Series & Parallel AC Circuits Analysis

ET 242 Circuit Analysis II

Electrical and Telecommunication Engineering Technology

Professor Jang

AcknowledgementAcknowledgement

I want to express my gratitude to Prentice Hall giving me the permission to use instructor’s material for developing this module. I would like to thank the Department of Electrical and Telecommunications Engineering Technology of NYCCT for giving me support to commence and complete this module. I hope this module is helpful to enhance our students’ academic performance.

OUTLINESOUTLINES

Introduction to Series - Parallel

ac Circuits Analysis

Analysis of Ladder Circuits

Reduction of series parallel Circuits to Series Circuits

ET 242 Circuit Analysis II – Series-Parallel Circuits Analysis Boylestad 2

Key Words: ac Circuit Analysis, Series Parallel Circuit, Ladder Circuit

Series & Parallel ac Networks - Introduction

In general, when working with series-parallel ac networks, consider the following approach:

1. Redraw the network, using block impedances to combine obvious series and parallel elements, which will reduce the network to one that clearly reveals the fundamental structure of the system.

2. Study the problem and make a brief mental sketch of the overall approach you plan to use. In some cases, a lengthy, drawn-out analysis may not be necessary. A single application of a fundamental law of circuit analysis may result in the desired solution.

3. After the overall approach has been determined, it is usually best to consider each branch involved in your method independently before tying them together in series-parallel combinations. In most cases, work back from the obvious series and parallel combinations to the source to determine the total impedance of the network.

4. When you have arrived a solution, check to see that it is reasonable by considering the magnitudes of the energy source and the elements in the circuit.

ET 242 Circuit Analysis II – Series-Parallel Circuits Analysis Boylestad 3

ET 242 Circuit Analysis II – Series-Parallel Circuits Analysis Boylestad 12

Ex. 16-1 For the network in Fig. 16.1: a. Calculate ZT. b. Determine Is. c. Calculate VR and VC. d. Find IC.

e. Compute the power delivered. f. Find Fp of the network.

a. As suggested in the introduction, the network has been redrawn with block impedances, as shown in Fig. 16.2. Impedance Z1 is simply the resistor R of 1Ω, and Z2 is the parallel combination of XC and XL.

Figure 16.1 Example 16.1.

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ET 242 Circuit Analysis II – Series-Parallel Circuits Analysis Boylestad 5

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ET 242 Circuit Analysis II – Parallel ac circuits analysis Boylestad 6

Ex. 16-2 For the network in Fig. 16.3: a. If I is 50A∟30o, calculate I1 using the current divider rule.

b. Repeat part (a) for I2.c. Verify Kirchhoff’s current law at one node.

Figure 16.3 Example 16.2.

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ET 242 Circuit Analysis II – Parallel ac circuits analysis Boylestad 2

Ex. 16-3 For the network in Fig. 16.5: a. Calculate the voltage VC using the voltage divider rule.

b. Calculate the current Is.

Figure 16.5 Example 16.3.

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b. Find the voltage Vab.

Figure 16.7 Example 16.4.

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ET 242 Circuit Analysis II – Series-Parallel Circuits Analysis Boylestad 8

Ex. 16-6 For the network in Fig. 16.12: a. Determine the current I.

b. Find the voltage V.

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ET 242 Circuit Analysis II – Series-Parallel Circuits Analysis Boylestad 9

ET 242 Circuit Analysis II – Parallel ac circuits analysis Boylestad 10

Ex. 16-7 For the network in Fig. 16.14: a. Compute I. b. Find I1, I2, and I3 c. Verify KCL by showing that

I = I1 + I2 + I3. d. Find total impedance of the circuit;.

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ET 242 Circuit Analysis II – Parallel ac circuits analysis Boylestad 11

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ET 242 Circuit Analysis II – Series-Parallel Circuits Analysis Boylestad 12

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Ladder networks were discussed in some detail in Chapter 7. This section will simply apply the first method described in Section 7.6 to the general sinusoidal ac ladder network in Fig. 16.22. The current I6 is desired.

ET 242 Circuit Analysis II – Parallel ac circuits analysis Boylestad 13

Ladder Networks

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Figure 16.23 Defining an approach to the analysis of ladder networks.