Chapter 8.4, Problem 27ES

The accompanying figure is a schematic diagram of a basic RL series electrical circuit that contains a power source with a time-dependent voltage of $V(t)$ volts $(V),$ a resistor with a constant resistance of R ohms $\Omega ,$ and an inductor with a constant inductance of L henrys $(\text{H)}\text{.}$ If you don’t know anything about electrical circuits, don’t worry; all you need to know is that electrical theory states that a current of $I(t)$ amperes (A) Flows through the circuit where $I(t)$ satisfies the differential equation $L\frac{dI}{dt}+RI=V(t)$

(a) Find $I(t)$ if R = $10\Omega ,L=5\text{H,}\text{V,}$ is a constant $\text{20V, and}I(0)=0\text{A}\text{.}$

(b) What happens to the current over a long period of time?