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Sinusoidal steady-state analysis

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Sinusoidal steady-state analysis

3.1. Introduction

Step to analyze AC Circuits:

Transform the circuit to the phasor or frequency domain.

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

Transform the resulting phasor to the time domain.

3.2. Nodal Analysis

Find in thecircuit of Fig. usingnodalanalysis.

Solution:

3.2. Nodal Analysis

3.2. Nodal Analysis

3.2. Nodal Analysis

Fromnode 1

Fromnode 2

3.2. Nodal Analysis

3.2. Nodal Analysis

Example 3.2

Compute and in thecircuit of Fig.

Solution:

Nodes 1 and 2 form a supernode as shownFig. Applying KCL at thesupernodegives;

Example 3.2

Voltagesourceconnectedbetweennodes 1 and 2;

3.3. Mesh Analysis

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

Applying KVL to mesh 1, weobtain

3.3. Mesh Analysis

3.3. Mesh Analysis

3.3. Mesh Analysis

Example 3.4

Solve for in thecircuit in fig, using mesh analysis.

As shownfig, meshes 3 and 4 form a supermeshduetothecurrentsourcebetweenthemeshes.

Example 3.4

For mesh 1

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