When I think of "weeding using electricity" the first thing that comes to mind is a electric string trimmer attached to an orange extension cord. But it turns out some research is being done using electricity itself to kill weeds.
Now, before you start playing the MacGyver theme song in your head, you should know that 1.) ELECTRICITY IS DANGEROUS! and 2.) researchers are using a tractor-mounted device to zap weeds. This probably isn't something you should be inventing at home, unless you're vying for a Darwin Award. But maybe someday there will be some options for small-scale use in the garden.
Here's a video clip of the machine at work in an orchard.
One of the ways that weeds can be killed is by physical injury. A common control method is using heat to kill weeds. (Warning: FIRE IS ALSO DANGEROUS!). There are electric weeding wands on the market for gardeners, but these use electricity to create heat. Small seedlings can be heated to a point that they die.
A problem with heat treatment is that typically only the top portion of the plant is affected. With electricity there is a possibility of also damaging the root which increases effectiveness.
Like most physical control methods, it works best on small plants. Larger plants will resprout and require additional treatments. Because you'll ask: this probably won't work on bermudagrass. Sorry.
For now this looks like a promising technology that's best suited for land measured in acres, not the garden. But it's always exciting to see new ideas to kill pesky weeds. Who knows what will come of this in the future?
To learn more about this project, check out this post on the UC Weed Science Blog.