Actually the flap motors are somewhat notorious (in earlier models) for continuing to hum away and either burn out, or give you 40 degrees when you least expect it!!! Some have no cutout at all, so you can leave it whirring away, so if you are the instructor, it is an excuse to nudge the student about situational awareness.......
Also a reason why lowering (electrically powered) wing flaps in a turn can be dangerous, but then I assume everyone already knows why?
If your a/c has pop type c/b's look at the amp rating for each circuit - that should give you a clue as to what draws more juice! The really old fuses from really old cessnas might not give you as much info about its' electrical system.
Oh, and the POH/operators/information manual might also reveal the electrical system in detail........and you might be surprised what draws a lot and what doesn't (or not of course).
Hope you win the bet?