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titanae

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## Homework Statement

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)

## Homework Equations

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

## The Attempt at a Solution

A) V_i = C(P_app - P_ex)(1- (e^(t/RC)))

B) V_T = C(- P_ex)((e^(t/RC))-1)

C) ??