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Originally Posted by SuperDanman
One question though - how do you determine how much current this thing can handle?
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The transformer you buy should be rated to pass a certain amount of current. It should be safe to use that value as the theoretical maximum current rating of the circuit.
If you're feeling more adventurous, connect an ammeter in series with the positive supply lead and a variable load, such as a potentiometer. Slowly decrease the resistance of the load and record the ammeter's reading when the magic smoke leaks out of any of the components. (NOTE: This is a BAD IDEA and should not actually be implemented.)