Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Superposition Theorem
The superposition theorem is applied to linear systems. For such systems, the output from two different inputs equals the sum of the outputs from each input separately. On applying this theorem many times we get the output from any number of inputs equal…
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**Use superposition to find \( V_0 \) in the circuit below.** **Circuit Description:** - **Voltage Source (\( V_1 \)):** 20V - **Current Source (\( I_1 \)):** 1A - **Dependent Current Source (\( I_2 \)):** 4A - **Resistors:** - \( R_1 \): 3 ohms - \( R_2 \): 8 ohms - \( R_3 \): 4 ohms - \( R_4 \): 12 ohms **Diagram Explanation:** The circuit diagram shows a configuration with a mix of voltage and current sources along with four resistors. The task is to determine the voltage \( V_0 \) across \( R_1 \) (3 ohms) using the superposition method. The circuit configuration requires analyzing each source independently, followed by combining their effects to find the resultant \( V_0 \). 1. **Voltage Source \( V_1 \) (20V) Analysis:** - Turn off the current sources (\( I_1 \) and \( I_2 \)) by replacing them with open circuits. - Calculate the contribution to \( V_0 \) due to \( V_1 \). 2. **Current Source \( I_1 \) (1A) Analysis:** - Turn off the voltage source \( V_1 \) by replacing it with a short circuit. - Handle the dependent current source \( I_2 \), as it depends on other circuit parameters. - Calculate the contribution to \( V_0 \) due to \( I_1 \). 3. **Dependent Current Source \( I_2 \) (4A) Analysis:** - Consider the operation as per its dependence. - Analyze the effect on \( V_0 \). **Combining Effects:** - Add the effects of each source to find the total voltage \( V_0 \) across \( R_1 \). Using superposition helps to simplify the analysis of complex circuits by focusing on one independent source at a time, making the problem more manageable.
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Transcribed Image Text:**Use superposition to find \( V_0 \) in the circuit below.** **Circuit Description:** - **Voltage Source (\( V_1 \)):** 20V - **Current Source (\( I_1 \)):** 1A - **Dependent Current Source (\( I_2 \)):** 4A - **Resistors:** - \( R_1 \): 3 ohms - \( R_2 \): 8 ohms - \( R_3 \): 4 ohms - \( R_4 \): 12 ohms **Diagram Explanation:** The circuit diagram shows a configuration with a mix of voltage and current sources along with four resistors. The task is to determine the voltage \( V_0 \) across \( R_1 \) (3 ohms) using the superposition method. The circuit configuration requires analyzing each source independently, followed by combining their effects to find the resultant \( V_0 \). 1. **Voltage Source \( V_1 \) (20V) Analysis:** - Turn off the current sources (\( I_1 \) and \( I_2 \)) by replacing them with open circuits. - Calculate the contribution to \( V_0 \) due to \( V_1 \). 2. **Current Source \( I_1 \) (1A) Analysis:** - Turn off the voltage source \( V_1 \) by replacing it with a short circuit. - Handle the dependent current source \( I_2 \), as it depends on other circuit parameters. - Calculate the contribution to \( V_0 \) due to \( I_1 \). 3. **Dependent Current Source \( I_2 \) (4A) Analysis:** - Consider the operation as per its dependence. - Analyze the effect on \( V_0 \). **Combining Effects:** - Add the effects of each source to find the total voltage \( V_0 \) across \( R_1 \). Using superposition helps to simplify the analysis of complex circuits by focusing on one independent source at a time, making the problem more manageable.
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