I have a 12VDC 500mA power supply and I want to power two (2) separate items, by using a "Y" adaptor. The first item is supposed to use this exact power supply, but the second item tells me to use a 12VDC 250mA power supply. They are both a couple different projects with LEDs. I do not want to use two (2) separate power supplies. What kind of problems can I expect, especially from the second item?
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The power supply is simply not powerful enough.
If you have two devices, of the same voltage rating (12V), you add the currents together to find out how much current your PSU needs to supply:
Device 1: 12V, 500mA
Total current needed: 750 mA
Since your supply is not designed to supply 750 mA, it would be foolish to try to use it to power both devices at the same time. The power supply is simply not powerful enough.
The results will vary from not supplying 12V anymore, to overheating and in the very worst case let off smoke and catch fire.
You might be able to use it to supply one when the other is off, but this depends on how much standby current each uses.
You have only one 6 watt rated power supply, but you want to source 9 watts. Best case scenario: it might work for a few seconds but then slowly the voltage will begin to drop and your power supply gets very hot. Absolute worst case scenario, after a while the PSU gets so hot it catches on fire due to a short OR overloading a transformer... potentially destroying your loads along with it.
No matter what, you will have issues with both loads not getting enough power.
If you exceed your current rating, you can expect more heat than it is designed to dissipate; which can lead to premature failure, sometimes in the form of angry smoke.
As others have noted, your statements lead to the belief that 750mA will be drawn, in an average use scenario. The better question is, is this the actual "worst case" scenario. While it would simply be safer to get a 750mA (Or 1A, for both safety margin and expansion capability), will the devices actually draw that much current?
Most commercial devices will incorporate a safety margin in the power supply that they are shipped with. You normally do not want to run a power supply at exactly it's rated limit. Your 500mA device might actually only draw 400mA or 300mA, or it could draw 490mA or 500mA. The current draw might also vary based on what the device is doing. Since you mentioned LEDs, for example, a RGB led strip might only draw 100mA when one color is at full on, but draw 400mA when all three colors are on. Using a Current Meter, you could measure the highest current draw in "worst case" use, for both devices, and use that to see if the 500mA power supply would work for your needs.
But if it is close to 500mA in a "worst case", most power hungry use, I would go with a 12V 1A power supply. They are easy to find and relatively cheap. Honestly, I would go with it anyway, since an average use case will likely be 750mA at Any Given Time. Always err on the side of safety.