My smart thermostat shut itself down reportedly (as it ran some time on internal chargeable battery and I browsed through the settings) because the C terminal stopped receiving 24V power supply. That terminal is wired from the C terminal in the control panel of the AC, which also has R, Y, G etc. I used a multimeter to test the AC side terminal by putting one probe on it and the other one on the grounding terminal inside the unit and it measured 0V. When I did the same thing with the R terminal, it measured 24V, which is what it should be.
In order to restore power supply to the thermostat, I tried to hardwire the C terminal in the AC to the R terminal but that burned the internal fuse that the R was connected to, which makes me think that a short occurred, which means the C terminal was actually energized. Another thing I found weird is that the C terminal is supplied by a wire that runs through the blower motor. Why would they wire it like that?
How can I test whether the C wire issue is on the source (AC) or in the thermostat itself. I am not sure where to put the other probe when testing the C wire on the thermostat, like I did on the grounding nut on the AC side.