I think it’s understood that if someone is taking a bath, and a running hair dryer falls in, they will be electrocuted. What I don’t understand is why? I understand that the human body is a better conductor then tap water, but why would the current travel through the human? Assuming that the drain is the only ground, and the person isn’t touching anything, wouldn’t the current travel directly from the hair dryer to the drain? What if the person is sitting at one end of the tub, and the hair dryer falls in directly over the drain? Would they still be shocked?

Current doesn't only takes the shortest path 'cos if the shortest path is full of electrons moving about, it is easier for some of them to go a longer way without bumping into each other than to get in line with the others. Compare to traffic in a busy city. Electrons don't bother about signs...

If I sit on the shore of Lake Michigan and a hair drier is dropped into the lake far away, do I get shocked?

Distance helps. Distance may solve the problem for you, but it is a losing proposition.

Electricity takes every path available to it. Use Ohms law to determine the current flow through each parallel path. Distance is a factor in the resistance put up by the water, which is why the fellow 500 yards from the hair dryer dropped in the lake doesn't feel a thing.

Funny this question should come up now...

"Mythbusters" just tested this out- and they had no trouble 'electrocuting' their dummy with a variety of appliances. Those with GFI or imersion protective devices were, in fact, effectively protected.

Also, out here Fish & Game uses electricity to stun fish for census purposes; it's amazing how large an area a little jolt will stun.

John, I heard that this will not work on fish with scales. The only fish to be effected are fish with skins such as (catfish, etc.) But I personally don't know this to be fact.

We have a site where we divert trout from swimming upstream into a controlled side channel to collect eggs etc. using an electric field which temporarily paralizes the fish. So growing scales won't protect you.

Shane

Scales won't protect you? Inspector, beware! :-)

When I was in the Army we used percussion to stun the fish. That's a fancy name for a grenade. Worked real well and we could take it on the boat (until we got caught).

Good ole dynamite fishing... illegal in most areas. Common joke here is the "dynamite fishing in the aquarium" using firecrackers. Nobody ever did it as far as I know, but everybody gets a laugh of the idea... will effectively shatter the aquarium.

Back to the topic though.
Between the water of where the hair-dryer was dropped in and the waste there would be a Voltage Gradient.
Regardless of the fact that there is no water flow down the waste, there is still a low impedance path to Earth.
There was a time here in New Zealand, under the 1976 Electrical Regulations, where a steel based emulsion-coated bath was required to be directly bonded to the main Earth Busbar in the Switch-board.
But, kick me if I'm wrong, I've never seen a bonded bath in the whole time that I've been an Electrician.
Hmm, must have been them trendy Aucklanders!.