Basement Wiring

Ok , first of all, I assume when you say #14/3 cable, you mean a cable with a black, white and bare wire. We do not count the bare ground, it is understood, so I will be calling it a 2 wire, or a black, white, and red will be a 3 wire.

All 120 volt lights and outlets in the bedroom will need an ARC Fault circuit, so may be 15 or 20 amp but must use a 2 wire, because you need to use a ARC Fault circuit breaker, and cannot use a shared neutral.

The bathroom requires a 20 amp circuit, if it is the only bathroom on the circuit then any light or fan in that room can be on the same circuit. There must be an outlet at the sink on that circuit, and the outlet must be a GFI.

A 20 amp circuit for the treadmill is good, the remaining family room outlets can be either all on a 15 or 20 amp circuit.

The fireplace does not need a circuit by itself, can be on any circuit.

So you will need:
1-#12-2 for bathroom (if you use a 3 wire, then you can have a spare circuit)
1-#14-2 or #12-2 cable for all bedroom lights and outlets.
1-#12-3 for black family room and red for treadmill
1- existing #14-3 for family room lights

Now you also need smoke detectors, AC with battery backup, and interconnected with each other and with any existing interconnectable smoke detectors.

One smoke must be in the bedroom, and one other one needs to be anywhere in the other rooms, usually in a central location of the general area. The smoke detector in the bedroom must not be connected to or affected by the ARC Fault breaker.

I am curious how you did calculations, can you explain? Also, I trust you will be checking with your local municipal building official to be sure you can wire this yourself, with a permit , of course. Then you can ask about any local codes tha must be followed as all I can comment on is National Electric Codes.

Hope this helps.

The smoke detector in the bedroom must not be connected to or affected by the ARC Fault breaker.

NOT True

I wouldn't use MWBC in my home...just not a good idea for residential applications. You effectively lose two circuits with a breaker tripping, and should you have a neutral come loose you could experience more serious problems with excessive voltage.

SSnook, this post is from 2006.

The Code in effect now is 2008 edition, and that requires the smoke detector to be Arc Fault protected.

However, some states. Maine for example, have taken exception to that requirement and do not want the detector Arc Fault protected.

Please refrain from answering questions older than a few months.