Determine the charge q(t) on the capacitor in an RLC-series circuit if L = 0.25 H, R = 10 Ω, C = 0.001 F, E(t) = 0 V, q(0) = 3 C, and q'(0) = 0. The governing equation is Lq'' + Rq' + 1/Cq = E(t).
Added by Mario M.
Step 1
First, we need to find the particular solution for the homogeneous equation Lq'' + Rq' + 1/c q = 0. The characteristic equation is Ls^2 + Rs + 1/c = 0, which has roots s1 = -R/2L + sqrt((R/2L)^2 - 1/LC) and s2 = -R/2L - sqrt((R/2L)^2 - 1/LC). Since the Show more…
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