Chapter 3.7, Problem 1P

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. $LI\text{'}+RI=E\left(t\right)$

In the circuit of Fig. 3.7.7, suppose that $L=5\text{H,}R=25\Omega$, and the source E of emf is a battery supplying 100 V to the circuit. Suppose also that the switch has been in position 1 for a long time, so that a steady current of 4 A is flowing in the circuit. At time $t=0$, the switch is thrown to position 2, so that $I\left(0\right)=4\text{and}E=0\text{for}t\underset{\_}{\underset{\_}{>}}0$. Find I (t ).