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 \(5000 \, \text{mm}^2\) and the average core length traversed by the mutual flux is 500 mm. The maximum allowable flux density in the core is \(B_{max} = 1 \, \text{Wb/m}^2\) 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).
\begin{center}
\includegraphics[width=0.5\textwidth]{24.jpeg}
\end{center}