Although it varies some from person to person, the 60-Hz current through
the chest that will lead to fibrillation is about 16 mA. Incidentally,
60-Hz is about the worst we could have picked in this regard.
So the question is: if your chest is submerged in the tub, and the
heater or hair dryer falls in, are you likely to get 16 mA or more
through the chest region.
If your house is up to code, and the product is designed correctly, you
won't, because GFCIs (ground-fault-circuit-interrupters) are required in
the bathroom. These typically trip out with less than 2 mA and
certainly trip out with 5-mA imbalance. The problem is that the fault
would be current from the "hot" wire going into ground rather than
neutral. To the extent you are part of the path from hot to neutral,
that won't trip the GFCI. To the extent you are part of the path from
hot to ground (other than neutral) then the GFCI can protect you.
So the question remains, how much current would go from hot to neutral
through the water, and if you are part of this path, how much goes
through you.
Unfortunately many heaters and hair driers have two-wire cords. If they
included a three wire cord to the actual device, with an exposed ground
inside the device, then when the device fell into the water and the
current began going not only from hot to neutral but also hot to ground,
the GFCI would trip if this internal hot to ground conducted more than 2
or 3 mA. Therefore, you _will_ be protected by a GFCI if the device
falling into the bathtub has three wires, one of which is grounded
independent of neutral. You might not be protected with a GFCI if the
device is two-wire, and your plumbing is plastic, and therefore no
ground fault is created when the device falls into the water.
Michael D. Edmiston, Ph.D.
Professor of Chemistry and Physics
Bluffton University
Bluffton, OH 45817
(419)-358-3270
edmiston@bluffton.edu