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Four 240v, 50Hz, 16kW motors are installed in a factory. Each has a power factor of 0.86 lagging and efficiency of 78.2% while running. Determine the shunt capacitance required to deliver unity power factor...

I'm not sure if I'm going about this question the right way. Any help would be much appreciated.

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The issue is that you are using the apparent power instead of the reactive power for Qc. The reactive power is apparent * sin(theta) or apparent *sin(acos(0.86)) = 12.14e3

All your other calculations look right, so use the same method from there on, and you should get about 0.67 mF.

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