The rule of thumb is: the faster the treatment, the higher the volts required and the more plants treated at once. Alternatively, the larger the plant, then the higher the amps required. In a study some years ago, we used 15kV rms at 50 kW for agricultural weed control to treat about 3 acres an hour. In general, one can use a 5kV rms at 2.5 kW transformer for small weeds. The voltages are high and very dangerous if misused, so I cannot give any more details of equipment or techniques. You should not try this at home. Note the voltages are in the thousands of volts. Using household electricity of a couple of hundred volts would eventually kill small plants, but may take ages.
Many years ago, I did studies of how the system worked on pea plants and sections of stem were studied both before and after treatment to find out what was happening. The current flows through the tissue and heats it up to boil the water in the cells. These rupture under the steam pressure and the cells lose their srtucture and function and die.
Plants with long, extensive, underground root systems e.g. dandelions or couch grass are not usually controlled by this technique, but others such as nettles with localised root structures are killed. This is because the current spreads out into the soil surrounding the roots and its destructive power is diminished.
There was an American system called 'Lasco', which was a commercial, electrical weed killing machine for farms. It used a generating system powered by the tractor power-take-off to generate 15kV rms at 60kW. Although several machines were sold and trials carried out in Belgium, it never seemed to be very successful.
The Russians and East Europeans liked to use very high voltage spark discharges for plant growth control e.g. 60-80kV! Their equipment produced a series of sparks, which were directed by special electrode systems to the plants. The power requirements were much lower e.g. 200-500W but the equipment was complex and only really suited to special applications.
A Bulgarian colleague is currently developing a method of accelerating the drying of tobacco leaves, by applying high voltage discharges to the main veins. this ruptures them slightly to allow their water to escape more rapidly than by kiln drying and allows the vein to dry at the same rate as the rest of the leaf. This can save up to 50% of kiln drying costs.
I must emphasise that the techniques described require a high degree of professional knowledge and experience to operate safely and no experiments should be tried at home.