How do you know which cable is positive and which is negative in a charger adaptor?

The best way is doing a continuity test with a multi-meter. On most meters the sign

is the Greek letter omega,,, set meter to continuity and touch both probes together,

set meter so you get a sound when they are touched together. Now place one probe

on the plug end and one on the service end, this will tell you which hole,, or inner or

outer sleeve is neg. On the outlet plug end 120v the larger of the two is neg.