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

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 _______.

A single-phase 400 V, 50 Hz transformer has an iron loss of 5000 W at the condition. When operated at 200 V, 25 Hz, the iron loss is 2000 W. When operated at 416 V, 52 Hz, the value of the hysteresis loss divided by the eddy current loss is ________.