are other methods, but if you haven't studied AC circuits yet an explanation of how they work would be too long for an answer here. $\endgroup$ – alephzero Nov 9 '18 at 14:24
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The trick is to watch the current over time as electrons are fed from the meter into the capacitor.

Basically you feed in a DC signal at a selected voltage and watch the current as it charges. After infinity time, the capacitor will stop accepting new electrons, but approaches that asymptotically. So by examining the shape of the curve, even briefly, you can characterize the ultimate capacity.

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