A single-phase two-winding transformer rated \(90 \mathrm{MVA}, 80 / 120 \mathrm{kV}\) is to be connected as an autotransformer rated \(80 / 200 \mathrm{kV}\). Assume that the transformer is ideal.

(a) Draw a schematic diagram of the ideal transformer connected as an autotransformer, showing the voltages, currents, and dot notation for polarity.

(b) Determine the permissible kVA rating of the autotransformer if the winding currents and voltages are not to exceed the rated values as a two-winding transformer. How much of the \(\mathrm{kVA}\) rating is transferred by magnetic induction?