Connecting New Wiring to a 20 Amp Breaker

Do not put a 20amp breaker. There are to many tragedies in the news already. Use a code book if you are willing to take the risks. 15 amp only. Extending the circuit is the only reason I see for your question. Knob and tube wiring is not a bad design, but not intended for modern loads. There is most likely no ground wire.

Size your wire, if it is less than 14 gauge, you should not touch it yourself. Do your homework, get a permit and do the work yourself. At least in my state, if you intend to occupy the home for more than two years. You assume the risks of living in a house. When you modified the wiring, no other person put in danger.

Chances are your existing circuit is way over extended. you might want to upgrade your panel. You could have only a few circuits, but you must size your feeder from the utility. Do you homework. This is not a quick answer, to many variables and way to scary.

Before you trust the information from well meaning folks on this board, contact a licensed electrician.