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A bad cap usually shorts or leaks internally. With a larger cap (like a microfarad or greater) you could charge the suspect cap to a certain voltage and compare the time it takes to bleed off a charge against a known good cap. Use a voltmeter with a high input resistance.
Aside from the quick meter checks for shorted and leaky capacitors, a fairly easy way to check for more subtle problems is to connect a judicously chosen resistor value in series with the capacitor and drive the series combination with a sinusoidal signal generator operated at the frequency of interest. Use a two channel (or XY) scope to measure the phase difference between the voltage developed across the resistor and the voltage across the capacitor. Ideally the phase difference should be 90 degrees, but it should be close to 90 in any case. Deviation from 90 is a measure of how lossy the capacitor is. A higher ESR will give greater deviation from 90. You can calculate the capacitor value from the voltage developed across the resistor, and the frequency and voltage the signal generator is set to by solving the following equation for C:
f=sig gen frequency in Hz
R=resistor in ohms
C=capacitance in farads
Eg=sig gen voltage (rms)
Er=resistor voltage (rms)
The equation assumes 90 degrees phase difference. Electrolytics require a DC bias for the test.
To check for breakdown under voltage (sometimes capacitors check fine at lower voltage), connect a DC power supply at the max rated voltage. The current should be next to zero for an electrolytic and immeasurable for most other types.