No, I have tried to connect ground and tip of one probe, on one channel, without Math
That's the only way it will work, unless you buy a special isolated probe or an isolated current probe.
ALL oscilloscopes have that issue - ie You HAVE to connect the GND wire of the probe, which then puts
the WHOLE oscilloscope at that potential. As I said, I OFTEN measure mains, Live side, BUT you need to
take precautions !!!! We use an ISOLATION transformer on the DEVICE under test. That gives us a
LOT of safety, as long as you only touch ONE connection at a time.
My scope works on battery, so it does not need mains to work.
Doesn't matter. The Probe GND is still Referenced (connected) to the oscilloscope GND / Frame etc
When I have tried to connect it without groundinghs, I got strange signal.
YES. The signal HAS to be across the probe tip and GND wire (which should be as short as possible).
When I tried to connect rear ground connector to ground via resistor (for safety at start),
power source was immediately turned off (protection).
Now you're experimenting in dangerous territory !! Don't do that.
So, for now I have no way to measure current (and get right results
) in circuits, connected to mains supply?
This is sad.
See above. All in the same boat, all have the same options