[ RC \fracdV_Cdt + V_C = E ]
Initial condition ( V_C(0) = 0 ): [ 0 = E + A \quad \Rightarrow \quad A = -E ]
[ V_C(t) = B e^-(t - t_1)/\tau ]
[ E = V_R(t) + V_C(t) = R i(t) + V_C(t) ]
[ \boxed\tau = 100 \ \textms ] At ( t_1 = 0.5 \ \texts ): exercice corrige electrocinetique
Solution:
With ( i(t) = C \fracdV_Cdt ), we get:
Initial condition at ( t = t_1^+ ): ( V_C(t_1) = 9.93 \text V ) (continuity of capacitor voltage).