How does a multimeter measure small voltages without being connected to ground?

Question

I have a multimeter powered by a 9 volt battery. I put it in AC voltage mode that allows me to measure 0.001 volts. I have the red probe connected and the black probe (common / ground) detached.

When I grasp the contact metal of the red probe in one hand, and place my free hand over an area that would set off my non-contact voltage tester such as a power bar, the multimeter reads an increase in 0.200V !

Why is my multimeter reading a voltage? Shouldn't this be an open circuit since the black probe is not connected to anything?

A similar question is asked here, but the question is a bit unclear and as I understand, the answer states the multimeter in that circumstance is picking up a voltage from the air like an antenna, and their multimeter may have the black probe connected. https://electronics.stackexchange.com/a/27869/293787

Answer 1

Draw a circuit diagram and replace the air between the disconnected (black) socket and the power bar with capacitor A and the air between your free arm and the power bar as capacitor B.

These are very poor capacitors - with small area of the plates and big distance between the plates, but are still capacitors. They have large impedance. Your body and the impedance of the multimeter are also very high so that's basically a voltage divider and the voltage in the middle of this divider so happens that it is 0.2 V.

The moment you connect the black socket one of the capacitors does not disappear but is instead shorted by your black lead connection to ground. So these connections over air are always there and appear as leakage sometimes but for the purposes of most schematics when things are not floating their effects are infinitely small. Sometimes, for example when large currents are switching, they cannot be ignored and are analyzed.