Virgil,
I think you are ohming an inductive load such as a transformer (for a doorbell or battery charger, etc), The reason I suggest an inducitve load is that the ohm reading has little to do with how much current the load will draw. If the load is a small one, you may not be able to measure it with a clamp on. As far as I know, you could even be reading a GFI receptacle.
I believe arc fault devices contain a 30 ma GFI. If there is the slightest neutral to ground connection or pathway downstream, the arc fault breaker will trip.
Take the following ohm measurement- disconnect the neutral of the circuit at the panel & see if you get a reading to ground. You should be reading millions of ohms, a lower reading could be low enough to trip the GFI portion of the breaker.
Dad blast these tornado magnets anyhow.
Tom