A single phase voltage source Vs =240∠0° V RMS supplies two loads in parallel with thefollowing parameters (all values RMS),1) 10 kVA at a 0.6 lagging power factor2) 2 kW at a 0.90 leading power factora) Draw the power triangle for each of the two loads and complete Table 1. [4]b) Calculate the power triangle of the combined loads and complete Table 1. Draw thecombined power triangle. [2]c) Apply S=VsI s* to the combined power to calculate the phasor current I s.[1]d) Calculate the required kVARs of capacitance in parallel with the loads to correct the powerfactor to 0.9 lagging. Complete Table 1 as required. [2]e) Calculate the new phasor current I sn for the new power factor corrected system.

This problem involves complex power, power factor correction, and phasor diagrams. Let's solve it step by step:

a) The power triangle for each load can be drawn using the given power factor and power. The power factor (PF) is the cosine of the angle between the power (P) and the apparent power (S).

For Load 1:

• Real Power (P1) = S1 * PF1 = 10kVA * 0.6 = 6kW
• Reactive Power (Q1) = S1 * sin(arccos(PF1)) = 10kVA * sin(arccos(0.6)) = 8kVAR (lagging)

For Load 2:

• Real Power (P2) = S2 = 2kW
• Reactive Power (Q2) = S2 * tan(arccos(PF2)) = 2kW * tan(arccos(0.9)) = -1kVAR (leading)

b) The combined load power triangle can be calculated by adding the real and reactive powers of the two loads:

• Total Real Power (P) = P1 + P2 = 6kW + 2kW = 8kW
• Total Reactive Power (Q) = Q1 + Q2 = 8kVAR - 1kVAR = 7kVAR
• Total Apparent Power (S) = sqrt(P^2 + Q^2) = sqrt((8kW)^2 + (7kVAR)^2) = 10.63kVA

c) The phasor current Is can be calculated using the formula S = VsIs*:

• Is = S / Vs = 10.63kVA / 240V = 44.29A

d) To correct the power factor to 0.9 lagging, we need to add capacitive reactive power (Qc). The new total reactive power (Qn) for a lagging power factor is given by:

• Qn = P * tan(arccos(0.9)) = 8kW * tan(arccos(0.9)) = 3.83kVAR
• Therefore, Qc = Q - Qn = 7kVAR - 3.83kVAR = 3.17kVAR

e) The new phasor current Isn for the power factor corrected system can be calculated using the new apparent power Sn = sqrt(P^2 + Qn^2):

• Sn = sqrt((8kW)^2 + (3.83kVAR)^2) = 8.83kVA
• Isn = Sn / Vs = 8.83kVA / 240V = 36.79A

Please note that all the calculations are approximate and the actual values may vary depending on the exact values of the power factors and the voltage.