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One important thing to note is that a capacitor can retain its capacitance intact but buid up a resistance 100 times its original design and lead to different failures (circuit stops working, capacitor explodes, capacitor shorts, ...).
Conclusion: measuring capacitance is not the key to measure a failed capacitor (and anyway you can't do it with the resistor in place in the circuit).
ESR (Equivalent Serie Resistance) is the measure of the resistance of that component. As per the litterature on the net it is typically :
According litterature, facing an AC at high frequency (>= 50kHz) a capacitor will basically behave like a resistor only (other coponents become neglectable).
Build a circuit with the capacitor C and a 10 ohm resistor R in serie. Feed the circuit with a square wave signal with f >= 50 kHz and amplitude = 200mV and measure the voltage difference around the resistor R.
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