Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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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:**
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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)**
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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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