A 250V, 50Hz single-phase supply feeds the following loads

(i) incandescent lamps taking a current of 10A at unity power factor,

(ii) fluorescent lamps taking 8A at a power factor of 0.7 lagging,

(iii) a 3kVA motor operating at full load and at a power factor of 0.8 lagging and

(iv) a static capacitor

Determine, for the lamps and motor,

(a) the total current,

(b) the overall power factor and

(c) the total power.

(d) Find the value of the static capacitor to improve the overall power factor to 0.975 lagging.