Chapter 3.7, Problem 2P

Problems 1 through 6 deal with the RL circuit of Fig. 3.7.7, a series circuit containing an inductor with an inductance of L henries, a resistor with a resistance of R ohms, and a source of electromotive force (emf), but no capacitor In this case Eq. (2) reduces to the linear first-order equation FIGURE 3.7.7. The circuit for Problems 1 through 6. $LI\text{'}+RI=E\left(t\right)$

Given the same circuit as in Problem 1, suppose that the switch is initially in position 2, but is thrown to position 1 at time $t=0$, so that $I\left(0\right)=0\text{and}E=100\text{for}t\underset{\_}{\underset{\_}{>}}0$. Find I (t ) and show that $I\left(t\right)\to 4\text{as}t\to +\infty$ .