Q$3)$ Power Factor and Correction $[10$ Marks$]$:

A load is supplied with a $600V(rms),60Hz$ voltage source. The electrical demand consists of a $75$ kW load at $0\mathrm{.}75$ lagging power factor.

a$)$ Determine the power factor angle. $[1]$

b$)$ Determine reactive power, apparent power, and show an appropriately labeled power triangle. $[3]$

c$)$ Determine the input current including the phase. $[1]$

d$)$ How much reactive power $($kVARs$)$ of capacitance must be placed in parallel to bring the power factor above $0\mathrm{.}92$ lagging? $[3]$

e$)$ With the capacitance added in part $($d$),$ what is the new input current in phasor form? $[2]$