The grounding varies by equipment. Things to remember are: > Some (mostly high-end consumer and pro equipment) pieces are chassis grounded to earth ground, some of these have a ground-lift switch and some not. If the equipment is powered from a two-prong cord, there should be no connection between either the ground, hot, or neutral and the equipment's chassis. The power should go to the transformer where it is isolated even if one of the transformer outs is grounded. > Even if you have isolated your ground either via the normal non-grounded equipment or an isolation transformer, there are still voltages in your equipment that can harm or kill you. This is more in tube gear (600v or so) and in higher-power SS gear (80vdc-up) so IMO this sketch above is nothing more than false security that can lead to carelessness and a shock. You need to take the same precautions in servicing powered gear whether it's on an isolation transformer or not, good safety practice is required either way. As far as protection for the equipment, if you plug your scope and the equipment being tested into the same isolation transformer it seems that you haven't prevented the potential for damage from accidental grounding of the scope to the wrong part of your equipment. I have an isolation transformer, but it's too large and noisy to be convenient so I do not use it, never really saw a need, just remain careful.