Question

A factory consumes 6.4 kW in its heating system, it has 12 bulbs of 60 W, a load of 5 HP due to a motor block and an applied load equivalent to (9 - j 12) ohm. The 4 loads are connected in parallel, the motors have a power factor of 0.72 behind with an efficiency of 82%. The heater is the resistance heater type responsible for generating high temperatures. The factory is connected to a 208V, 60Hz supply.

a) Calculate the average power, the apparent power, the reactive power and power factor (pdf) for each branch

b) Find the total number of Watts, Volt Ampere Reactive and Volt Amper, as well as the power factor (pdf) of the system. Draw the triangle of powers.
c) Calculate the total current phasor.

Answer 1

Cet diagram: 24 "DB 2M '2 Vs 208V Goltz www ►g. thun -j12 - Heater of 6.4KW 12 bulbs SHP Reactive Motor load of Gow 5HP mator will provide 5 HP 5x785.5=3678.5W in / As its efficienez is given to be 82%, . Input active power consumed by Mador. 3679.5 (4.84.95 0.82 Jince its power factor is given to be 0.f2 (lag.) if Apparent power of motor - Sm, then Sm x 0.722 ļ484 .75 » 208*/2m/x 0-7229986-7 12ml 29.94A :: Rm > 29.94 [cost0:42 a 29.947-66°>(21.56–320.73)A In case of the reactive load, ZL=g-jizz 15 2-53-182 208 Di 213.866_58-13° -(8-32 +011.17 A 6.bgre? Io ease of the heater, Di 330.77 A 132-53.13 208 26 the Bulbs, 60012 208 3.66 A And in case of b Total no. of watts Is 2.DH+ PB + 2m + 2 = (66.11-39.68) A 64.84 (-8.586° zrxa cosa > 208466-8% x cos(-80586) 13335.56 Watt. Total VAR z rodz 208864.84313486.72 VA Total VAR zvor.finq=298864.890 bin 8.586 ?2013.48 LAR power factor = cos fo586° Power triangle 20.9988 (lagi) . 13335.36W 2013 .48 VARI 13486 72vA ) 1 for Heater Average power 6.6kW, Reactive powers in Apparent power 36.6kw. for Bulbs: Average power af20w, Reactive power to i. Apparent power 72ow. for moder: 2m > 29.94 Z-404 ". Arenag power 208 29.99x cos 44', Reactive power 2086 29.990 linger 24683.8W = 6321.76 nie And Apparent power a 208829.9426227.5A for the Reactive lond: Rj z 13.866 253.13 :. Average powers 208x13.826x Cos 53.13² 21730.68W Reactive power era 2088 13.866 x Sin 53.100 2 2367.3 VAR and Apparent power = 2088 13.866 288 6.128 VA - Total Current ire. De 3 = 64.84 %-8.586° - Phassor Vs = 208 20° De=69.892-8.586