A three$-$phase $423\mathrm{.}69$kW$,0\mathrm{.}82$pf lagging, $4160$V$,$wye$-$connected induction motor has a full load efficiency of $88\%$at a lagging power factor of $0\mathrm{.}75,$and is connected to a feeder. In order to correct the power factor of the load to a lagging power factor of $0\mathrm{.}9$by connecting three capacitors at the load. Find:

a$)$The rating of the capacitor bank

b$)$The capacitance of each unit if the capacitors are connected in delta