1. Lesson 11: Nodal Analysis II

2. Learning Objectives
Apply Nodal Analysis to circuits with current sources.
Solve for multiple unknown voltages in a complex DC circuit.
Use calculator to solve Equations.

3. 1. Identify the nodes REVIEW
What are the voltages of the three nodes a,b,c below?

4. 2. Write equations for branch currents
REVIEW
2. Write equations for branch currents
In nodal analysis, we usually write the branch currents directly in terms of node voltages and branch resistances.
Care must be taken in keeping the polarity correct!

5. 2. Write equations for branch currents
REVIEW
2. Write equations for branch currents
You can make the problem simpler by arbitrarily assuming current leaves each node
This simplifies the resulting equations and prevents polarity errors.

6. 3. Substitute into KCL and solve for the unknowns
REVIEW
3. Substitute into KCL and solve for the unknowns

7. Current Sources
A current source makes the equations simpler, since now you know what the branch current is.
Pay attention to POLARITY!

8. Example Problem 1
Determine Vb in the circuit below

9. Example Problem 2
Write the equation for the two nodes in the circuit below:
Mathematica Solution

10. SOLVE function for multiple equations
SOLVE (3 + a/6 + (a-b)/5 = 0 and (b-a)/5 + b/8 + (b+12)/6=0,{a,b})

11. Example Problem 3
Solve for IUNK.
Mathematica Solution

12. Example Problem 4
Solve for Vab.
Mathematica Solution