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

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

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

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

Example 1 – continued

Example 1 – alternate constraint loops

Example 1 – more alternate constraint loops

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

Example 2 – alternate approach

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

Example 3 – continued

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

Example 4 – continued