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In the circuit below, please show your detailed calculations to solve for the magnitude and phase of voltage at node vo. Express your answer in the time domain after completing your phasor analysis. R1 R2 C2 R4 500 1000 2002 C3 С1 3.9mF V1 7.8mF :3.9mF Vo 5 Vpk 1kHz 0° L2 10mH R3 L1 100Q 10mH

In the circuit below, please show your detailed calculations to solve for the magnitude and phase of voltage at node vo. Express your answer in the time domain after completing your phasor analysis. R1 R2 C2 R4 500 1000 2002 C3 С1 3.9mF V1 7.8mF :3.9mF Vo 5 Vpk 1kHz 0° L2 10mH R3 L1 100Q 10mH

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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### Transcription and Explanation for Educational Purposes #### Text Transcription: "In the circuit below, please show your detailed calculations to solve for the magnitude and phase of voltage at node \(V_o\). Express your answer in the **time domain** after completing your phasor analysis." #### Circuit Diagram Description: The circuit consists of the following components: - **Source \(V_1\):** - Voltage: 5 V peak (Vpk) - Frequency: 1 kHz - Phase: 0° - **Resistors:** - \(R_1 = 50 \, \Omega\) - \(R_2 = 100 \, \Omega\) - \(R_4 = 200 \, \Omega\) - \(R_3 = 100 \, \Omega\) - **Capacitors:** - \(C_1 = 3.9 \, \text{nF} \) - \(C_2 = 3.9 \, \text{nF} \) - \(C_3 = 7.8 \, \text{nF} \) - **Inductors:** - \(L_1 = 310 \, \text{mH} \) - \(L_2 = 310 \, \text{mH} \) - **Output Voltage \(V_o\):** - Node \(V_o\) is located at the connection between \(R_3\), \(C_3\), and \(R_4\). #### Explanation: The task involves analyzing the given RLC circuit to determine the magnitude and phase of the voltage at node \(V_o\). The analysis starts by using phasor representation to handle the sinusoidal inputs and reactive components. Steps to perform the analysis: 1. **Impedance Calculations:** - Determine the impedance of each capacitor and inductor at the given frequency (1 kHz). - Capacitive impedance: \( Z_C = \frac{1}{j \omega C} \) - Inductive impedance: \( Z_L = j \omega L \) 2. **Phasor Analysis:** - Apply Kirchhoff's laws and use impedance values to solve for voltages or currents in the phasor domain. 3. **Convert Results to Time Domain:**
Transcribed Image Text:### Transcription and Explanation for Educational Purposes #### Text Transcription: "In the circuit below, please show your detailed calculations to solve for the magnitude and phase of voltage at node \(V_o\). Express your answer in the **time domain** after completing your phasor analysis." #### Circuit Diagram Description: The circuit consists of the following components: - **Source \(V_1\):** - Voltage: 5 V peak (Vpk) - Frequency: 1 kHz - Phase: 0° - **Resistors:** - \(R_1 = 50 \, \Omega\) - \(R_2 = 100 \, \Omega\) - \(R_4 = 200 \, \Omega\) - \(R_3 = 100 \, \Omega\) - **Capacitors:** - \(C_1 = 3.9 \, \text{nF} \) - \(C_2 = 3.9 \, \text{nF} \) - \(C_3 = 7.8 \, \text{nF} \) - **Inductors:** - \(L_1 = 310 \, \text{mH} \) - \(L_2 = 310 \, \text{mH} \) - **Output Voltage \(V_o\):** - Node \(V_o\) is located at the connection between \(R_3\), \(C_3\), and \(R_4\). #### Explanation: The task involves analyzing the given RLC circuit to determine the magnitude and phase of the voltage at node \(V_o\). The analysis starts by using phasor representation to handle the sinusoidal inputs and reactive components. Steps to perform the analysis: 1. **Impedance Calculations:** - Determine the impedance of each capacitor and inductor at the given frequency (1 kHz). - Capacitive impedance: \( Z_C = \frac{1}{j \omega C} \) - Inductive impedance: \( Z_L = j \omega L \) 2. **Phasor Analysis:** - Apply Kirchhoff's laws and use impedance values to solve for voltages or currents in the phasor domain. 3. **Convert Results to Time Domain:**
This image contains data from an electrical circuit analysis at a frequency of 1000 Hz. The table lists various nodes and components with their respective magnitude (mag) and phase values in degrees. 1. **Frequency**: 1000 Hz 2. **Nodes and Components**: - **V(n001)**: - Magnitude: 5 - Phase: 0° - **V(n002)**: - Magnitude: 3.00297 - Phase: 36.0914° - **V(n003)**: - Magnitude: 1.44656 - Phase: 86.144° - **V(n005)**: - Magnitude: 0.482188 - Phase: 86.144° - **V(n004)**: - Magnitude: 1.44656 - Phase: 86.1518° - **V(vo)**: - Magnitude: 0.482188 - Phase: 86.1557° - **V(n006)**: - Magnitude: 3.00493 - Phase: 36.0914° - **I(C1)**: - Magnitude: 0.0478249 - Phase: -126.092° - **I(C2)**: - Magnitude: 0.0235221 - Phase: -172.018° - **I(C3)**: - Magnitude: 0.00482188 - Phase: 86.1557° - **I(L1)**: - Magnitude: 0.0478249 - Phase: -53.9077° - **I(R2)**: - Magnitude: 0.0230228 - Phase: -3.84733° - **I(R4)**: - Magnitude: 0.00482188 - Phase: -93.8443° - **I(R1)**: - Magnitude: 0.0235221 - Phase: -172.018° - **I(R3)**: - Magnitude: 0.0624547 - Phase: 145.495° - **I(V1)**
Transcribed Image Text:This image contains data from an electrical circuit analysis at a frequency of 1000 Hz. The table lists various nodes and components with their respective magnitude (mag) and phase values in degrees. 1. **Frequency**: 1000 Hz 2. **Nodes and Components**: - **V(n001)**: - Magnitude: 5 - Phase: 0° - **V(n002)**: - Magnitude: 3.00297 - Phase: 36.0914° - **V(n003)**: - Magnitude: 1.44656 - Phase: 86.144° - **V(n005)**: - Magnitude: 0.482188 - Phase: 86.144° - **V(n004)**: - Magnitude: 1.44656 - Phase: 86.1518° - **V(vo)**: - Magnitude: 0.482188 - Phase: 86.1557° - **V(n006)**: - Magnitude: 3.00493 - Phase: 36.0914° - **I(C1)**: - Magnitude: 0.0478249 - Phase: -126.092° - **I(C2)**: - Magnitude: 0.0235221 - Phase: -172.018° - **I(C3)**: - Magnitude: 0.00482188 - Phase: 86.1557° - **I(L1)**: - Magnitude: 0.0478249 - Phase: -53.9077° - **I(R2)**: - Magnitude: 0.0230228 - Phase: -3.84733° - **I(R4)**: - Magnitude: 0.00482188 - Phase: -93.8443° - **I(R1)**: - Magnitude: 0.0235221 - Phase: -172.018° - **I(R3)**: - Magnitude: 0.0624547 - Phase: 145.495° - **I(V1)**
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