An induction motor is connected to a 3–phase line and runs at a synchronous speed of 1200 rpm. The copper loss and iron loss in the stator are totaled to 5 kW. As an engineer, you are required to provide the derivation, consideration and assumption that have been taken in your calculation. If the motor runs at 1152 rpm, determine: i. The active power transmitted to the rotor, P. ii. The rotor I 2R losses, Pjr. iii. The motor torque, Tm. iv. The mechanical power, Pm. v. The mechanical power delivered to a load Pi, knowing that the windage and friction losses are equal to 2 kW. vi. The efficiency of the motor, η

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?