$1.$ A three$-$phase$50$ hz$,440$V$,$ and a wye$-$connected induction motor draws a $7\mathrm{.}5$A current at a lagging power factor of $0\mathrm{.}82.$ A delta$-$connected capacitor bank is connected in parallel to the motor to improve the power factor to $0\mathrm{.}94,$ lagging. Find the following:

$($a$)$ The rating of such a capacitor bank

$($b$)$ The capacitance$$