The message <
[email protected]>
You're confusing ohm's law with the power law. Ignoring changes of
resistance due to temperature, the current is directly in proportion to
the voltage. It is power which is proportional to the square of the
voltage (or current, take your pick).
FYI, regarding metal halide lamps, the use of a halide and a high
temperature envelope in close proximity to the filament is not to make
the filament last longer at elevated temperature, it's to allow the lamp
to maintain its lumen output over its shortened lifetime by recycling
the tungsten vapour back onto the filament to save it from depositing on
the envelope and acting as a light blocking filter.
The tungsten halide cycle relies upon the envelope operating at much
higher temperatures than possible with conventional glass to prevent the
deposition of tungsten on the inner surface. The silicate glass used
(the so called "Quartz Glass") usually operates at temperatures between
250 and 300 deg C. If you undervolt such a lamp, the cooler temperature
on the envelope will compromise this effect and, although the filament
life will be extended, the envelope will suffer blackening and reduce
the lumen output.
The reason why the tungsten halide cycle doesn't improve the filament
life is because the tungsten vapour is deposited onto the cooler parts
of the filament and its supports. The hotter parts of the filament still
erode in pretty much the same way as in an ordinary vacuum or nitrogen
filled lamp. This erosion thins the filament causing it to run even
hotter in what is basically a runaway process.
This wear mechanism is further agravated by the high current surge when
such lamps are switched on from cold (cold filament resistance being
only about one tenth of the operating temperature resistance). Since the
ever so slightly to start with thinner parts of the filament heat up
faster than the remaining thicker parts of the filament and to a
slightly higher temperature than normal, the thinner parts suffer more
loss of tungsten until they either fail at the next switch on (the usual
fate for a household lamp) or else fail several hours after the fatal
switch on event.
Such "Thousand Hour" lamps can survive several thousands of hours, if
left burning continuously and not subjected to switch on surges such
lamps usually have to contend with in a normal domestic service
environment.
Regarding the maximum field current question, there is no point in
allowing more current than the maximum based on the 12 volt excitation
voltage since this will have been set, by design, for magnetic
saturation or very close to. Additional current over and above this will
produce very little extra magnetic flux but considerably more heat.
Also, since this waste heat is a drain of power from the alternator's
output, the overall efficiency will be significantly reduced.