Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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### Circuit Analysis Exercise #### Problem Statement: Determine the value for the voltage \( V_x \) using the following three methods: 1. **Nodal Analysis** 2. **Mesh Analysis** 3. **Thevenin's theorem** by finding the Thevenin equivalent circuit seen by the 4Ω resistor. #### Circuit Description: The given circuit features a combination of resistors, an independent current source, an independent voltage source, and a dependent current source. Refer to the circuit diagram below for component placement and connection: - **Current Source**: 10A source - **Voltage Source**: 100V source - **Resistors**: - A 1Ω resistor in series with the 10A current source - Two 4Ω resistors in series-parallel configuration - A 6Ω resistor in series with the 100V voltage source - **Dependent Current Source**: \( 2I_a \), where \( I_a \) is the current flowing through the 1Ω resistor #### Diagram Analysis: - The `10A current source` is located at the extreme left of the circuit. - The `1Ω resistor` lies in series to the 10A current source, placed just to its right. - The `\(I_a\)` denotes the current through the `1Ω resistor`. - A `4Ω resistor` is connected in series immediately to the right of the 1Ω resistor. - The node where the series 4Ω connects also branches upward to another `4Ω resistor`, continuing rightward. - The rightmost 4Ω resistor connects to a `6Ω resistor`. - The `100V voltage source` is depicted at the extreme right of the diagram, in series with the 6Ω resistor. - At the central node between the two 4Ω resistors lies the voltage \( V_x \). - The dependent current source \( 2I_a \) connects the bottom node with the central node where \( V_x \) is located. ##### Analysis Methods: **A. Nodal Analysis:** - Use Kirchhoff’s current law (KCL) to determine the node voltages. - Express the current through each resistor in terms of node voltages and solve the resulting system of equations. **B. Mesh Analysis:** - Apply Kirchhoff’s voltage law (KVL) to each independent loop. - Define mesh currents, set up equations according to
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Transcribed Image Text:### Circuit Analysis Exercise #### Problem Statement: Determine the value for the voltage \( V_x \) using the following three methods: 1. **Nodal Analysis** 2. **Mesh Analysis** 3. **Thevenin's theorem** by finding the Thevenin equivalent circuit seen by the 4Ω resistor. #### Circuit Description: The given circuit features a combination of resistors, an independent current source, an independent voltage source, and a dependent current source. Refer to the circuit diagram below for component placement and connection: - **Current Source**: 10A source - **Voltage Source**: 100V source - **Resistors**: - A 1Ω resistor in series with the 10A current source - Two 4Ω resistors in series-parallel configuration - A 6Ω resistor in series with the 100V voltage source - **Dependent Current Source**: \( 2I_a \), where \( I_a \) is the current flowing through the 1Ω resistor #### Diagram Analysis: - The `10A current source` is located at the extreme left of the circuit. - The `1Ω resistor` lies in series to the 10A current source, placed just to its right. - The `\(I_a\)` denotes the current through the `1Ω resistor`. - A `4Ω resistor` is connected in series immediately to the right of the 1Ω resistor. - The node where the series 4Ω connects also branches upward to another `4Ω resistor`, continuing rightward. - The rightmost 4Ω resistor connects to a `6Ω resistor`. - The `100V voltage source` is depicted at the extreme right of the diagram, in series with the 6Ω resistor. - At the central node between the two 4Ω resistors lies the voltage \( V_x \). - The dependent current source \( 2I_a \) connects the bottom node with the central node where \( V_x \) is located. ##### Analysis Methods: **A. Nodal Analysis:** - Use Kirchhoff’s current law (KCL) to determine the node voltages. - Express the current through each resistor in terms of node voltages and solve the resulting system of equations. **B. Mesh Analysis:** - Apply Kirchhoff’s voltage law (KVL) to each independent loop. - Define mesh currents, set up equations according to
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