Dude you need to stick with the cheap avantco 3500 watt induction burner just go with a Hotrod heat stick (I went with 1500 watts) from brewhardware. I only have a 15 gallon kettle though. Works great for me. Was $175 for the 3500 watt and $150 or so for the heat stick. But the components of the...
You would have to insulate the kettle. I know people have done 12 gallons. I have done 7.5 easily with the 3500 watt. Do a search on the Avantco IC3500 induction burner on here. Give it a read and see if it suits your purposes.
But it is probably one of the cheapest ways to make beer inside.
You should look into an induction burner. If you already have a kettle and a mash tun, all you need is a $150ish induction burner (IC3500) and probably an adapter for the plug to fit either a dryer or range plug.
It's MUCH cheaper and good for apartments.
IF you do smaller than 5 gallon...
I just started my induction build. It will hit mash temps (to go into an igloo cooler) in 36 min uncovered and unwrapped in insulation. I boiled it on a cheap kettle I bought at an outlet for $45.