Please show ALL steps taken to solve this problem. Willrate LIFESAVER! Thanks a

Question

Please show ALL steps taken to solve this problem. Willrate LIFESAVER! Thanks a bunch! In the circuit shown below, two loads A and B are connected in parallel. The supply voltage is 1.0kV-rms at 60 Hz. Load A consumes 10kW of power at 90 percent lagging power factor. Load B takes an apparent power of 15kVA at 80% leading power factor. Assume the supply voltage as reference. Calculate the currents IA, IB, and the supply current as phasors. Also find the total supplied P and Q, and the supply power factor.

Explanation / Answer

Load A PA = 10kW PFA= 0.8 laggin Phase difference between V and IAis A = cos-1 (0.9) =26o PA = V2 /ZA Magnitude of Imepdance of load A
ZA = V2 /PA ZA = (1000)2 /10000 ZA = 100 Magnitude of current |IA |= V /ZA |IA |= 1000 / 100 |IA |= 10A IA = 10/_-26oA Load B Apparent power SB = 15kVA Load B Apparent power SB = 15kVA PFB = 0.9 leading Phase difference between V and IBis B = cos-1 (0.8) =37o SB = VIB Magnitude of current through loadB |IB |= SB / V = 15000 /1000 |IB | = 15A IB = 15/_37oA Total curent I = IA + IB I = 10/_-26o +15/_37o I = 8.988 - j4.383 + 12 + j9 I = 20.988+j4.617 I = 21.4 /_12.4oA Phase difference between V and Iis = 12.4o Total reisitive power P = VIcos P = (1000)(21.4)cos(12.4) P = (21400) (0.9766) P = 20899 W Total reactive power Q = VIsin Q= (1000)(21.4)sin(12.4) Q = (21400) (0.215) Q = 4579.6VAR Total power factor PF = cos = cos (12.4) PF = 0.9766 Total reactive power Q = VIsin Q= (1000)(21.4)sin(12.4) Q = (21400) (0.215) Q = 4579.6VAR Total power factor PF = cos = cos (12.4) PF = 0.9766 Total power factor PF = cos = cos (12.4) PF = 0.9766

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