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Mesh Analysis and Constrained Loops: Educational Examples

Learn how to apply mesh analysis, identify constrained loops, and solve circuit problems through practical examples from Chapter 3.3. Understand the concept of mesh currents and how to handle current sources within circuits. Practice using KVL and Ohm’s Law to calculate mesh currents and desired parameters.

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Mesh Analysis and Constrained Loops: Educational Examples

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  1. Lecture 9 Review: Mesh analysis Constrained loops Additional mesh analysis examples Related educational materials: Chapter 3.3

  2. Review: Mesh Analysis • Choose mesh loops and identify mesh currents • Kill sources • Identify enclosed, non-overlapping areas in circuit • Circuit elements bounding these areas form mesh loops • Mesh currents flow around the mesh loops • Replace sources, identify constrained loops • Apply KVL around mesh loops • Use Ohm’s Law to write KVL in terms of mesh currents • Solve equations to determine the mesh currents • Use mesh current to determine desired parameters

  3. Constrained Loops • Constrained loops go through current sources • They identify known currents in the circuit • Constrained loops are somewhat arbitrary, but: • Each current source creates a constrained loop • The direction and magnitude of the constrained loop must be consistent with the source through which it passes

  4. Mesh Analysis – Example 1 • Use mesh analysis to determine the current i4

  5. Example 1 – continued

  6. Example 1 – alternate constraint loops

  7. Example 1 – more alternate constraint loops

  8. Mesh analysis – example 2 • Determine i10, the current through the 10 resistor

  9. Example 2 – alternate approach

  10. Mesh analysis – example 3 • Use mesh analysis to determine the current i

  11. Example 3 – continued

  12. Mesh analysis – example 4 • Use mesh analysis to determine the current i10

  13. Example 4 – continued

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