Ground Fault Protection
Safety codes often require "ground fault circuit interrupter" inclusion for electrical power outlets. The operation of such a device depends on making a comparison of the current levels in two wires, one wire for the "hot" side of the power line and the other wire for the "neutral" side.
Assuming some kind of load, perhaps a hair dryer or perhaps an electric razor, normal operation would be as shown in the following simplified sketch.
However much current the load draws from the power line, two identical sensing coils wrapped on a transformer core carry that same current and impose flux in opposite directions in that core. Thus, a third winding also wrapped on that core, a sense winding, receives no net excitation and therefore delivers no output signal.
If a ground fault were to happen on the hot side of the power line, there would of course be all kinds of spectacular spitzensparken, fussinmussin and smokineven going on. There'd certainly be no question about detecting that.
However, if a ground fault should happen to occur on the neutral side, there wouldnt be any pyrotechnics, but the current's balancing act would get disrupted as seen in this second sketch.
The ground fault shunts part of the lower coil's current away from that coil. In consequence of that, the flux produced by the two identical coils is no longer canceled to zero. There is a net flux imposed on the core to which the sense coil responds with a signal. Mere milliamps of current unbalance can be sensed this way, even if the load current is many amperes large.
The sense signal can then be used to trigger a responsive circuit to switch off of the load's power.