In a factory, a three-phase, 4-kV, 400-kVA synchronous machine is installed along with other induction motors. The following are the loads on the machine:

(i) Induction motors: 500 kVA at 0.8 power factor lagging

(ii) Synchronous motor: 300 kVA at unity power factor

Determine the overall power factor of the factory loads.

1
\(\frac{7}{\sqrt{58}}\) lagging
2
\(\frac{7}{\sqrt{58}}\) leading
3
\(\frac{9}{\sqrt{58}}\) leading
4
\(\frac{9}{\sqrt{58}}\) lagging
5
none of these

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