Design a problem to help other students better understand how to find the rms voltage across and the rms current through an electrical element given a Fourier series for both the current and the voltage. In addition, have them calculate the average power delivered to the element and the power spectrum.

The voltage and current through an element are respectively
v(t) = [30 cos (t + 35°) + 10cos(2t – 55˚) + 4 cos(3t - 10°)] V
i(t) = [2 cos (t–10˚) + cos(2t – 10°)] A
(a) Find the average power delivered to the element
(b) Plot the power spectrum.