AC Steady-State Analysis(Using the Loop Analysis)

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

The loop equations are

$\mathbf I_1=4A$

$\mathbf I_2=2\mathbf I_x$

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

$\mathbf I_x=\mathbf I_3-\mathbf I_1$

Combining these equations,

$\mathbf I_3=\frac{4-8j}{2-j}=3.2-2.4j=4\angle-36.87\,^{\circ}A$

Therefore, $\mathbf V_o=1\times \mathbf I_3=4\angle-36.87\,^{\circ}V$