EXAMPLE 4 Consider the electric circuit shown in the figure and modeled by the differential equation below. LI+RI = E(t) dt Find an expression for the current in a circult where the resistance is 12 01, the inductance is 4 H, a battery gives a constant voltage of 48 V, and the switch is turned on when t-0. What is the limiting value of the current? SOLUTION With L-4, R-12, and E(t)- 48, the equation becomes +127-48 or di dt and the initial value problem is di 12-31 I(0) - 0. We recognize this equation as being separable, and we solve it as follows: J12 -In112-311