12 VDC 10 Ω 1.01 F 0.5 H
An RLC circuit, as shown in the figure, with
resistance R=10 ohms, capacitance C=0.01 farads and an inductor L=0.5 H, it also has a voltage source E(t) = 12 volts. Assuming that at time t=0 there is no charge on the capacitor and no current in the circuit, determine the charge on the capacitor and the current in the circuit from the moment the switch is closed. In solving this exercise you must calculate and present the following:
c) Determine the particular solution of the non-homogeneous differential equation qp, posing the simultaneous equations and their corresponding solution to establish the value of the indeterminate coefficients.
d) Determine the general solution for the charge on the capacitor, that is, q(t) = qh + qp
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