1. Chapter 4B Circuit Analysis Techniques
B) Mesh Current

2. Node Voltage and Mesh Current methods
derive a minimal set of equations
solve all circuit variables
Node Voltage uses KCL
Mesh Current uses KVL
NV more powerful than MC
MC only solves "planar circuits"

3. Mesh Current Method
Basic idea—What is the voltage v ?

4. Mesh Current Method
What if unknown currents?
branch current:

5. Mesh Current Method
ia,ib label unknown mesh currents

6. MC solves unknown mesh (loop) currents
Mesh: closed path around a loop (normally clockwise)
all other voltages and branch currents can be derived from ia, ib, ic

7. It can be proven...
The number of MC equations needed to fully solve a circuit is equal to the number of meshes.
Circuits like the previous with a lot of nodes can often be solved with fewer equations with MC than NV
Circuits with a lot of meshes can often be solved with fewer equations using NV than MC

8. Problem 1 Use mesh current analysis to find the voltage across each resistor. V15 = 1.52 V; V10 = 1.02 V; V7.5 = 762 mV

9. Find i1 using Mesh Current Method
label mesh currents
write KVL for each mesh
solve equations
derive i1 from ia,ib

10. Problem 3 Determine all of the mesh currents in the circuit. I1 = -0
Problem 3 Determine all of the mesh currents in the circuit. I1 = mA; I2 = 1.59 mA; I3 = 1.42 mA

12. Do handout problems 1,2

13. MC Special Cases Dependent sources Current Source in single mesh
Current Source between two meshes (Supermesh)

14. Current Source in single mesh Problem 2 Use MC to find Vz. [Vz = 1V]

15. Current Source In Two Meshes Find ia, ib, ic [1.75,1.25,6.75]

17. Dependent Sources: Use MC to find power in R4 (16W)

19. Do Handout problems 3, 4

20. Handout Problems

21. 1) Problem 2 Use mesh analysis to determine the two defined currents, Ix and Iy. Ix = Ia = 639 mA;Iy = Ib-Ia = -687 mA

22. 2) Find a) three mesh currents, [5,2
2) Find a) three mesh currents, [5,2.5,2] b) Power of 80V source (-400W del)

25. 3) Problem 1 Use mesh current analysis to find the power associated with each voltage source. [P1.5 = 9.18 mW;P3.0 = 17.6 mW]

26. 4) Problem 1 Use MC to find Vx. [Vx = -12.9 V]