Consider a series circuit (Figure 4) consisting of a resistor of R ohms, an inductor of L

Question:

Consider a series circuit (Figure 4) consisting of a resistor of R ohms, an inductor of L henries, and a variable voltage source of V(t) volts (time t in seconds). The current through the circuit I(t) (in amperes) satisfies the differential equation

dI R + - -I dt L V(t) - -V(t) L R

Assume that R = 110 ohms, L = 10 henries, and V(t) = e^−tvolts.
(a) Solve Eq. (9) with initial condition I(0) = 0.

dI R + - -I dt L V(t) R -V(t) L

(b) Calculate t_m and I(_tm), where t_m is the time at which I(t) has a maximum value.
(c) Use a computer algebra system to sketch the graph of the solution for 0 ≤ t ≤ 3.