SINUSOIDAL STEADY-STATE ANALYSIS

3.1. Introduction

Step to analyze AC Circuits:

1. Transform the circuit to the phasor or frequency domain.

2. Solve the problem using circuit techniques (nodal analysis, mesh analysis, superposition, etc.)

3. Transform the resulting phasor to the time domain.

3.2. Nodal Analysis

Find in the circuit of Fig. using nodal analysis.

Solution:

3.2. Nodal Analysis

3.2. Nodal Analysis

3.2. Nodal Analysis

From node 1

From node 2

3.2. Nodal Analysis

3.2. Nodal Analysis

Example 3.2

Compute and in the circuit of Fig.

Solution:Nodes 1 and 2 form a supernode as shown Fig. Applying KCL at the supernode gives;

Example 3.2

Voltage source connected between nodes 1 and 2;

3.3. Mesh Analysis

Determine current in the circuit of fig, using mesh analysis.

Applying KVL to mesh 1, we obtain

3.3. Mesh Analysis

3.3. Mesh Analysis

3.3. Mesh Analysis

Example 3.4

Solve for in the circuit in fig, using mesh analysis.

As shown fig, meshes 3 and 4 form a supermesh due to the current source between the meshes.

For mesh 1

Example 3.4

For mesh 2

Example 3.4

Example 3.4

Example 3.4

Example 3.5

Example 3.5

Example 3.5

Example 3.5

Example 3.6

Example 3.6

Example 3.6