$4.$ A balanced three phase, star connected phase load of $50$ kVA with power factor $0\mathrm{.}8$ lagging is connected to a three phase $50$ Hz supply via a line of impedance $\backslash ((0\mathrm{.}4+$j $1)\backslash$Omega $\backslash )$ per phase. The voltage at the load is $400$ V line to line.

$($i$)$ Draw a per phase equivalent circuit of this system.

$($ii$)$ Calculate the line current in complex number form.

$($iii$)$ Calculate the impedance of the load.

$($iv$)$ Calculate the magnitude of the line to neutral voltage at the supply.

$($v$)$ Calculate real power $($P$)$ and reactive power $($Q$)$ drawn from the supply.