When the winding $\text{c-d}$ of the single-phase, $50 \mathrm{~Hz},$ two winding transformer is supplied from an $\mathrm{AC}$ current source of frequency $50 \mathrm{~Hz},$ the rated voltage of $200 \mathrm{~V (rms),} 50 \mathrm{~Hz}$ is obtained at the open-circuited terminals $a-b$. The cross sectional area of the core is $5000 \mathrm{~mm}^{2}$ and the average core length traversed by the mutual flux is $500 \mathrm{~mm}.$ The maximum allowable flux density in the core is $ B_{\text {max }}=1 \mathrm{~Wb} / \mathrm{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 $50 \mathrm{~Hz}$ are $(5+j 100 \pi \times 0.16) \Omega$ and $(11.25+j 100 \pi \times 0.36) \Omega ,$, 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).
