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Can I use an op-amp in voltage follower configuration as variable voltage power supply?

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I see that this works in theory, but I my gut feeling says there is a drawback or caveat of which I’m not aware. Basically what I want to achieve is described best by the circuit diagram below.

schematic

simulate this circuit – Schematic created using CircuitLab

I have a power supply (2A @ 12VDC) that I want to use to make a variable voltage power supply. In the voltage follower configuration, whatever is on the non-inverting terminal on the op-amp is present on the output terminal. The extra current at the output terminal needed to keep the voltage up is provided by the op-amp’s supply. Since I’m using a linear pot as a voltage divider to set the input voltage to the op-amp, will this work as an effective variable power supply from 0V to almost 12V? If not, why can this configuration not be used this way?


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