For a first crude experiment 0.85 silver nitrate were dissolved in 40 ml distilled water, 5 ml aqueous ammonia were added and the solution then filled up to 60 ml, using again distilled water. 20 ml of the solution were poured into a petri dish. Then two electrodes made from silver wire were added and 15 V applied by a lab power supply. The outer electrode is the anode, the inner electrode the cathode. The cathode was placed in the middle of the petri dish, it should just touches the surface of the solution. Here is a time lapse video of the experiment:
I measured time (iphone stop watch) and current (lab power supply display) to obtain following scatter plot:
Hey Markus, I was thinking about your experiment here a little more in depth and why not try and run the voltage up in steps of 0.5vdc @ 150mA since you are using a regulated power supply?
I think you will get a far more revealing scatter plot, I'm just suggesting this because the substrate you are using (silver nitrate,) is electrically conductive and has the same potential difference as the conductors themselves.