- #1

oxon88

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## Homework Statement

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.

## The Attempt at a Solution

for 60% p.f:-

θ

_{1}= Cos

^{-1}(0.6) = 53.13 degrees

Q

_{1}= 50,000*tan(53.13) = 66.667 kVAR

for 90% p.f:-

θ

_{2}= Cos

^{-1}(0.9) = 25.84 degrees

Q

_{2}= 50,000*tan(25.84) = 24.22 kVAR

Q

_{capacitor}= Q

_{2}- Q

_{1}= -42.45 kVAR

X

_{c}= V

_{RMS}/Q

_{c}= (10

^{4})

^{2}/ -42450 = -2356 Ωω = 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?

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