Chapter 10, Problem 15P

A constant current $i_s\left(t\right)=100\text{mA}$ is applied to the RL circuit shown in Fig. P10.15. Assume that the switch has been closed for a long time. At t = 0, the switch is opened instantaneously. For $t\ge 0$, the current $i\left(t\right)$ flowing through the resistor satisfies the following differential equation and initial condition:

¡(O) = 5OmA.

(a) Find the 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?

(e) Mark each of the following statements as true (T) or false (F):

__________Increasing the value of resistance R will increase the time the voltage $v\left(t\right)$ reaches 99 of its steady-state value.

__________Increasing the value of inductance L will decrease the time the voltage $v\left(t\right)$ reaches 99 of its steady-slate value.

__________Doubling the value of resistance R will double the time constant of the response.

__________Doubling the value of inductance L will double the time constant of the response.