For a y-connected load, the time-domain expressions for three line-to-neutral voltages at the terminals are as follows:
van = 101 cos(ωt + 33∘) v
vbn = 101 cos(ωt − 87∘) v
vcn = 101 cos(ωt + 153∘) v
determine the time-domain expressions for the line-to-line voltages vab, vbc, and vca. report your answer so the magnitude is positive and all angles are in the range of negative 180° to positive 180°.

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)?