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20095ee110_1_hw4 - EE 110 Fall 2009 Homework#4 Due November...

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EE 110, Fall 2009, Homework #4, Due November 5, 2009 Problem 1: Refer to Figure 1 for this problem. (a) Write the integro-differential equa- tions that govern the behavior of vol- tage v ds (t). (b) Convert the equations in part (a) into the s-domain using the Laplace transform. (c) Draw the s-domain equivalent of the circuit shown in the figure including the initial conditions appropriately. (d) Obtain an expression for V ds (s), the Laplace transform of v ds (t), by using node voltage or mesh current method on the s-domain circuit obtained in part (c). (e) Compute v ds (t). (f) Identify transient and steady state components of v ds (t). (5 + 5 + 5 + 10 + 10 + 5 = 40 points) Problem 2: Refer to Figure 2 for this problem. For the first two parts of the problem, do not subs- titute any numerical values. (a) Transform the circuit shown in Figure 1 into the s-domain. We are interested in the behavior of the circuit for t 0. Let I(s) be the Laplace transform of i(t)u(t). (b) Obtain an expression for V o (s), the Laplace
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