When the winding c-d of the single-phase, 50 Hz, two winding transformer is supplied from an AC current source of frequency 50 Hz, the rated voltage of 200 V (rms), 50 Hz is obtained at the open-circuited terminals a-b. The cross sectional area of the core is 5000 mm$$^2$$ and the average core length traversed by the mutual flux is 500 mm. The maximum allowable flux density in the core is $$B_{max} = 1$$ Wb/m$$^2$$ and the relative permeability of the core material is 5000. The leakage impedance of the winding a-b and winding c-d at 50 Hz are (5 + j100$$\pi$$ $$\times$$ 0.16) $$\Omega$$ and (11.25 + j100$$\pi$$ $$\times$$ 0.36) $$\Omega$$, respectively. Considering the magnetizing characteristics to be linear and neglecting core loss, the self-inductance of the winding a-b in millihenry is ___________ (Round off to 1 decimal place).

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_______.