It is voltage that determines movement of DNA in the gel. Strictly speaking, it is the voltage gradient over the gel that determines movement of DNA. The voltage gradient depends on resistance, and so will be less in the chambers of the tank with (low resistance) buffer, and more in the part of the tank with gels covered in a thin layer of buffer, where the resistance is higher. Increasing the layer of buffer above the gels will increase the current by reducing the overall resistance – and will also decrease the voltage gradient. It is complicated!
As a rough guide, most of us would aim at a voltage gradient of about 1 V/cm over the part of the tank where the slides are placed, with a layer of 1-2 mm of buffer above the slides.
"FAQ by Andrew Collins, Gunnar Brunborg and Jonas Nygren, 2006, NewGeneris FP7-project"