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1)A station supplies 250 kVA at a lagging power factor (p

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1)A station supplies 250 kVA at a lagging power factor (p.f) of 0·8.

A synchronous motor is connected in parallel with the load. If the combined load is 250 kW with a lagging p.f. of 0.9, determine : (i) the leading kVAR taken by the motor. (ii) kVA rating of the motor. (iii) p.f. at which the motor operates. 
 
2) A factory consists of the following (i) An induction motor of 150 h.p with 0.7 p.f lagging and 80% efficiency. (ii) A synchronous motor of 100 h.p with 0.85 p.f leading at 90% efficiency. (iii) A lightning load of 50kW. Find the annual electric charges if the tariff is Rs 100 per annum per kVA maximum demand plus 7 paise per kWh ; assuming the load to be steady throughout the year. 
 
3) A 3-phase, 400 V synchronous motor having a power consumption of 50 kW is connected in parallel with an induction motor which takes 200 kW at a power factor of 0·8 lagging. (i) Calculate the current drawn from the mains when the power factor of the synchronous motor is unity (ii) At what power factor should the synchronous motor operate so that the current drawn from the mains is minimum?