b$)$ Three loads are connected in parallel across a $230$ V$,60$ Hz supply. Take the supply voltage as the reference phasor. Load $1$ takes a power of $8$ kW at a lagging power factor of $0\mathrm{.}8,$ load $2$ takes a power of $12$ kW at a leading power factor of $0\mathrm{.}5$ and load $3$ takes a power of $5$ kW at unity power factor.

$($i$)$ Find the magnitudes and corresponding phase angles of the current drawn by each load.

$($ii$)$ Determine the overall power factor as seen by the supply.

$($iii$)$ Calculate the power rating of the power factor correction equipment needed to improve the overall power factor to $0\mathrm{.}9$ leading.