Consider the simple RL circuit shown below.
A step function e(t) is applied at t = 0. Solve the circuit for i(t) and vL(t) from
t = 0 to t = 10 ms as follows:
1. Solve (by hand) the differential equation of the continuous time system in terms
of the homogeneous plus steady-state solutions.
2. Discretize the circuit and write a computer program to obtain the step-by-step
solution in the following cases:
(a) Using the trapezoidal rule with ∆t1 = 0.1 ms.
(b) Using the backward Euler rule with ∆t1 = 0.1 ms.
(c) Using the trapezoidal rule with ∆t2 = 0.8 ms.
(d) Using the backward Euler rule with ∆t2 = 0.8 ms.
3. Plot (a) and (c) on the same graph. Plot (a) and (b) on the same graph. Plot (c)
and (d) on the same graph.
4. Make sure all graphs have labels that identify the variables and conditions.
5. Suggest possible improvements in your solution with respect to the basic solution
method explained in class.