when using an oscilloscope to make measurments across components to a mains connected device, is it better to put the isolation transformer on the scope or the device being tested?
If you isolate the scope (by breaking its ground prong connection), and then connect the scope probe ground clip to the "hot" side of the line, you have created a death trap. Touching the scope cabinet with one hand, while also touching something that is grounded with the other hand may kill you...
Putting a 1:1 Isolation Transformer between the Line and the Device under test allows you leave the scope cabinet grounded.