Also, you described an unregulated power supply. This means that different loads on something like that will get different voltages. You might want to make sure that you use something like a 7812 chip to regulate it, because mfgs use a specific transformer thats just right for the load, and you might not get lucky. Search for 7812 circuits.
On the other hand, it might work just fine. It depends on the power filtering circuits in the device being powered.
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