1. Lesson 9: Nodal Analysis 2

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

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

4. Example Problem 1 Solve for node voltage Vb
Draw your current arrows leaving node b.
Go straight to the branch current equations:
Write KCL equations and solve for Vb:

5. SOLVE for Multiple Equations
Here writing our branch current equation yields two equations with two unknowns.
KCL Equations:
You can do the math by hand (see hand calculations, which are very long) or use the SOLVE function:
SOLVE (3 + a/6 + (a-b)/5 = 0 and (b-a)/5 + b/8 + (b+12)/6=0,{a,b})
Mathematica Solution

6. Example Problem 2
Solve for IUNK.
KCL Equations:
Mathematica Solution

7. Example Problem 3 Solve for Vab. First, we need to find Vc:
Now solve for Va and Vb :
We know that Vab = Va – Vb:

8. Example Problem 3 Short Cut
Solve for Vab.
Short cut using the solver:
Now use your solver function to solve for I1, I2 and I3 (or a, b and c), however you label it:
Mathematica Solution
You should get the same answer as doing it by hand…

9. QUESTIONS?