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Power supplies all have output current. You forgot to say how much current your power supply must produce.
How about making a variable regulated power supply?
An LM317 IC can provide up to 1.5A from 1.25V to any high voltage but limit it to 15V if you want then it won't get too hot when it is set for lower voltages.
The datasheet shows many simple circuits but most have the more expensive LM117.
Look at the datasheet for the LM317, it has a circuit for a 5A regulator. (Using a high-power transistor to bypass the regulator.) It also shows the circuit for a current limiter. Chances are that the LM338 can be used in the same way, check the datasheet.
On the subject of LM317's, what's the difference between the LM117, LM217 and LM317 ? It doesn't say in the datasheet.
Better to use multiple output secondary and make the supplies independent. The components won't cost much.
Finally for such designe one may consider Switching power supplies which will be definitely cheap and efficient.
The LM338 reduces its max output current when it has more than 10V across it.
So it the input is 20V and you turn down the output to 5v then its max output current is about 1.5A.
Its max output current when it has 30V across it is only 1.0A.
The LM117 has a minimum load current spec of 5mA. The LM317 has a minimum load current spec of 10mA. This is its operating current that flows through the load. It is spec'd with an input-to-output voltage of 40V and is a little less at lower voltages.
When there is no load then the voltage-setting resistors are the load. If nothing sinks the operating current to ground then the output voltage rises.
The LM117 can have an upper voltage-setting resistor of 240 ohms max but the LM317 must have 120 ohms max.
These are linear regulators that produce heat. They need a heatsink for cooling if the power dissipation is high. They shutdown if they get too hot.
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