Exercice Corrige Electrocinetique ✧

[ 0 = R i + V_C \quad \Rightarrow \quad RC \fracdV_Cdt + V_C = 0 ]

[ V_C(t) = E + A e^-t/RC ]

Thus ( B = 9.93 \ \textV ).

[ RC \fracdV_Cdt + V_C = E ]

[ V_C(t) = B e^-(t - t_1)/\tau ]

Solution:

[ E = V_R(t) + V_C(t) = R i(t) + V_C(t) ] exercice corrige electrocinetique

Initial condition at ( t = t_1^+ ): ( V_C(t_1) = 9.93 \text V ) (continuity of capacitor voltage).

Initial condition ( V_C(0) = 0 ): [ 0 = E + A \quad \Rightarrow \quad A = -E ] [ 0 = R i + V_C \quad

[ \boxed\tau = 100 \ \textms ] At ( t_1 = 0.5 \ \texts ):

[ V_C(t_1) = 10 \left(1 - e^-5\right) \approx 10 (1 - 0.0067) \approx 9.93 \ \textV ] The capacitor is almost fully charged. The source is disconnected, and the capacitor discharges through ( R ). The differential equation becomes: The source is disconnected, and the capacitor discharges