$($b$)$ A $3-$phase transmission line $25$ km in length supplies a balanced load of $10$ MW with $0\mathrm{.}8$ lagging power factor and $33$ kV at the receiving end of the line. The resistance and reactance per km per conductor are $0\mathrm{.}35$ and $0\mathrm{.}6$ respectively. A shunt capacitor is connected at the receiving end of the line so as to maintain the sending end voltage at $33$ kV $.$

$($i$)$ Find the impedance of the transmission line and the load current.

$(4$ marks$)$

$($ii$)$ Taking the receiving end voltage as the reference, compute the phase angle of the sending end voltage.

$(4$ marks$)$

$($iii$)$ Determine the current $($magnitude only$)$ in the shunt capacitor that can maintain the sending voltage at $33$ kV $.$

$(6$ marks$)$

$($iv$)$ Compute the shunt capacitor rating.

$(2$ marks$)$