AC Steady-State Analysis(Using the Norton's Theorem)

Problem-Solving Strategy for AC Steady-State Analysis

STEP 1. For relatively simple circuits (e.g., those with a single source), use

- Ohm’s law for ac analysis—that is, $\mathbf V = \mathbf I\mathbf Z$

- The rules for combining $\mathbf Z_s$ and $\mathbf Y_p$

- KCL and KVL

- Current and voltage division

STEP 2. For more complicated circuits with multiple sources, use

- Nodal analysis

- Loop analysis

- Superposition

- Source transformation

- Thévenin’s and Norton’s theorems

Note: This post is based on Irwin's Basic Engineering Circuit Analysis 11th ed.

If there are any errors in solution, please let me know in the comments

Applying KVL,

$-6-j\mathbf I_1+1(\mathbf I_1-\mathbf I_3)+j(\mathbf I_1-\mathbf I_2)=0$

$\mathbf I_2=4A$

$1(\mathbf I_3-\mathbf I_2)+1(\mathbf I_3-\mathbf I_1)+1\mathbf I_3=0$

So, $\mathbf I_N=\mathbf I_3=(5+2j)A$

$Z_{Th}=2\Omega$

Therefore, $\mathbf V_o=(5+2j)\times\frac{2}{2+1}=3.33+1.33j=3.59\angle21.8^{\circ}V$

Releated posts: Norton's Theorem