Confused about AC measuring cicuit

Please see the circuit below, which is one of many similar circuits for measuring AC signals. If the AC source is independent of the Arduino's power source (e.g., the Arduino is running on a 9v battery), then how can the Arduino read the voltage on the output of this circuit. There's no ground for the voltage being sampled? It would be like powering an Arduino from a 9v battery and then connecting an Analog pin to the positive side (only) of a separate D cell battery -- isn't it? What am I missing?

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Right, I got that. My question was how the current produced by that circuit and fed to the analog pin of the Arduino finds it's way to ground such that the Arduino can measure it. I'm guessing it's the ground shown under 2 Watts at the bottom of the circuit? If that's tied to the Arduino ground, then I suppose it works like 2 batteries in parallel?

If you are thinking of connecting that circuit to the household AC line, DON'T DO IT. It is extremely dangerous.

With a two prong plug you have a 50:50 chance of shorting the hot lead to Arduino/PC ground, possibly destroying quite a bit of equipment and killing someone in the bargain.

Posted circuit diagram:

If you want to monitor household AC line voltage, here is how to do it safely, using an AC power adapter transformer.