A quick scan of a textbook shows that a good equivalent circuit of a transformer includes the ideal transformer in the middle with additional ideal components added to the primary and secondary. On the primary is a shunt R and a shunt L. The shunt R represents the core losses, while the shunt L is the primary self inductance. Then there is a series reactance (inductive) which is the primary leakage reactance preceded by a series R which is the primary winding resistance. Now, on the secondary side ther is a series reactance (inductive) which is the secondary winding leakage reactance followed by a series R which is the seconary winding resistance.
If you put all these elements into a simulator and then attach your load capacitor and assign reasonable values for everything, you will be able to analyze the effect.