Question

please answer all parts with steps

(15%) A three phase source supplies power to an induction motor drawing 10 kW at at 240 V and 0.60 power factor lagging, Find, >(a) The reactive power supplied by the source. (o) The apparent power drawn from the source. (c) The complex power drawn from the source. (d)The magnitude of the source current. If a capacitor is connected in parallel with the load, will the source current magnitude increase or decrease. (e)

Answer 1

Given p = 10 kw @ 0.60 pf lag v_c = 240 v peaxtive power supplied by source Long right double arrow Q = p tan theta cos theta = 0.6 theta = 53.13 degree Long right double arrow Q = 10 times tan 53.13 kvar Q = 13.33 kvar apparent power draw from source Vertical-bar s Vertical-bar = squareroot p^2 + Q^2 = squareroot 10^2 + 13.33^2 kva Vertical-bar s Vertical-bar = 16.667 kva complex power dear from source s = p + Q = 10 + j13.33 kva magnitude of source current p = squareroot 3 v_c I_c cos theta Long right double arrow i_L = p/squareroot 3 times 240 times 0.6 I_L = 40.1 amps.if a capacitor connected in parallel with load, power factor improves & p remains same. Long right double arrow I_c alpha p/cos theta Long right double arrow I_L alpha 1/cos theta as cos theta increases current decreases.