A point charge of 1 nC carries over two paths in an electric field of = 2 + V / m. The first path starts at A (2, 30º, 0) and ends at point C (4, -90 º, 0) through the point B (2, -90 º, 0). The second path starts from the point A (2, 30º, 0) and ends at the point C (4, -90º, 0) through the point D (4, 30º, 0). Calculate the energy consumed while the load is transported separately on both paths.

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)?