Hello.

For typical battery (nothing but capacitor), current direction is clear as electrons can't not flow across the two plates in battery so they can only choose wire as a path from cathode to anode.
But in secondary side in transformer, basically electron also can go through the "connected" coil so I guess electron can choose this path. Maybe it is more favorable as it is short path from cathode to anode.
The Ohm's law on resistor forces me to think that current path should be the same to case of the battery but It doesn't physically convince me.
How we can determine current direction and why?

For typical battery (nothing but capacitor), current direction is clear as electrons can't not flow across the two plates in battery so they can only choose wire as a path from cathode to anode.
But in secondary side in transformer, basically electron also can go through the "connected" coil so I guess electron can choose this path. Maybe it is more favorable as it is short path from cathode to anode.
The Ohm's law on resistor forces me to think that current path should be the same to case of the battery but It doesn't physically convince me.
How we can determine current direction and why?
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