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# We can solve eq 325 to obtain the unknown mesh

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Unformatted text preview: ircuit has N meshes, the mesh-current equations can be expressed in terms of the resistances as R1N i1 v1 R2N i2 v2 . . = . . . . . . . R11 R21 . . . R12 R22 . . . ... ... . . . RN 1 RN 2 . . . RN N iN (3.25) vN or simply Ri = v (3.26) where Rkk = Sum of the resistances in mesh k Rkj = Rj k = Negative of the sum of the resistances in common with meshes k and j , k = j ik = Unknown mesh current for mesh k in the clockwise direction vk = Sum taken clockwise of all independent voltage sources in mesh k , with voltage rise treated as positive R is called the resistance matrix, i is the output vector; and v is the input vector. We can solve Eq. (3.25) to obtain the unknown mesh currents. EXAMPLE 3.8 Write the node-voltage matrix equations for the circuit in Fig. 3.27 by inspection. 2A 1Ω v1 3A | v v Figure 3.27 | e-Text Main Menu 5 Ω v2 10 Ω 8Ω 1A 8Ω v3 4Ω v4 2Ω 4A For Example 3.8. | Textbook Table of Contents | Problem Solving Workbook Contents CHAPTER 3 Methods of Analysis 97 Solution: The circuit in Fig. 3.27 h...
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