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Hi Ante,
Gary made one or two.
The datasheet has a max rating for the IC's idle current which is 10mA for the LM317 in a large case and only 5mA for the more expensive LM117. The reference voltage of 1.25V flows through the resistor which is only 5.2mA for a 240 ohm resistor. Since the max idle current for the LM317 is 10mA then you can expect some of them to have more than only 5.2mA so the output voltage will rise without a load.

Unfortunately, the datasheet shows a circuit with a 240 ohm resistor on its 1st page and that is the circuit most people use. It uses an LM117.

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Will it work for 3A?

and... ( from the site )

"NOTE: &nbspR2 is determined by the voltage across the 220 uF Cap.

        (Volts - 1.2)
R2 = -------------
          .015

Any Resistor close to the calculated value should be fine. Its only purpose is for an approximate 15 mA current flow which will create a quite stable -1.2 volt supply. "

does it mean voltage across the cap of the complete circuit?

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