Consider an L-R circuit as shown in (Figure 1). The battery provides a voltage V. The inductor has inductance L, and the resistor has resistance R. The switch is initially open as shown. At time t 0,...

What is the differential equation governing the growth of current in the circuit as a function of time after t=0?

Express in terms of dI(t)/dt, I(t), V_b,R, and L

Solve the differential equation obtained in Part A for the current I(t) as a function of time after the switch is closed at t=0.

Express in terms of V_b, R, and L. Use the notation exp(x) for e^x

Extracted text: Consider an L-R circuit as shown in (Figure 1). The battery provides a voltage V. The inductor has inductance L, and the resistor has resistance R. The switch is initially open as shown. At time t 0, the switch is closed. Figure 1 of 1 I(t) R