Examine your lease before you jet off to greener pastures. If I was the landlord and I was responsible for your light bill, and expected you to pay it - it would be in the lease agreement. There is very likely no clause in there for faulty equipment or similar, leaving you responsible for the outstanding bill. You've bought a house to move into, so your credit is displaying that you're a stable person in job and income.
Knowing that, I wouldnt think twice about not only taking you to court for the remaining amount, but also getting a lawyer to cover all my bases and, in the end, charge the electric bill, the court fees, my "missed opportunity" time and the lawyer fees, all to you. If you cant afford it then and there, I would push for the court to garnish your wages until its paid for. During that time, I would also be expecting the state you live in, to charge its highest approved interest rate on the amount you owe until paid.
You can argue that there is a faulty line that has caused the electric bill to spike, which that repair should not be your responsibility (again, check the lease to make sure its not). The judge will ask if you tried to work it out with the landlord, (which you should at least attempt to before leaving. Get documentation that you tried. Certified Letter to the landlord with a Return Receipt.), and if all else failed, the judge may be lenient enough upon you to lessen the amount owed on the electric bill. But, the kicker here is, you may very likely still be fucking dunked on because it went to court and be responsible for all fees associated with the court case.
This is all based on your landlord not being a complete moron. But very much a fuck around and find out situation because I deal with this dumb shit all of the time. Again, you're displaying that you're competent with money - so the courts are already going to be on the landlords side.