AC Steady-State Analysis(Using the Thévenin'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

$\mathbf V_1=2\times(-j)=-2j$

Using KCL in the middle of the node,

$\frac{-2j-\mathbf V_{Th}+12}{1}+2+\frac{-2j-\mathbf V_{Th}}{1}=0$

$\mathbf V_{Th}=(7-2j)V$

$Z_{Th}=(0.5-j)\Omega$

Thus, $\mathbf V_o=(7-2j)\times\frac{1}{0.5-j+1}=3.846+1.23j=4.038\angle 17.745^{\circ}V$