$[$Distribution System$]$

If a power system has $10,000$kVA capacity and is operating at a power factor of $0\mathrm{.}7$ and the cost of a synchronous capacitor $($i$.$e$.,$ synchronous condenser$)$ to correct the power factor is $$10$perkVA, Determine the investment of the design required to correct the power factor to:

$($a$)0\mathrm{.}85$ lagging power factor.

$($b$)$ Unity power factor.

$($c$)$ Draw the phasor diagram before the installation any capacitor and after last installation. Part c please