Does a bunch of potentiometer controller need external power?

x20 pot 10kΩ
for arduino uno r3?

Not sure what your question is...

... but a potentiometer is usually connected between common (with the Arduino) GND and a voltage supply... so yes, you need something to supply the voltage.

Does that mean 20 pots at the same time? Then you'll need a multiplexer.

The total current then will be 20*0.5=10mA, should not be a problem when powered from the Uno.

In any case an ADC (of the Uno...) and pots should be powered from the same supply for ratiometric (voltage independent) analog reading.

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You do have to think what you will do with all that data that is available to that poor little microprocessor.

Your topic has been moved to a more suitable location on the forum. Installation and Troubleshooting is not for advice on (nor for problems with) your project.

Find the parallel resistance of all your pots -

Then calculate current draw of the equivalent resistor - E=IR

Don't forget to take into consideration any other devices connected to the power supply - LEDs, displays, etc.

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