In Exercises 3538, consider a series circuit (Figure 4) consisting of a resistor of R
Chapter 9, Problem 37(choose chapter or problem)
In Exercises 3538, 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 dt + R L I = 1 LV (t) Assume that V (t) = V is constant and I (0) = 0. (a) Solve for I (t). (b) Show that limt I (t) = V /R and that I (t) reaches approximately 63% of its limiting value after L/R seconds. (c) How long does it take for I (t) to reach 90% of its limiting value if R = 500 ohms, L = 4 henries, and V = 20 volts?
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