Determine capacitance by measuring the charging time
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There are many ways to determine the capacitance of a capacitor. You can use an oscillating circuit where the capacitor is a part of it and measure the frequency of oscillation to find the capacitance. Or, you can also use a resistor-capacitor network and measure the rate of voltage rise across the capacitor to determine the capacitance, if the value of the resistor is known.
Here’s a similar project where a PIC16F88 microcontroller measures the time required by a capacitor to charge through a known resistor from 0 to half of the reference voltage provided, and the capacitance is determined based on that information.