Chapter 10, Problem 21P

The switch in the circuit shown in Fig. P10.21 has been in position 1 for a long time. At t=0, the switch is moved instantaneously to position 2. For $t\ge 0$, the current $i\left(t\right)$ flowing through the inductor satisfies the following differential equation and initial condition:

$0.2\frac{di\left(t\right)}{dt}+10i\left(t\right)=5$, $i\left(0\right)=-1\text{A}$.

(a) Find ¡he transient solution, $i_{tran}\left(t\right)$ .What is the time constant of the response?

(b) Find the steady-state solution $i_{ss}\left(t\right)$.

(c) Determine the total solution $i\left(t\right)$.

(d) Sketch the total solution $i\left(t\right)$. How long does it take for the response to reach 99% of its steady-state value?