$($a$)$ Explain the term power factor correction.

$($b$)$ State ONE advantage of power factor correction.

$($c$)$ Sketch a labelled diagram to show how a motor starter and delta connected capacitor bank can be arranged to correct the power factor of an individual three$-$phase induction motor.

$($d$)$ Calculate the required capacitance per phase to achieve unity power factor if the motor in Q$6($c$)$ has a full$-$load reactive power of $4\mathrm{.}82$ kVAr when connected to a $440V,60Hz$ supply.

$($e$)$ Explain why a star connected capacitor bank requires three times the capacitance per phase to achieve the same power factor correction as a delta connected capacitor bank for the same load.