Electrical – Why are multimeters much more sensitive than oscilloscopes

The Fluke meters I am familiar with are specified as +/-(given percent of measurement + given number of least significant digits). For the given info, using the 400 ohm range, this yields +/-(0.004 * 0.22 + 2 * 0.1) = +/-0.20088 or approximately +/-0.2 ohms, if the meter is accurately calibrated.

When measuring low resistance values, especially at the sub 1 ohm level, you will need to consider the impedance of your probes and the connections to the meter and the resistor. If you make a resistance measurement with your probes shorted together, you can get an idea of the resistance of you probe connections.

To more accurately measure sub 1 ohm resistors without using a Wheatstone bridge or other indirect measurement methods, I would recommend using a bench DVM with a 4-wire (Kelvin) resistance measurement capability. This will remove the resistance of your probes from the measurement.

After you run this test for 10 minutes, wipe off the water and take a close look at the copper where the water drop was. You will see some discoleration. Essentially the copper was corroded a bit where the water drop was. As you probably notice, bare copper left in the elements is no longer that bright copper color after a while. The same thing happened to your copper electrodes, except that the electric current speeded up the process.

The reason the resistance goes up is because the corrosion layer has significantly more resistivity than copper. This is one reason the mating surfaces of electrical connectors aren't made from copper. They are usually made from material that doesn't oxidize, like gold or nickel, or forms a conductive oxide, like tin.