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Mesh and Node Equations More Circuits Containing Dependent

# Mesh and Node Equations More Circuits Containing Dependent...

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Mesh and Node Equations: More Circuits Containing Dependent Sources Introduction The circuits in this set of problems each contain a single dependent source. These circuits can be analyzed using mesh equation or using node equations. When doing so, it is useful to express the controlling current or voltage of the dependent source as a function of the mesh currents or node voltages. Node equations are discussed in Sections 4.3, 4.4 and 4.5 of Introduction to Electric Circuits by R.C. Dorf and J.A Svoboda. Section 4.5 considers circuits that contain dependent sources. Mesh equations are discussed in Sections 4.6 and 4.7. Section 4.7 considers circuits that contain dependent sources. Worked Examples Example 1: Consider the circuit shown in Figure 1. Find the value of the gain, A, of the VCVS. Figure 1 The circuit considered in Example 1. Solution: Figure 2 shows the circuit from Figure 1 after replacing the voltmeter by an equivalent open circuit and labeling the voltage measured by the voltmeter. We will analyze this circuit by writing and solving node equations. Figure 3 shows the circuit after selecting a reference node and numbering the other nodes. Let v 1 , v 2 and v 3 denote the node voltages at nodes 1, 2 and 3, respectively.

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Figure 2 The circuit from Figure 1 after replacing the voltmeter by an open circuit. Figure 3 The circuit from Figure 2 after labeling the nodes.
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