Recall that the differential equation for the instantaneous charge q(t) on the capacitor in an lrc-series circuit is l d 2q dt 2
+ r dq dt + 1 c q = e(t). see this excerpt about lrc-series circuits. use the laplace transform to find q(t) when l = 1 h, r = 20 ω, c = 0.005 f, e(t) = 160 v, t > 0, q(0) = 0, and i(0) = 0. q(t) =
DE which is the differential equation represents the LRC series circuit where L d²q/dt² + Rdq/dt +I/Cq = E(t) = 150V. Initial condition is q(t) = 0 and i(0) =0. To find the charge q(t) by using Laplace transformation by Substituting known values for DE L×d²q/dt² +20 ×dq/dt + 1/0.005× q = 150 d²q/dt² +20dq/dt + 200q =150
