The resistance of the electrophoresis chamber varies a lot, depending on type, dimensions, and on the saline used. However, a typical value for standard agarose gel electrophoresis to separate DNA fragments would be somewhere around 100 kOhm. Typical voltages range from 50-150 V. Depending on the gel used, gels can heat up and melt at higher voltages. Run time is usually between 0.5 - 2 hours. During this time, the resistance of the gel can increase. To get quantitative results independent of the changing resistance, the sample runs in parallel with a know "DNA ladder" that has fragments of known sizes. Thus comparing your result to this ladder gives you a calibrated read-out, no matter how much voltage or current changed.
Thus, this techniques does not need any precision voltage/current source. I am just astonished for what prices these simple devices are being sold.