Find the ordinary differential equation relating a current source i_s(t) = cos(?₀t) with the current i_L(t) in an inductor, with inductance L = 1 Henry, connected in parallel with a resistor of R = 1? ?(see Figure 0.23). Assume a zero initial current in the inductor.

(a)?Obtain a discrete equation from the ordinary differential equation using the trapezoidal approximation of an integral.

(b) Create a MATLAB script to solve the difference equation for T_s = 0.01 and for three frequencies for i_s(t), ?₀ = 0.005?, 0.05?, and 0.5?. Plot the input current source i_s(t) and the approximate solution i_L(nT_s) in the same figure. Use the MATLAB function plot. Use the MATLAB function filterto solve the difference equation (use helpto learn about filter).

(c) Solve the ordinary differential equation using symbolic MATLAB when the input frequency is ?₀ = 0.5?. Compare is(t) and i_L(t).

Figure 0.23:

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Transcribed Image Text:

iL (t) i, (t) ( ↑ 1H