Using V_i(t_i) = V_T
show that
P_ex = [(e^(t_i/RC) - 1 )P_app] / (e^(t_tot/RC) - 1)
Eq 1: R(dV_i/dt) + (1/C)V_i + P_ex = P_app , 0 <= t <= t_i
Eq 2: R(dV_e/dt) + (1/C)V_e + P_ex = 0 , t_i <= t <= t_tot
A) Solve EQ 1 for V_i(t) with the initial condition V_i(0) = 0
B) Solve EQ 2 for V_e(t) with the initial condition V_e(t_i) = V_T
C) Using V_i(t_i) = V_T, show
P_ex = [((e^(t_i)/RC) - 1) * P_app] / ((e^(t_tot)/RC) - 1)
Knowns
V_i(0) = 0
V_e(t_i) = V_i(t_i) = V_T
V_e(tot) = 0
R, C, P_ex, P_app are constants
My solutions
A) V_i = C(P_app - P_ex)(1- (e^(t/RC)))
B) V_T = C(- P_ex)((e^(t/RC))-1)
C) ??
k This is the entire problem, does this help any??