Consider the RL circuit shown in Figure P9.66. Assume that the current i(t) has reached
Chapter 9, Problem 9.66(choose chapter or problem)
Consider the RL circuit shown in Figure P9.66. Assume that the current i(t) has reached a steady state with the switch at position A. At time t = 0, the switch is moved from position A to position B.
(a) Find the differential equation relating i(t) and v2 fort > 0-. Specify the initial condition (i.e., the value of i(0-)) for this differential equation in terms of v1
(b) Using the properties of the unilateral Laplace transform in Table 9.3, determine and plot the current i(t) for each of the following values of v1 and v2:
(i) v1 = 0 V, v2 = 2 V
(ii) v1 = 4 V, v2 = 0 V
(iii) v1 = 4 V, v2 = 2 V
Using your answers for (i), (ii), and (iii), argue that the current i(t) may be expressed as a sum of the circuit's zero-state response and zero-input response.
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