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Feb 16, 2011 at 13:10 comment added Bossavit It's not "a certain amount of current" but an uncertain one. How much current flows in the situation you describe depends on unspecified parameters, mainly, the contact resistance, and/or the area of effective contact between the wire and the object.
Feb 15, 2011 at 16:29 comment added Ted Bunn Maybe I'm just being stupid here. If you connect a thin wire to point A and another at point B, and apply a potential difference between the two, a certain amount of current will flow (spread out through the entire object). The ratio is the resistance.
Feb 15, 2011 at 16:02 history answered Bossavit CC BY-SA 2.5