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Often the outer barrel (C) is used for ground (-), with A being the positive (+) contact, but check your setup with a voltmeter, they are often used either way. I've blown up two answering machines by not checking polarities first and just plugging in an AC adaptor that had the correct rating. I think A-B just acts a single-pole N.C. switch, for use as a simple presence detector (whether the adaptor is plugged in or not). - CAL
The polarity is dependent upon the output of the power supply and the connection of the jack into the existing circuit. Power supplies are available with either polarity, as well as with a "universal" design wherein the polarity is set by the relative position of the cord end plug with respect to the cord.
As to the question regarding points A and B in the diagram... this jack is a switching type of jack wherein the battery current is supplied to the load via the closed contacts at A&B when no plug is in the jack. Inserting a plug into the jack opens the switch at A&B, while passing current to the load through the contact that is riding against the plug outer surface.