When measuring a resistance using a multimeter it is a few percent out. Why

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.

Keep in mind that your coil is made of a long and thin wound wire, so it also has a resistance. Though it heavily depends on the gauge and length of the wire, I would say, 3 Ohm makes sense.

Finally, the total impedance is the sum of the (Ohm's) resistance of R and the coil, plus the impedance of the coil:

$$Z(f)=R_R+(\underbrace{\color{blue}{R_L+2\pi jLf}}_{coil})$$

First of all, this is a complex expression. If you measure the voltage across the coil, it is

$$V_L=Re\left(\frac{R_L+2\pi jLf}{R_R+R_L+2\pi jLf}\right)\cdot V_0$$

However, you can thrust your multimeter here, as it measures the pure ohm's resistance. Maybe, it can also measure the inductance. For correct results of the oscilloscope, you will have to do the math.