Here’s an example from the Christiano et al. paper that shows that the width of the basic electrical flow oracle could be as large as . The effective resistance of the black edges is , so half the current flows on the top red edge. If we set (which is the max-flow), this means a current of goes on the top edge.
Again, each black gadget has a unit effective resistance, and if you do the calculation, the effective resistance between and tends to the golden ratio. If we set we set (which is almost the max-flow), this means a constant fraction of the current, or about goes on the edge . Once that is deleted, the next red edge carries a lot of current, etc. Until all red edges get deleted.