Re: Proper sizing of a breaker
Your motor will draw just over half of the capacity of the transformer. You do not need to have a primary side breaker that can carry the entire capacity of the transformer. I think that is what you were asking.
But keep in mind that we size primary breakers at a value no more than a certain percentage of their full load current. In addition, we size motor branch circuit breakers at a value no more than a certain percentage of their full load current. This gives you two upper bound criteria, and you can't exceed either one.
I would start by looking at the motor load, as seen from the secondary side (i.e., 15 amps). I would pick a secondary side breaker on the basis of Article 430 (i.e., one that will allow the motor to start without tripping, and that still protects the motor branch circuit). Next, reflect the value of that secondary breaker's current rating onto the primary side. Pick a primary breaker that is no more than that reflected current value. Finally, make sure your selected breaker does not exceed the transformer breaker limits of Article 450.