15 amp circuit wiring

I am running a new 15A circuit to a new bath that will supply at least three single gang plugs, a vanitylight/plug, and a ceiling fan/light that may also include a heat source (i.e., heat light or heating element). I thought the electrician told me to run 14/3 NWB wire from the circuit box to the bath. After running the wire (which wasn't easy), I started wondering if the wire shouldn't have been 12/3 wire. Will the 14/3 wire be adequate. If necessary I could pull the 12/3 wire through. Any comments would be appreaciated.

 

I believe you need the 12 wire.

 

Code requires the bathroom receptacle to be on a 20-amp circuit. A 20-amp circuit requires 12-gauge wire. Your 14-gauge wire violated the electrical code, and will not be approved by the inspector.

As to whether the rest of your plan is good or not, it depends on how many watts those lights are and how many watts the heater might be. Since you are running /3 wire, does this mean you intend to have a multiwire circuit? If not, why are you running /3 instead of /2?

I think you meant "NM-B" when you said NWB, didn't you?

There are a lot of other codes that apply to a bathroom, such as GFCI and receptacle-to-sink distances. Why so many receptacles in one bathroom? It's not prohibited, but most inspectors don't like to see more than one per sink.