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Answer all parts of the question. 1. For the given RLC circuit, answer the following questions. Consider initial conditions to be zero. Show necessary steps and supporting work to receive full credit. Giving a numerical result without showing supporting work may result in no credit being given. a) Derive transfer function Vo(s)/Vs(s). b) For input vs(t) = u(t). (i) Draw the pole zero diagram of the output. (ii) What is the type of damping the output of the circuit exhibits? c) For input vs(t) = 4 cos (2t + 15°) V. (i) Derive the steady state time domain expression of vo(t) for t≥ 0. 1 H vs(t) 1 F + vo(t) 292

Answer all parts of the question. 1. For the given RLC circuit, answer the following questions. Consider initial conditions to be zero. Show necessary steps and supporting work to receive full credit. Giving a numerical result without showing supporting work may result in no credit being given. a) Derive transfer function Vo(s)/Vs(s). b) For input vs(t) = u(t). (i) Draw the pole zero diagram of the output. (ii) What is the type of damping the output of the circuit exhibits? c) For input vs(t) = 4 cos (2t + 15°) V. (i) Derive the steady state time domain expression of vo(t) for t≥ 0. 1 H vs(t) 1 F + vo(t) 292

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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--- ### RLC Circuit Analysis **Question 1:** For the given RLC circuit, answer the following questions. Consider initial conditions to be zero. Show necessary steps and supporting work to receive full credit. Giving a numerical result without showing supporting work may result in no credit being given. a) Derive transfer function \(V_0(s)/V_s(s)\). b) For input \(v_s(t) = u(t)\): - (i) Draw the pole-zero diagram of the output. - (ii) What is the type of damping the output of the circuit exhibits? c) For input \(v_s(t) = 4 \cos (2t + 15^\circ)\) V: - (i) Derive the steady-state time domain expression of \(v_0(t)\) for \(t \geq 0\). --- **RLC Circuit Diagram:** The circuit consists of the following components connected in series: - Input voltage source \(v_s(t)\) - Inductor with inductance \(1 \, H\) - Capacitor with capacitance \(1 \, F\) - Resistor with resistance \(2 \, \Omega\) The output voltage \(v_0(t)\) is taken across the resistor. ``` v_s(t) ─── L(1H) ─── C(1F) ──── v_0(t) ──── R(2Ω) ──| |-------------------------------------------| ``` --- **Steps to Approach the Questions:** a) **Derivation of Transfer Function \( V_0(s)/V_s(s) \):** - Apply Kirchhoff's Voltage Law (KVL) and transform the circuit into the s-domain. - Solve for \( V_0(s)/V_s(s) \) using impedance and algebraic manipulation. b) **Analysis for \( v_s(t) = u(t) \) (Step Input):** - (i) Draw the pole-zero diagram based on the characteristic equation derived from the transfer function. - (ii) Determine the damping type (underdamped, critically damped, or overdamped) using the poles' locations in the s-plane. c) **Steady-State Response for \( v_s(t) = 4 \cos (2t + 15^\circ) \) V:** - Use the
Transcribed Image Text:--- ### RLC Circuit Analysis **Question 1:** For the given RLC circuit, answer the following questions. Consider initial conditions to be zero. Show necessary steps and supporting work to receive full credit. Giving a numerical result without showing supporting work may result in no credit being given. a) Derive transfer function \(V_0(s)/V_s(s)\). b) For input \(v_s(t) = u(t)\): - (i) Draw the pole-zero diagram of the output. - (ii) What is the type of damping the output of the circuit exhibits? c) For input \(v_s(t) = 4 \cos (2t + 15^\circ)\) V: - (i) Derive the steady-state time domain expression of \(v_0(t)\) for \(t \geq 0\). --- **RLC Circuit Diagram:** The circuit consists of the following components connected in series: - Input voltage source \(v_s(t)\) - Inductor with inductance \(1 \, H\) - Capacitor with capacitance \(1 \, F\) - Resistor with resistance \(2 \, \Omega\) The output voltage \(v_0(t)\) is taken across the resistor. ``` v_s(t) ─── L(1H) ─── C(1F) ──── v_0(t) ──── R(2Ω) ──| |-------------------------------------------| ``` --- **Steps to Approach the Questions:** a) **Derivation of Transfer Function \( V_0(s)/V_s(s) \):** - Apply Kirchhoff's Voltage Law (KVL) and transform the circuit into the s-domain. - Solve for \( V_0(s)/V_s(s) \) using impedance and algebraic manipulation. b) **Analysis for \( v_s(t) = u(t) \) (Step Input):** - (i) Draw the pole-zero diagram based on the characteristic equation derived from the transfer function. - (ii) Determine the damping type (underdamped, critically damped, or overdamped) using the poles' locations in the s-plane. c) **Steady-State Response for \( v_s(t) = 4 \cos (2t + 15^\circ) \) V:** - Use the
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