Asingle-phase, 50-kva, 2400/240-v, 60-hz distribution transformer has the following parameters: resistance of the 2400-v winding: r1 = 0.75 ω resistance of the 240-v winding: r2 = 0.0075 ω reactance of the 2400-v winding: x1 = 1.0 ω reactance of the 240-v winding: x2 = 0.01 ω (neglect the exciting admittance) the transformer is supplying a rated load of 50 kva at a rated secondary voltage of 240-v and 0.8 power factor lagging. if the transformer is used as a step-down transformer at the load end of a feeder whose impedance is 0.5 + .0 ω, find the voltage vs and the power factor at the sending end of the feeder.

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)?