Good question. Very good question. Above my head also somewhat.
The lamp itself is resistive and as Mayhem mentions, unless the resistive load is sufficient (normally 75w) for the dimmers to work with, it won't without a ghost loading somewhere around to make them function on most electronic dimmers but not all types of dimmers especially variable resistance types. A household
dimmer being a variable resistance type for the most part should work given it's quality or range. At lower rates, that
dimmer also will not be sufficient to incandess the lamp without going to at least almost full first. Were that load on a
SCR dimmer or of sufficient load on a resistance
dimmer be it from other fixtures on the
dimmer of sufficient load or it's own lamp wattage than it would be effective no matter the
dimmer type or
transformer. (Chopping of the sinewave verses reducing the
voltage.)
On the other
hand, the
transformer is a inductive load as classically stated in that it induces a
lag time on the lights effected by the
dimmer and further disrupts
phase harmonics in much a similar way to the
dimmer itself which is for all intensive purposes a
transformer. It is also possible that this
lag,
phase harmonic
shift and other variables on the load side of your electronic
dimmer can be harmful to it by way of extra heating onto it and other reasons. It's also possible your dimmers will conpensate for this especially if not as high of a resistive loading is in
effect. Such inductive loading is evidenced by if you
send a low
voltage lamp to full on a light board and it's going to take a moment or three longer than a
line voltage lamp to go to full by way of the
transformer. The
lag time is inductive loading and also measured by some amount of heat or loss in the
transformer. Max out the loading in wattage on a
dimmer without accounting for
transformer effects on it and it's very likely you will not blow it out but overheat it.
A final factor is in the low
voltage lamp itself. A common low
voltage lamp requires full
voltage for optimum operation of the
halogen effect gas within it. Otherwise, that gas when operated at temperatures less than design will attack the
pinch seal of the lamp itself an not prolong it's life. (The other than noble gasses in the lamp prolonging normal
filament life will seek out and eat away at the cooler parts of the lamp thus the
pinch seal.) Some question of the effects of series operation of low
voltage lamps on dimmers but not a
transformer, or
stage lighting lamps such as in a strip light, but for the most part, your 12v lamp when dimmed will not act as per
halogen lamps. They will operate at the expected
halogen effect color temperature the lamp is designed for as per a normal
halogen lamp, but for the most part only have the life of a
incandescent lamp operated as it were over it's rated
voltage. A low
voltage lamp on a
dimmer frequently will not be a very good long term option for
stage lighting use. For a specific show sure, but other than that is not much to work with in efficiency. The life will be greatly reduced.
The volume in
line voltage verses low
voltage power is normally sufficient, no matter if it's
voltage chopping or
voltage dimming that the
halogen effect on the lamp's
filament is not having such problems with dimming.