The voltage, v(t) and current i(t) input to a circuit is given by v(t) = 240 cos(2πt) and i(t) = v(t) 2 .What is the Power consumed by the circuit?. P = R T 0 v(t)i(t)dt, where T is the time period of the waveform v(t). (Steps would suce if you cannot quickly get the nal value).

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)?