Consider a series circuit (Figure 4) consisting of a resistor of R ohms, an inductor of L
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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
Assume that R = 110 ohms, L = 10 henries, and V(t) = e−t volts.
(a) Solve Eq. (9) with initial condition I(0) = 0.
(b) Calculate tm and I(tm), where tm 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.
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