A single phase, 50 kVA, 1000 V/100 V two winding transformer is connected as an autotransformer as shown in the figure. The kVA rating of the autotransformer is _________.

Assuming an ideal transformer, The Thevenin's equivalent voltage and impedance as seen from the terminals x and y for the circuit in figure are

For a specified input voltage and frequency, if the equivalent radius of the core of a transformer is reduced by half, the factor by which the number of turns in the primary should change to maintain the same no load current is

A single-phase transformer has no-load loss of 64 W, as obtained from an open circuit test. When a short-circuit test is performed on it with 90% of the rated currents flowing in its both LV and HV windings, he measured loss is 81 W. The transformer has maximum efficiency when operated at