G4 bulbs are both made as 12 volt and 230 volt, so it may have a unit to drop the voltage to 12 volt, but can't be sure.
For the moment let me consider it has got a voltage dropper, there are true transformers, but in the main they use switch mode, or pulse width modulated voltage droppers, some are made to be dimmable, but the whole idea with a quartz bulb is to keep the bulb super hot so tungsten will not be deposited on the bulb, so keeping the voltage to exactly 12 volt is the whole idea, so why dim it? It will reduce life of the bulb if used dimmed.
Quartz bulbs also have other problems, like red hot bits of quartz when they fail and rays which can damage our skin, so they are always put behind glass, which will hold the red hot bits and filter out the harmful rays, moving to LED removes this problem so the globes over the bulbs can be left off.
At extreme height then bits will cool before they hit floor and rays are not a problem, but not likely to be high enough in normal living room so need glass covers.
The voltage dropper is often limited in output not just maximum but also minimum so an electronic transformer marked 20 - 105 VA must have a 20 watt load, now when you dim a bulb although rated 20W it is likely only drawing 10W, so with the electronic transformer rated 20 - 105 VA you can dim a 50W bulb but not a 20W bulb. So problem could be simply the bulbs are too small, also the bulb has a coil of wire, which forms an inductance, the electronic transformer gives out power in the kHz range, so some times the bulbs coil just happens to react with electronic transformer.
So one make, dimmer, electronic transformer, and bulb, theory you can mix and match in practice it can cause problems.
You don't say what type of light fitting uses the G4 bulbs, it could be a chandelier or a down lighter, with the latter you will be left with holes, so you want something to fill the holes.
The problem with GU10 is when fitted with LED lamps part of the lamp is a cooling fin, so the light is less then 50mm, over 3W much of the light is lost, unless it reflects of a white surface, and at 3W you need so many it looks like a planetarium, so better to select a larger unit, around 100mm diameter is better, there are both units needing a hole, and units which are surface mount.
If not down lighter, then £2.50 for a three watt LED can work out expensive and again you will likely need around 10 for standard size living room, so it may be better to change the fitting.
I am not sure about dimming a LED, to be able to be dimmed the LED has to use a very simple driver, so the bulb will normally give around 75 lumen per watt, where non dimming can use better quality drivers inside the bulb so can give 100 lumen per watt, some even 120 lumen per watt. Also when you dim an LED the colour does not change, so there is not the ambiance found with tungsten bulbs. As a result all my dimming switches have been removed.
With LED lights the base needs to stay cool, and with a white ceiling reflecting the light off the ceiling removes many shadows, so with a chandelier you want bulb bases at the bottom so base stays cool and light is reflected off the ceiling.
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