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1. In the circuit shown in Figure 1, let Vs(t) = 5 u(t), RỊ = 20, R2 = 12, R3 = 12, L= 0.5H, C = 0.2F, i(0") = 2A, v(0') = 3V. R1 Va R2 Vo a b i(0-) v(0-) vo(t) R3 Figure 1 (a) Draw the circuit in the s-domain for t> 0. (b) Write a node equation at node a by summing the currents leaving node a. (c) Write a node equation at node b by summing the currents leaving node b. Vi(s) = V.(s). (d) Find Vo(s) in the s-domain. (e) Find vo(t) in the time domain by taking the inverse Laplace transform of Vo(s).

1. In the circuit shown in Figure 1, let Vs(t) = 5 u(t), RỊ = 20, R2 = 12, R3 = 12, L= 0.5H, C = 0.2F, i(0") = 2A, v(0') = 3V. R1 Va R2 Vo a b i(0-) v(0-) vo(t) R3 Figure 1 (a) Draw the circuit in the s-domain for t> 0. (b) Write a node equation at node a by summing the currents leaving node a. (c) Write a node equation at node b by summing the currents leaving node b. Vi(s) = V.(s). (d) Find Vo(s) in the s-domain. (e) Find vo(t) in the time domain by taking the inverse Laplace transform of Vo(s).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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1. In the circuit shown in Figure 1, let \( v_s(t) = 5 \, u(t), \, R_1 = 2\Omega, \, R_2 = 1\Omega, \, R_3 = 1\Omega, \, L = 0.5H, \, C = 0.2F, \, i(0^-) = 2A, \, v(0^-) = 3V \). **Figure 1 Description:** The circuit includes: - A voltage source \( v_s(t) \) connected to resistor \( R_1 \). - A series connected to inductor \( L \) and a node labeled \( a \). - A parallel branch connected through resistor \( R_2 \) leading to node \( b \) and capacitor \( C \). - Capacitor \( C \) is in parallel with resistor \( R_3 \). - The voltage across the capacitor: \( v(t) \). **Questions:** (a) Draw the circuit in the s-domain for \( t \geq 0 \). (b) Write a node equation at node \( a \) by summing the currents leaving node \( a \). (c) Write a node equation at node \( b \) by summing the currents leaving node \( b \). \( V_b(s) = V_o(s) \). (d) Find \( V_o(s) \) in the s-domain. (e) Find \( v_o(t) \) in the time domain by taking the inverse Laplace transform of \( V_o(s) \).
Transcribed Image Text:1. In the circuit shown in Figure 1, let \( v_s(t) = 5 \, u(t), \, R_1 = 2\Omega, \, R_2 = 1\Omega, \, R_3 = 1\Omega, \, L = 0.5H, \, C = 0.2F, \, i(0^-) = 2A, \, v(0^-) = 3V \). **Figure 1 Description:** The circuit includes: - A voltage source \( v_s(t) \) connected to resistor \( R_1 \). - A series connected to inductor \( L \) and a node labeled \( a \). - A parallel branch connected through resistor \( R_2 \) leading to node \( b \) and capacitor \( C \). - Capacitor \( C \) is in parallel with resistor \( R_3 \). - The voltage across the capacitor: \( v(t) \). **Questions:** (a) Draw the circuit in the s-domain for \( t \geq 0 \). (b) Write a node equation at node \( a \) by summing the currents leaving node \( a \). (c) Write a node equation at node \( b \) by summing the currents leaving node \( b \). \( V_b(s) = V_o(s) \). (d) Find \( V_o(s) \) in the s-domain. (e) Find \( v_o(t) \) in the time domain by taking the inverse Laplace transform of \( V_o(s) \).
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