(ET) Batteries and lighting

[Rhett George <rtg ee duke edu>]

 - Greetings -

The question recently developed about the lifetime of incandescent bulbs
running on voltages other than the rated voltage.  Many moons ago in a 
lecture I learned that bulb life varies approximately according to the 
following formula

(actual life/nominal life) = (nominal voltage/actual voltage)^11

That is, voltage ratio raised to the 11th power.  The lecturer suggested 
that a 230 V bulb rated for a thousand or so hours would last about 3000
years running on 115 V.

If the auto induestry starts producing cars with 42 V systmes (with engine
running) the actual on-board battery voltage, fully charged, will be the
same as many of our tractors, about 39.6 V.  Sounds like a ready supply
of bulbs at a very useful voltage.

Incidentally, since a bulb burns more brightly with increasing voltage,
and since tungsten has a very large coefficient of resistance as a function
of temperature, increasing the voltage on a 12 V headlamp from 8 V to 11 V
to 14 V results in a very small increase in current.  Because of this, I 
find a headlamp quite useful as a load for testing the lifetime of a lead-
acid battery (Peukert curve).  Just read the voltage every so often and 
note
that the current has remained almost constant.

Keep on Elec-Traking.
                                        Rhett George