GATE 2023 EE – Question 53

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 mm² 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/m² 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 $(5+j100\pi\times0.16)\ \Omega$ and $(11.25+j100\pi\times0.36)\ \Omega$, 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).