Consider the electric circuit shown in Figure 7.6.6. Suppose that R1 = R2 = 4 , C = 1 2
Chapter 7, Problem 20(choose chapter or problem)
Consider the electric circuit shown in Figure 7.6.6. Suppose that R1 = R2 = 4 , C = 1 2 F, and L = 8 H. a. Show that this circuit is described by the system of differential equations d dt _I V _ = 1 2 1 8 2 12 _I V _, (32) where I is the current through the inductor and V is the voltage drop across the capacitor. Hint: See of Section 7.1. b. Find the general solution of equations (32) in terms of realvalued functions. c. Find I (t) and V(t) if I (0) = 2 A and V(0) = 3 V. d. Determine the limiting values of I (t) and V(t) as t . Do these limiting values depend on the initial conditions? R1 R2 L C FIGURE 7.6.6 The circuit in 20. 2
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