Electricity - again

Erik Olson wrote:
> From: David Webb <dwebb at ti_com>
> I may be wrong about this but I was under the impression that the reason low
> volgates are used for heating cables is that wires tend to waste more
> electricity to heat a wattage W when voltage V is lower than at the same
> wattage W when another voltage V1 is higher.

I don't really understand what the above e-mail was trying to say,
(been racking my brain for a bit trying to decipher it). 

Watts is watts.  Power, heat, same stuff.  Where in many circuits, you
have some concept of efficiency (which is how much of the electrical
energy is converted into heat instead of light, sound, whatever),
heaters are guaranteed to be 100% INefficient.  They convert all the
electricity into heat!   <<<

Perhaps what David is thinking of is the case of power transmission
lines, where a required amount of electrical power is transmitted more
efficiently at high voltage than at low voltage.  (I just looked up an
example in my freshman Physics book; a sure sign that this thread has
gotten out of hand).

I think the reason that lower voltage is more attractive for undergravel
heating cables is that it allows for more reasonable cable dimensions to
be used.  To generate 100W of power, cables subjected to 120 volts
require a resistance 25 times greater than cables subjected to 24
volts.  When we are talking about using continous cable to develop the
resistance (like in UG heating cables), the cables have to be pretty
thin or really long to get enough resistance.  The upshot is that
reasonable size wire and shorter lengths can be used at 24V DC than at
110V AC.  

I can think of two reasons why a 50m run of 40 ga heating cable is
undesirable.  This energy has to be transmitted to the water column
before it can melt a hole in the bottom of the aquarium.  The increased
surface area of the wires will help in this.  Second, and perhaps more
importantly, a potential ground looks better if the resistance through
the potential short (one's body) is smaller relative to the circuit. 
This is more likely with 144ohms of resistance in the cables than with
5.8 ohms of resistance.

All this is moot if the cables are properly constructed.  The safest
course, however, is certainly to use a $6 GFCI outlet with an aquarium. 
Their whole raison d'etre is to snuff out potential shorts of the type
being discussed here.