A $3-$phase, $\backslash (50-\backslash$mathrm$\{$Hz$\}\backslash )$ transformer is to have primary, secondary and tertiary windings for each phase. The specification is as follows: Primary to be $6600$ V and delta connected. Secondary to be $1000$ V and delta connected. Tertiary to be $440$ V and star connected. Determine suitable numbers of turns to ensure that the peak flux does not exceed $0\mathrm{.}03$ Wb $.$

If the secondary is to supply a balanced load of $100$ kVA at $0\mathrm{.}8$ p$.$f$.$ lagging and the tertiary is to supply a balanced load of $50$ kW at u$.$p$.$f$.,$ determine the primary line$-$current and power factor for this condition. Neglect all transformer imperfections.