Mesh and Node Equations More Resistive Circuits

Mesh and Node Equations More Resistive Circuits - Mesh and...

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Mesh and Node Equations: More Resistive Circuits Introduction The circuits in this set of problems consist of independent sources, resistors and a meter. In particular, these circuits do not contain dependent sources. These circuits can be analyzed using mesh equation or using node equations. Node equations are discussed in Sections 4.3 and 4.4 of Introduction to Electric Circuits by R.C. Dorf and J.A Svoboda. Mesh equations are discussed in Section 4.6. Worked Examples Example 1: Consider the circuit shown in Figure 1. Find the value of the resistance, R . Figure 1 The circuit considered in Example 1. Solution: Figure 2 shows the circuit from Figure 1 after replacing the ammeter by an equivalent short circuit and labeling the current measured by the ammeter. This circuit can be analyzed using mesh equations or using node equations. To decide which will be easier, we first count the nodes and meshes. This circuit has 5 nodes. Selecting a reference node and then applying KCL at the other four nodes will produce a set of four node equations. The circuit has three meshes. Applying KVL to these three meshes will produce a set of three mesh equations. Hence, analyzing this circuit using mesh equations instead of node equations will produce a smaller set of equations. Further, notice two of the three mesh currents can be determined directly from the current source currents. This makes the mesh equations easier to solve. We will analyze this circuit by writing and solving mesh equations. 1
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Figure 3 shows the circuit after numbering the meshes. Let i 1 , i 2 and i 3 denote the mesh currents in meshes 1, 2 and 3, respectively. Figure 2 The circuit from Figure 1 after replacing the ammeter by a short circuit. Figure 3 The circuit from Figure 2 after labeling the meshes. The mesh current i 1 is equal to the current in the 1 A current source so 1 1 A i = The mesh current i 2 is equal to the current in the 3 A current source so 2 3 A i = 2
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The mesh current i 3 is equal to the current in the short circuit that replaced the ammeter so 3 0.5 A
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Mesh and Node Equations More Resistive Circuits - Mesh and...

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