a$)$ Two $440$ Volt three phase alternators operating in parallel supply the three loads specified below:

$900$kVA @ p$.$f$.0\mathrm{.}8$ lag

$900$kW @ U$.$P$.$F$.$

$50$kW @ p$.$f$.0\mathrm{.}95$ lead

$400$kW @ p$.$f$.0\mathrm{.}9$ lag

Calculate each of the following if one alternator provides $1500$ kilowatts at unity power factor:

$($i$)$ The Power Factor of the second alternator

$($ii$)$ The output current of the second alternator

b$)$ Explain what is meant by the term power factor