1ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Lecture 2Fundamentals of Electrical

Engineering

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

2ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

downhill: resistoruphill: battery

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

3ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

POWER AND ENERGY

2

1

)(

)()()(t

t

dttpw

titvtp Watts

Joules

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

If the current flows opposite to the passive configuration, the power is given by p = -vi

Current is flowing in the passive

configuration

4ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Resistors and Ohms Law

RiviRv

abab a

b

The units of resistance are Volts/Amp which are called ohms. The symbol for ohms is omega:

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Resistance Related to Physical Parameters

ALR

is the resistivity of the material used to fabricate the resistor. The units of resitivity are ohm-meters

(-m)

5ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Power dissipation in a resistor

RvRivip

22

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

6ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Lecture 3Circuit Laws,

Voltage & Current Dividers

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

KIRCHHOFFS CURRENT LAW

The net current entering a node is zero.

Alternatively, the sum of the currents entering a node equals the sum of the currents leaving a node.

7ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

KIRCHHOFFS VOLTAGE LAW

The algebraic sum of the voltages equals zero for any closed path (loop) in an electrical circuit.

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

8ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

eqiRRRRiiRiRiRvvvv )( 321321321

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

eqRv

RRRv

Rv

Rv

Rviiii

321321321

111

9ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Circuit Analysis using Series/Parallel Equivalents

1. Begin by locating a combination of resistances that are in series or parallel. Often the place to start is farthest from the source.

2. Redraw the circuit with the equivalent resistance for the combination found in step 1.

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

3. Repeat steps 1 and 2 until the circuit is reduced as far as possible. Often (but not always) we end up with a single source and a single resistance.

4. Solve for the currents and voltages in the final equivalent circuit.

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ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Voltage Division

total321

111 vRRR

RiRv

total321

222 vRRR

RiRv

Of the total voltage, the fraction that appears across a given resistance in a series circuit is the ratio of the given resistance to the total series resistance.

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Current Division

total21

2

11 iRR

RRvi

total21

1

22 iRR

RRvi

For two resistances in parallel, the fraction of the total current flowing in a resistance is the ratio of the other resistance to the sum of the two resistances.

11

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Lecture 4Node/Loop Analysis

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Node Voltage Analysis

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ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Lecture 5Node/Loop Analysis

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Mesh Current Analysis

13

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Choosing the Mesh Currents

When several mesh currents flow through one element, we consider the current in that element to be the algebraic sum of the mesh currents.

Sometimes it is said that the mesh currents are defined by soaping the window panes.

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

14

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

0)(10100150150)(1020

122

211

iiiiii

Solve for the mesh currents:

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

0)(10100150150)(1020

122

211

iiiiii

10025101501030

21

21

iiii

Putting the equations into the standard format:

15

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Super-mesh

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Combine meshes 1 and 2 into a supermesh. In other words, we write a KVL equation around the periphery of meshes 1 and 2 combined.

01042 32311 iiiiiMesh 3:

0243 13233 iiiii512 ii

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ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Lecture 7

Thvenin Equivalent Circuits

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Thvenin Equivalent Circuits

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ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

oct vV

Thvenin Equivalent Circuits

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

t

tsc R

Vi

Thvenin Equivalent Circuits

18

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Thvenin Equivalent Circuits

sc

oc

ivRt

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Finding the Thvenin Resistance Directly

We can find the Thvenin resistance by zeroing the sources in the original network and then computing the resistance between the terminals.

When zeroing a voltage source, it becomes a short circuit. When zeroing a current source, it becomes an open circuit.

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ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

20

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

scn iI

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Step-by-step Thvenin/Norton-Equivalent-

Circuit Analysis1. Perform two of these:

a. Determine the open-circuit voltage Vt = voc.

b. Determine the short-circuit current In = isc.

c. Zero the sources and find the Thvenin resistance Rt looking back into the terminals.

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ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

2. Use the equation Vt = Rt In to compute the remaining value.

3. The Thvenin equivalent consists of a voltage source Vt in series with Rt .

4. The Norton equivalent consists of a current source In in parallel with Rt .

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Source Transformations

22

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Maximum Power Transfer

The load resistance that absorbs the maximum power from a two-terminal circuit is equal to the Thvenin resistance.

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

SUPERPOSITION PRINCIPLE

The superposition principle states that the total response is the sum of the responses to each of the independent sources acting individually. In equation form, this is

nT rrrr 21

23

ELECTRICAL ENGINEERING: PRINCIPLES AND APPLICATIONS, Third Edition, by Allan R. Hambley, 2005 Pearson Education, Inc.

Superposition Principle