Sorry Bill, but I have to disagree. Amp•Turns have to match on both sides. In a series connected transformer worrying about voltage across the transformer leads to many false paths. For example in a CT, the most common example of a series transformer, the secondary current is proportional to the primary current by the ratio. If the CT is shorted, full current flows and no voltage is developed. If the CT is open circuited, the current still flows, but enough voltage is developed the force all of the secondary current through the magnetizing branch. This can result in thousands of volts across the secondary while still having essentially zero volts across the primary.
In this case if R2 is open, the zero current in Ib will cause full line-neutral voltage to appear across V1 because Ia will also be zero. If R1 is open then Amp•Turn balance requires Ib/2=Ib, for which the only solution is Ib=0.
All of this assumes an ideal transformer. In reality there will be some magnetizing branch current and Ia will only be very close to zero for R2 open and Ib will only be very close to zero for R1 open.