+il v(7)dz + cila = 9 +C Consider the source-free parallel RLC circuit. Applying KCL to the top node gives 1 - dv = 0 R

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Il V 7 Dz Cila 9 C Consider The Source Free Parallel Rlc Circuit Applying Kcl To The Top Node Gives 1 Dv 0 R 1 (143.28 KiB) Viewed 29 times

+il v(7)dz + cila = 9 +C Consider the source-free parallel RLC circuit. Applying KCL to the top node gives 1 - dv = 0 R dt The resulting second order differential equation with respect to v(t) is dv 1 do 1 + + V=0 dt2 RC dt LC Assuming that v(0) = 5V, i(0) = 0, L = 1H, C = 10mF. We consider three cases with different values of resistance R. = (a) R= 1.9232 (b) R=512 (C) R = 6.25 12 In each of the cases below, find the expression of v(t) and use MATLAB to plot it over the interval between 0 and 1 second. For each case, your submission must include • Your derivation of the expression of v(t) • Your plot with a title that indicates the level of damping (overdamped, critically-damped or underdamped), a x-label (with the proper unit) and (3) a y-label (with the proper unit). The fontsize of the title and labels must be adequate. • the MATLAB script used to generate the plot.