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(i) For the circuit described in Q4(b), use Nodal Analysis to show that the circuit behaviour for t > 0 can be described by a characteristic equation of the form given in equation 4.1. s2 + 2as + w3 (4.1) Where the variables have their usual meaning, and where a and wo can be expressed in terms of the resistance, capacitance and inductance values. (ii) P Calculate the values of a and wo, and hence find a value for wa The switch-inductor-capacitor network of Figure 4.2 is instead attached across the terminals a, b of the circuit shown Figure 4.1. Calculate the current that will be measured through the 30 Q resistor for t»0 (a long time after the switch was closed).

(i) For the circuit described in Q4(b), use Nodal Analysis to show that the circuit behaviour for t > 0 can be described by a characteristic equation of the form given in equation 4.1. s2 + 2as + w3 (4.1) Where the variables have their usual meaning, and where a and wo can be expressed in terms of the resistance, capacitance and inductance values. (ii) P Calculate the values of a and wo, and hence find a value for wa The switch-inductor-capacitor network of Figure 4.2 is instead attached across the terminals a, b of the circuit shown Figure 4.1. Calculate the current that will be measured through the 30 Q resistor for t»0 (a long time after the switch was closed).

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
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I am looking for solutions to Q4 part (c) and (d) please. I have uploaded the full question as I assumed this all fell under the 1 question and they are all interlinked. Thanks in advance for your time and help

Question 4 4. (a) Construct a Thévenin equivalent circuit across the terminals a, b for the circuit shown in Figure 4.1. 25 N a 8 V 1 A 30 Ω b Figure 4.1 (b) The switch-capacitor-inductor network shown in Figure 4.2 is placed across the terminals of a Thévenin equivalent circuit with an open circuit voltage of 10 V and Thévenin equivalent resistance of 10 0. There is no energy stored in either the capacitor or inductor at time t = 0. For the resulting circuit, give the following values, assuming the switch is closed at t = 0: (i) the initial voltage across the capacitor (t = 0) (ii) the final steady state voltage across the capacitor (t >> 0) (ii) the initial current through the inductor (t = 0) (iv) the final steady state current through the inductor (t >> 0) t = 0 a b 10 nF 100 µH Figure 4.2 Question 4 is continued on the next page
Transcribed Image Text:Question 4 4. (a) Construct a Thévenin equivalent circuit across the terminals a, b for the circuit shown in Figure 4.1. 25 N a 8 V 1 A 30 Ω b Figure 4.1 (b) The switch-capacitor-inductor network shown in Figure 4.2 is placed across the terminals of a Thévenin equivalent circuit with an open circuit voltage of 10 V and Thévenin equivalent resistance of 10 0. There is no energy stored in either the capacitor or inductor at time t = 0. For the resulting circuit, give the following values, assuming the switch is closed at t = 0: (i) the initial voltage across the capacitor (t = 0) (ii) the final steady state voltage across the capacitor (t >> 0) (ii) the initial current through the inductor (t = 0) (iv) the final steady state current through the inductor (t >> 0) t = 0 a b 10 nF 100 µH Figure 4.2 Question 4 is continued on the next page
(c) (i) For the circuit described in Q4(b), use Nodal Analysis to show that the circuit behaviour for t>0 can be described by a characteristic equation of the form given in equation 4.1. s2 + 2as + wž (4.1) Where the variables have their usual meaning, and where a and wo can be expressed in terms of the resistance, capacitance and inductance values. (ii) Calculate the values of a and wo, and hence find a value for wa (d) The switch-inductor-capacitor network of Figure 4.2 is instead attached across the terminals a, b of the circuit shown in Figure 4.1. Calculate the current that will be measured through the 30 Q resistor for t>>0 (a long time after the switch was closed).
Transcribed Image Text:(c) (i) For the circuit described in Q4(b), use Nodal Analysis to show that the circuit behaviour for t>0 can be described by a characteristic equation of the form given in equation 4.1. s2 + 2as + wž (4.1) Where the variables have their usual meaning, and where a and wo can be expressed in terms of the resistance, capacitance and inductance values. (ii) Calculate the values of a and wo, and hence find a value for wa (d) The switch-inductor-capacitor network of Figure 4.2 is instead attached across the terminals a, b of the circuit shown in Figure 4.1. Calculate the current that will be measured through the 30 Q resistor for t>>0 (a long time after the switch was closed).
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