A voltage vL(t) = 5 cos (1000nt) V appears across a 50-mH inductor, where n is a positive integer that controls the frequency of the input signal. The amplitude of the input signal is constant. Assume iL(0) = 0 A. Use MATLAB and symbolic variables to compute an expression for iL(t).
On the same axes, plot iL(t) versus time for n = 1, 2, 3, 4, and 5, over an appropriate time scale.
On another set of axes, plot the amplitude of iL(t) versus the coefficient n.
As n approaches infinity, what happens to the amplitude of the current? What type of circuit element does the inductor behave like as n approaches infinity?