Lesson 9: Nodal Analysis 2

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

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

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:

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

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

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

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…

QUESTIONS?