A balanced star connected load of (2+j3) Ω per phase and a balanced delta-connected load of(6+j6) Ω per phase are connected in parallel to a three phase, 400V, 50Hz supply. Calculate thephase current in each load, the total current in each supply line, the total power supplied and theoverall power factor.

To solve this problem, we need to follow these steps:

Step 1: Calculate the phase voltage for the star connected load. Since it's a balanced star connected load, the phase voltage Vph = Vline/√3 = 400/√3 = 230.94V

Step 2: Calculate the phase current for the star connected load. The phase current Iph = Vph/Z = 230.94/(2+j3) = 69.28∠-56.31A (where ∠-56.31 is the phase angle)

Step 3: Calculate the line current for the star connected load. Since it's a star connection, the line current is equal to the phase current, so Iline_star = Iph = 69.28∠-56.31A

Step 4: Calculate the phase voltage for the delta connected load. Since it's a balanced delta connected load, the phase voltage Vph = Vline = 400V

Step 5: Calculate the phase current for the delta connected load. The phase current Iph = Vph/Z = 400/(6+j6) = 33.33∠-45A

Step 6: Calculate the line current for the delta connected load. Since it's a delta connection, the line current is √3 times the phase current, so Iline_delta = √3*Iph = 57.74∠-45A

Step 7: Calculate the total current in each supply line. The total current in each supply line is the sum of the line currents of the star and delta connected loads, so Iline_total = Iline_star + Iline_delta = 69.28∠-56.31A + 57.74∠-45A = 127.02∠-50.65A

Step 8: Calculate the total power supplied. The total power supplied P = √3VlineIline_totalcosθ = √3400127.02cos(-50.65) = 35.36kW

Step 9: Calculate the overall power factor. The overall power factor is the cosine of the phase angle, so PF = cos(-50.65) = 0.63 lagging.

So, the phase current in each load is 69.28∠-56.31A for the star connected load and 33.33∠-45A for the delta connected load, the total current in each supply line is 127.02∠-50.65A, the total power supplied is 35.36kW, and the overall power factor is 0.63 lagging.