ps2_08 - EE 350 PROBLEM SET 2 DUE 9 September 2008 Reading...

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EE 350 PROBLEM SET 2 DUE: 9 September 2008 Reading assignment: Lathi Sections 1.6 through 1.8 Recitation #2 will be held this week. Problem 7: (15 points) The input to the RL circuit shown in Figure 1 is the voltage f ( t ) and the output is the current y ( t ). The current in the inductor at time t =0is i L (0). - + f(t) y(t) RL i (t) L Figure 1: RL circuit with input voltage f ( t ) and output current y ( t ). 1. (2 points) Find an expression for the zero-input response, y z - i ( t ), for t 0. 2. (2 points) Give a physical explanation as to why the value of the zero-input response must be constant for this particular system. Hint: Is energy dissipated in the resistor as heat for t 0? 3. (2 points) Is the system zero-input linear? Justify your answer. 4. (4 points) Find an expression for the zero-state response, y z - s ( t ), for t 0. 5. (2 points) Is the system zero-state linear? Justify your answer. 6. (1 point) What is the total response of the system, y ( t ), for t 0? 7. (2 points) Is the electrical system shown in Figure 1 linear? Justify your answer. Problem 8: (16 points) Consider the circuit shown in Figure 2(a) where the input is the current f ( t ) and the output is the voltage y ( t ). Because the circuit contains no energy storage elements such as inductors or capacitors, the zero-input response is always zero. That is, the response y ( t ) consists only of the zero-state response. R 1 R 2 R 1 R 2 (a) (b) y(t) f(t) f(t) + - p(t) Figure 2: Simple resistive circuits with input current f ( t ). In (a) the output is the voltage across R 2 while in (b) the output is the power dissipated in R 2 . 1. (2 points) Find a relationship between the input f ( t ) and the output y ( t ) in terms of the resistances R 1 and R 2 .
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This note was uploaded on 10/13/2008 for the course EE 350 taught by Professor Schiano,jeffreyldas,arnab during the Fall '07 term at Penn State.

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ps2_08 - EE 350 PROBLEM SET 2 DUE 9 September 2008 Reading...

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