Lecture 9

1. Lecture 9 Review: Mesh analysis Constrained loops Additional mesh analysis examples Related educational modules: Sections 1.6.2

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