Analysis the wiring of a house circuit having fluorescent labs, incandescent lamp and a single phase motor is supplied from a 230 V, 50 Hz single-phase supply. The load details: (i) fluorescent lamps taking a current of 8 A at a power factor of 0.9 leading, (ii) incandescent lamps taking a current of 6 A at unity power factor, (iii) a motor taking a current of 12 A at a power factor of 0.65 lagging. Determine the total current taken from the supply and the overall power factor. Find also the value of a static capacitor connected in parallel with the loads to improve the overall power factor to 0.98 lagging. Illustrate the solution with relevant phasor diagram.

Consider a power plant with water as the working fluid that operates on an ideal rankine cycle. it has a net power output of 45mw. superheated steam enters the turbine at 7mpa and 500°c (h=3411.4 kj/kg; s=6.8 kj/kg k) and is cooled in the condenser at a pressure of 10 kpa by running cooling water from a lake through the tubes of the condenser at a rate of 2000 kg/s. (a) show the cycle on a t-s diagram (a right schematic is fine - you do not need to calculate the temperatures at each point); (b)-determine the work done by the turbine and the pump in kj/kg; (c)-the mass flow rate of water used by the power plant; (d)-the thermal efficiency of the cycle; (e)-the temperature rise of the cooling water. assume the cooling water is incompressible with cp 4.18 kj/kg°c.