Question

) For the circuit shown in Figure 1, analytically determine ve() and i() for 12 0, assuming the inductor has no stored energy at the switching event. For numerical verification purposes, your Matlab and Multisim plots should be over the range t 0,5] seconds. 1A 0.04FD) 8 2 1H Figure 1. Circuit for Problem I.

Answer 1

The (t > 0) ckt in Laplace-domain (S-domain) (1) by current division rule: - I_L (S) = (1/S) times [(8 times 25/S)/[(8 times 25/S) + (8 times S) + (25/S times S)] = 1/S times (25 times 8/S)/[(25 times 8/S) 8S + 25] [(25 times 8/S)/(25 times 8) + 8 S^2 + 25 S] = [25/S (S^2 + (25/8) S + 25)] = (1/S) - (8S + 25/8 S^2 + 25S + 200) \r\n = (1/S) - (S + (25/8/S^2 + (25/8) S + 25) S^2 + 2 (25/16) S + (25/16)^2 + (25 - (25/16)^2] (S + 25/16)^2 + (squareroot 22.568)^2 4.75 [(S + a)^2 + w^2] form = (1/S) - { [S/(S + 25/16)^2 + (squareroot 22.568)^2 4.75 + (25/8)/(4.75) [(4.75)/(S + 25/16)^2 + (4.75)^2] } downarrow taking Inverse Laplace Therefore i_L (t) = n (t) - {e^- (25/16) t cos (4.75 t) - 0.657 e^- (25/16) t sin (4.75 t) } rightarrow i_L (t) = u (t) - e^- (25/16) t cos (4.75 t) - 0.657 e^- (25/16) t sin (4.75 t)