I have some difficulties in parts 3 and 4 of the following problem:
(1) A sufficient time has elapsed after closing the switch S, and a steady state is established in the circuit with a constant current I0 flowing. Find the expression for I0.
(2) Then the switch S is opened. At this moment, the time t is defined as t = 0. Find vAB (t = 0+), the voltage appearing between the two switch terminals A and B immediately after opening the switch (t = 0+). vAB (t) is taken positive at terminal A with respect to terminal B.
(3) A sufficient time has elapsed after opening the switch S, and a steady state is established in the circuit. Find vAB (t = ∞), the voltage appearing between the two switch terminals A and B in the steady state.
(4) Find the expressions for i(t) and vAB(t) for t > 0 after opening the switch S at t = 0. Here, i(t) is
the current flowing in the circuit. In this Question (4), use the following circuit constants:
The Attempt at a Solution
(1) Io = Vo/R
(2) Vab = Vr1 = Vo(R1 / (R1+R2))
(3) Vab = Vc = Vo
(4) After KVL, laplace, (using Vo/R as Io of the inductor) I get i(t) as:
i(t) = e^(-t) + 3 e^(-5t)
And to get the voltage between a and b:
Vab(t) = Vr1(t) + Vc(t) = 4 i(t) + 5Int(i(t) dt) = -e^(-t) + 9 e^(-5t)
However, I checked Vab at t=0 and t=infinite, and does not match neither part 2 nor part 3, so something is wrong here...