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Page in Swedish, but has a photo: https://www.jula.se/catalog/hem-och-hushall/hemelektronik/batteriladdning/batterieliminatorer/batterieliminator-409049/

This device allows you to select between 3-12 volt. However, it also forces you to pick between different "versions" (not possible to adjust on the device itself): 300 mA, 600 mA, 1000 mA or 1500 mA. All except for the first one are more expensive.

I know what "mA" stands for "milli ampere", but what does it mean in the context? If I buy the cheapest 300 mA one, what does that entail? Why do I need to pick between the others when buying it? Why is this not a "setting", just like the volt adjuster?

I was going to use this to power a Game Boy Color while it's not using batteries.

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The current rating is the maximum current that the device will provide. If your device requires a higher current than the device will provide, it will likely overheat the power supply and may also create unusual circumstances within the electronic device.

Consider as an analogy that amperes is water flow. Your device requires a certain amount of water to be flowing in order to work. If the opening in the dam is insufficient to provide this amount of flow, it will still flow, but will not provide the necessary energy to the device to work properly.

If the power supply is rated higher than that which is required by your device, no harm is expected. The power supply will only provide that which is required, and not overheat, and perhaps will survive longer.

Update/edit: Website handheldlegend.com has apparently performed a test on the GameBoy Color to determine power consumption/current draw at maximum volume. It appears that the site is promoting a lower power draw LCD panel, but that does not invalidate the results, table below from the linked site:

game boy color power consumption table

One can note from the table that the current draw increases with battery voltage depletion. This is consistent with physics of electrical power. The indicated power supply is likely to provide consistent voltage up to the maximum rated current, allowing one to use only the top line of the table as the reference.

The indicated current draw for that line is below the 300 mAh capacity of the less-expensive power supply, allowing one to avoid purchasing the top of the line model.

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The 300mA model can feed devices which do not try to sink higher current than 300 milliamperes. You should measure how much your Game Boy apparatus sinks from batteries when it's used and the display is as bright and busy as possible and the sounds are as loud as possible. The job needs a multimeter and definitely a person who knows what he does. I guess you are not in your best just in that area, so get help!

The next time you need help (to prevent the deaths of your G.B. and the battery eliminator) is when the battery eliminator is taken into use.

If the GB takes less than 300mA the 300mA model is OK. If it takes say 400mA, you need a model that can output at least 400mA, preferably more. The 600mA model should be selected. If it happens that G.B. takes just 300mA or 301mA you cannot be sure does the 300mA model stay alive. It surely has some tolerance, but also the input mains AC voltage varies and the measurement can easily have few percent error. In that case, too get the 600mA model.

I guess (=cannot see it without a schematic, because I am not a clairvoyant) there's the simplest possible voltage regulation principle in use - one which makes voltage adjustment possible with a screwdriver which turns a potentiometer in the regulation circuit. But it doesn't give higher maximum output current if the output voltage is reduced, so all speculations like "it gives 300mA at 12V, I should get 600mA at 6V, because the power stays the same" are useless.

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