$($b$)$ A $3-$phase transmission line, which is $20$ km long, provides a balanced load of $10$ MW with a power factor of $0\mathrm{.}8$ lagging at the receiving end, where the voltage is $33$ kV $.$ The line has a resistance of $0\mathrm{.}5$ and a reactance of $j0\mathrm{.}5$ per km $.$ To maintain the voltage at the sending end at $35$ kV $,$ a shunt capacitor is connected at the receiving end of the line.

$($i$)$ Find the load current.

$(5$ marks$)$

$($ii$)$ Find the capacitor rating that can maintain the sending end voltage at $35$ kV $.(5$ marks$)$

$($iii$)$ Find the capacitor rating that can maintain the sending end voltage at $33$ kV $.(5$ marks$)$

$($Total: $25$ marks$)$