Heating Cable voltage: Physics Lesson :)

Len Trigg writes (regarding heating cable voltages):

> Well, I did think about this before I bought them, but I figured these
> cables would be no more dangerous than a standard aquarium heater which
> also uses mains voltage.  As long as I take appropriate precautions
> (GFI, fuses, turning the appliances off before putting arms and legs in,
> keeping oscars and other chew-happy fish out of the tank), I'm willing to
> take the risk.  But I'm also interested in hearing some more detailed 
> explanations on exactly how much more dangerous the 240V,0.3A option
> is over the 12V,6.25A option.

Sure thing.  Let us say that the water in your tank has a finite 
resistance R.  Then if there is a break in your heating cable, it will 
allow voltage V to flow directly through the water.  Ohm's law tells us:

  V = I * R

Since the water has a constant resistance, the current through the water 
will be proportional to the voltage V.  The key here is not the current 
rating of the CABLES, but rather how much current you can have if the 
mains voltage will become exposed.  The 240 volt system allows TEN TIMES 
as much current to run through the tank as a 24 volt system.

But that's not the end of it!  There's also the issue of what happens when
you merely expose the mains leads to the water (a more likely scenario). 
Let's look at the resistance of the heating element itself.  Let us consider
comparable 24 volt and 240 volt heating elements that must provide similar
power P (wattage).  Again, electronics tells us: 

      P = I * V = V * V / R         or   R = V * V / P

The resistance of a wire providing the same wattage goes as the intended 
voltage squared.  The point of this is that the 240 volt wire is 100 
times more resistive than the 24 volt one.  

Now what happens if, say, the insulation doesn't completely work between
your power cord and the heating cable.  The mains voltage is now 
exposed directly to the water.  The current now has a choice...
continue to go through the cable, or through the water.  With the 24 volt
cable, most of the current will continue to pass through the cable, because
of its low resistance.  With a 240 volt cable, most of the current will pass
through the WATER! 

Some other thoughts:  Yes, you sort of run the same risk with your normal 
tube heater.  However, the tube heater is easier to detect some failures
(ie, broken glass, a half-filled tube, etc) and certainly easier to 
replace.  Heating cables are inherently more delicate.  GFCs and breakers 
will help reduce the shock risk in either situation.

Dr. Erik D. Olson			licensed and bonded to teach High School
olson at phys_washington.edu 		Physics over e-mail. :)