A transformer with toroidal core of permeability $$\mu $$ is shown in the figure. Assuming uniform flux density across the circular core cross-section of radius r $$ \ll $$ R, and neglecting any leakage flux, the best estimate for the mean radius R is

A 3-phase 900 kVA, 3 kV / $$\sqrt 3 $$ kV (Δ/Y), 50 Hz transformer has primary (high voltage side) resistance per phase of 0.3 Ω and secondary (low voltage side) resistance per phase of 0.02 Ω. Iron loss of the transformer is 10 kW. The full load % efficiency of the transformer operated at unity power factor is _______ (up to 2 decimal places).

If the primary line voltage rating is 3.3 kV (Y side) of a 25 kVA. $$Y-\triangle$$ transformer (the per phase turns ratio is 5:1), then the line current rating of the secondary side (in Ampere) is_______.

A three-phase, three winding $$\triangle$$ / $$\triangle$$ / Y (1.1 kV/6.6 kV/400 V) transformer is energized from AC mains at the 1.1 kV side. It supplies 900 kVA load at 0.8 power factor lag from the 6.6 kV winding and 300 kVA load at 0.6 power factor lag from the 400 V winding. The RMS line current in ampere drawn by the 1.1 kV winding from the mains is _______.