Problem 9.6-1

Once t > 0, the current source does not deliver any current anymore.

We have a series RLC circuit. We can notice that we have

Thus we know that we will have s1 = s2 = -α = - R/(2*L) = 2000

And we also know that the answer will be a critically damped response, thus

Vc(t) = (A₁ + A₂t)*exp( - 2000*t)

We are looking for A₁ and A₂.

For t = 0 we have Vc(0) = A1, and by the equivalent source we have a voltage of

V = R*I = 100*30.10^-3 = 3 V, so A₁ = 3 V

For A2, we need to use the derivative. We have

dV(t)/dt = (3 + A₂t)*( - 2000*exp( - 2000*t)) + A₂*exp( - 2000*t) = i(t)/C

For t = 0 we have 3*( - 2000) + A₂= i(0)/C, but i(0) = 0 A

Finally we get Vc(t) = (3 + 6000*t)*exp( - 2000*t)