Excerpted from:
http://www.inspect-ny.com/aircond/aircond15g.htm
When testing a compressor, one must discharge the capacitor first! It'll otherwise have enough power stored on it to be at least very painful. (Author and others have been zapped!) Some systems will automatically discharge the capacitor, but shorting its leads with a screwdriver (after verifying that the power's off) is a safe way to ensure that you won't get shocked. Motor starting capacitors can hold a charge for days!
If oil has leaked out of a capacitor: Don't touch any oil that leaked out: old capacitors may contain PCB oils, an extremely carcinogenic (cancer causing) material which require special disposal.
Once the capacitor has been discharged (as described just above), then it can be tested with a multi meter. Either use the meter's built in capacitor test function, or use this trick: Charge the capacitor by using the sense current the meter puts out when set to ohms. You should observe a rapidly rising resistance before the meter indicates over range/infinity. Disconnect the test leads, and switch over to volts. Then, reconnect the test leads. A voltage reading should be observed, approaching zero.
If the capacitor doesn't hold a charge, or the resistance reading never approaches infinity, it probably needs replacement.
Also, the capacitor may be defective if the compressor hums but does not start. Visual inspection may reveal it to be bulged, or have a blown out safety plug.
References and More Reading:
"Troubleshooting Compressor Problems," Henry Puzio, Fuel Oil & Oil Heat with Air Conditioning Magazine, June 1993, p. 39
Tom Morris, Engineer, capacitor discussion and correction to the original data. Email to D Friedman 5/29/2006 - Thanks Tom for critical editing. The text above explaining about capacitors was suggested by Mr. Morris. The original text of the 1993 compressor diagnosis article had the resistance explanation backwards.
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