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5. current input Consider the system shown below. Assume that the system is subject to a step (a) (b) u₁ (t) = = 0 for u₁(t) = 2 Amp and has initial conditions ec(0) = 2V, and I₁(0) = 1 Amp, where ec is the voltage across the capacitor and IL is the current through the inductor. (d) How many energy storage elements are in this system? What state variables would you use to represent the energy storage elements in this system? (c) Write the state variable equations in state-space representation. If you pick the first state variable (q1) that is associated with the capacitor and the second state variable (92) that is associated with the inductor, you should expect to get the following state-space representation: t≤ 0; for t> 0. = A i(t). Apply Laplace transform to the state-space representation, and also for the Laplace transform of the current in the inductor IL(t). Recall that the initial condi- tions are ec(0) = 2V, and IL(0) = 1 Amp. (e) 1₁ Use system parameters L = 1H, C = 0.5 F, and R = 40. Determine the time domain solution for IL(t). B 91 92 R + C IL [8] [1₁] D E L Figure 1: System for problem 5

5. current input Consider the system shown below. Assume that the system is subject to a step (a) (b) u₁ (t) = = 0 for u₁(t) = 2 Amp and has initial conditions ec(0) = 2V, and I₁(0) = 1 Amp, where ec is the voltage across the capacitor and IL is the current through the inductor. (d) How many energy storage elements are in this system? What state variables would you use to represent the energy storage elements in this system? (c) Write the state variable equations in state-space representation. If you pick the first state variable (q1) that is associated with the capacitor and the second state variable (92) that is associated with the inductor, you should expect to get the following state-space representation: t≤ 0; for t> 0. = A i(t). Apply Laplace transform to the state-space representation, and also for the Laplace transform of the current in the inductor IL(t). Recall that the initial condi- tions are ec(0) = 2V, and IL(0) = 1 Amp. (e) 1₁ Use system parameters L = 1H, C = 0.5 F, and R = 40. Determine the time domain solution for IL(t). B 91 92 R + C IL [8] [1₁] D E L Figure 1: System for problem 5

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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5. current input Consider the system shown below. Assume that the system is subject to a step (a) (b) and has initial conditions ec(0) = 2V, and I₁(0) = 1 Amp, where ec is the voltage across the capacitor and IL is the current through the inductor. u₁ (t) = = 0 for t≤ 0; u₁(t) = 2 Amp for t> 0. (d) How many energy storage elements are in this system? What state variables would you use to represent the energy storage elements in this system? (c) Write the state variable equations in state-space representation. If you pick the first state variable (q1) that is associated with the capacitor and the second state variable (92) that is associated with the inductor, you should expect to get the following state-space representation: = A B i(t). Apply Laplace transform to the state-space representation, and also for the Laplace transform of the current in the inductor IL(t). Recall that the initial condi- tions are ec(0) = 2V, and I₁(0) = 1 Amp. (e) 91 92 Use system parameters L = 1H, C = 0.5 F, and R = 40. Determine the time domain solution for IL(t). R + 1₁ :c IL [8] [₁] D E L Figure 1: System for problem 5
Transcribed Image Text:5. current input Consider the system shown below. Assume that the system is subject to a step (a) (b) and has initial conditions ec(0) = 2V, and I₁(0) = 1 Amp, where ec is the voltage across the capacitor and IL is the current through the inductor. u₁ (t) = = 0 for t≤ 0; u₁(t) = 2 Amp for t> 0. (d) How many energy storage elements are in this system? What state variables would you use to represent the energy storage elements in this system? (c) Write the state variable equations in state-space representation. If you pick the first state variable (q1) that is associated with the capacitor and the second state variable (92) that is associated with the inductor, you should expect to get the following state-space representation: = A B i(t). Apply Laplace transform to the state-space representation, and also for the Laplace transform of the current in the inductor IL(t). Recall that the initial condi- tions are ec(0) = 2V, and I₁(0) = 1 Amp. (e) 91 92 Use system parameters L = 1H, C = 0.5 F, and R = 40. Determine the time domain solution for IL(t). R + 1₁ :c IL [8] [₁] D E L Figure 1: System for problem 5
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