capacitance power factor question.

oxon88

1. The problem statement, all variables and given/known data

A 50 KW load operates from a 60 Hz 10KV rms line with a power factor of 60% lagging. Determine the capacitance that must be placed in parallel with the load to achieve a 90% lagging power factor.


3. The attempt at a solution



for 60% p.f:-

θ₁ = Cos^-1(0.6) = 53.13 degrees

Q₁ = 50,000*tan(53.13) = 66.667 kVAR

for 90% p.f:-

θ₂ = Cos^-1(0.9) = 25.84 degrees

Q₂ = 50,000*tan(25.84) = 24.22 kVAR



Q_capacitor = Q₂ - Q₁ = -42.45 kVAR



X_c = V_RMS /Q_c = (10⁴)² / -42450 = -2356 Ω


ω = 2.∏.f = 2.∏.60 = 377

C = 1 / ω.X_c = 1 / 377*2356 = 1.126 μF



can anyone check if i'm on the right path here please?

oxon88

anyone?

NascentOxygen

I posted a response to this about 6 hours ago, saying that's the answer I got.

Not sure where my reply went.

oxon88

Ok thats good. thank you