Lesson 9 Nodal Analysis 2 1 Learning Objectives

Lesson 9: Nodal Analysis 2 1

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

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

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: 4

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: Mathematica SOLVE ( 3 +Solution a/6 + (a-b)/5 = 0 and (b-a)/5 + b/8 + (b+12)/6=0, {a, b}) 5

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

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

Example Problem 3 Short Cut Solve for Vab. Short cut using the solver: Now use your solver function to solve for I 1, I 2 and I 3 (or a, b and c), however you label it: Mathematica Solution You should get the same answer as doing it by hand… 8

QUESTIONS? 9