Instead of using a resistor I could simply turn down the supply voltage to 1V leaving me with 1A still passing through the coil,, or,,
I could use a second source connected in parallel with the first source that is at 9V instead of 10V leaving me with a 1V drop and 1A of current still passing through the coil.
If that second source was at 10V then there would be no voltage difference across the coil and no current would flow.
If I had a group of coils all connected in series and closed upon themselves, so say 36 coils in a circle all connected in series with the first coil and the last coil also connected.
My first source is connected one side to a coil to coil connection point, then 18 connections later the other side of my source.
I now have 18 coils seeing the current flow relative to the coil winding direction CW and I have 18 coils seeing it flow CCW, my first source would energize all 36 coils.
My second source then advances one connection set with the same polarity, this stops current flow through 2 of the coils and leaves the other 34 still seeing basically no change.
Disconnect the first source advance one connection set past the second source and connect,, rinse and repeat.
This ends up having basically 17 coils with a N electromagnetic pole emanating and 17 coils with a S electromagnetic pole emanating, these "polarities" are then rotating around the ring of coils as the connections are moving around the ring of connections.
The partial simple test-beds I have tested this with work but I do not know if it is of any use since I have not built one with all the connections and stuff to just spin the contactor and see what happens.