Considering the doc of the Nano (V3) :
The Arduino Nano can be powered via the Mini-B USB connection, 6-20V unregulated external power supply (pin 30), or 5V regulated external power supply (pin 27). The power source is automatically selected to the highest voltage source.
The FTDI FT232RL chip on the Nano is only powered if the board is being powered over USB. As a result, when running on external (non-USB) power, the 3.3V output (which is supplied by the FTDI chip) is not available and the RX and TX LEDs will flicker if digital pins 0 or 1 are high.
I understand that when the Nano is powered by usb, the 3.3V output is not available.
But !
I power the nano with an 9V batery through an 7805 regulator.
If I use a voltmeter to get a measure from then 3.3V pin and ground I get 3.35 volts....
Why I got this level ?
In the second time, another question :
Is there a way to use external batery with regulator (7805) on 5v pin or Vin pin and use at the same time the usb connection without damaging the Uno ?
Thanks