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INTRODUCTION TO CIRCUITS& ELECTRONICS

ECE 3336

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Technology & Electrical Engineering
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Introduction to Circuits & Electronics
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Will this course make you an electroniccircuit design wiz?

May be, not necessarily (it takes in-depthtraining and years of practice to be a circuitdesigner)

Can this course make you a smart user(informed user) of electronic circuits?

Yes, if you study hard

Is this course easy?

No

Is this course hard?

Not really

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Introduction to Circuits & Electronics

Input Output

It doessomething

useful:-information-power

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Transition from the firstindustrial revolution to the

second industrial revolution

Remember this?

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Source of water

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Fetch water

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Circuits & Electronics:to control the flow of

electrons for:

- work: power, energy

- information:communication, computation

Plumbing: control the

flow of water

molecules

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INTRODUCTION TO CIRCUITS& ELECTRONICS

ECE 3336

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ECE 3336Introduction to Circuits & Electronics

Prof. Han LeECE Dept.

Lecture Set #1

Voltage, Current, Energy and Power

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WHAT ARE CURRENT AND

VOLTAGE?

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Overview

In this part, we will cover:

Definitions of current and voltage

Hydraulic analogies to current and voltage

Reference polarities and actual polarities

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Current: Formal Definition

Current is the net flow of charges, per time, past anarbitrary plane in some kind of electrical device.

We will only be concerned with the flow of positivecharges. A negative charge moving to the right is

conceptually the same as a positive charge moving tothe left.

Mathematically, current is expressed as

dqi

dt

Current,

typically inAmperes [A]

Charge, typically inCoulombs [C]

Time, typically inseconds [s]
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The Ampere

The unit of current is the [Ampere],which is a flow of 1 [Coulomb] ofcharge per [second], or:

1[A] = 1[Coul/sec]

Remember that current is definedin terms of the flow of positivecharges.

One coulomb of positive charges per second flowingfrom left to right

- is equivalent to -

one coulomb of negative charges per second flowingfrom right to left.

Andre Marie Ampere(1775-1836)

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What is the Dealwith the Square Brackets [ and ]?

The unit of current is the

[Ampere], which is a flowof 1 [Coulomb] of chargeper [second], or:

1[A] = 1[Coul/sec]

Remember that currentis defined in terms of theflow of positive charges.

In these notes, we placeunits inside squarebrackets ([ and ]). This isdone to make it clear thatthe units are indeedunits, to try to avoidconfusion. This step is

optional. Showing unitsis important. Using thesquare brackets is notimportant, and is not

required.

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How to measure current
http://www.youtube.com/watch?v=k99UhAy34Co

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Hydraulic Analogy for Current

It is often useful to think in terms of hydraulicanalogies.

The analogy here is that current is analogous tothe flow rate of water:

Charges going past a plane per time is analogous to

volume of water going past a plane in a pipe pertime.

W t fl C t

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Water flow Current

So, if we put a plane (a screen, say) across a waterpipe, and measure the volume of water that movespast that plane in a second, we get the flow rate.

In a similar way, current is the number of positive

charges moving past a plane in a current-carryingdevice (a wire, say) in a second.

The number of charges per second passing theplane for each [Ampere] of current flow is called a

[Coulomb], which is about 6.24 x 1018

electroncharges.

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Voltage: Formal Definition

When we move a charge in the presence ofother charges, the potential energy of thatcharge changes. Voltage is the change inpotential energy, per charge, as we movebetween two points; it is a potential difference.

Mathematically, this is expressed as

Voltage,

typically inVolts [V]

Energy, typically inJoules [J]

Charge, typically inCoulombs [C]

dwvdq
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What is a [Volt]?

The unit of voltage is the [Volt]. A[Volt] is defined as a [Joule perCoulomb].

Remember that voltage is defined interms of the energy gained or lost by

the movement of positive charges.

Alessandro GiuseppeAntonio Anastasio Volta

(17451827)

One [Joule] of energy is lost from anelectric system when a [Coulomb] ofpositive charges moves from onepotential to another potential that isone [Volt] lower.

Charles Augustin de Coulomb

(17361806)

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Hydraulic Analogy for Voltage

Hydraulic analogy: voltage isanalogous to height. In a gravitationalfield, the higher that water is, themore potential energy it has.

The voltage between two points

is analogous to

the change in height between twopoints, in a pipe.

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Hydraulic Analogy:Voltage and Current

height ~ voltageflow rate ~ current

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V=g h Flow mass

Power P=V x Flow mass

Power P=V x I

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Hydraulic Analogy With Two Paths

This diagram is intended toshow a water pipe that

breaks into two parts and

then combines again. The

size of the blue arrows are

intended to reflect the

amount of water flow at

that point.

Two Pipes Analogy

Water is flowingthroughthe pipes.

There is a heightdifference acrossthesepipes.

We can extend this analogy tocurrent throughand voltageacrossan electric device

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Current Through

If we have twopipes connectingtwo points, the flowrate through onepipe can bedifferent from theflow rate through

the other. The flowrate depends onthe path.

Flow rate in thesmaller pipe

is less than it is

in the

larger pipe.

Like flow rate,

current is pathdependent.

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Voltage Across

No matter whichpath you follow,the height is the

same acrossthose two points.The height doesnot depend on thepath

Height

Like height, voltageis path independent.

The heightbetween two

points does

not change

as you go

through the

two pipes.

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Polarities

It is extremely important that we know thepolarity, or the sign, of the voltages andcurrents we use. Which way is the

current flowing? Where is the potentialhigher? To keep track of these things,two concepts are used:

1. Reference polarities, and

2. Actual polarities.

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Reference Polarities

The reference polarity is a directionchosen for the purposes of keeping track.It is like picking North as your referencedirection, and keeping track of your

direction of travel by saying that you aremoving in a direction of 135 degrees. Thisonly tells you where you are going withrespect to north, your reference direction.

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Actual Polarity

The actual polarity is the direction something isactually going. We have only two possible

directions for current and voltage.

If the actual polarity is the same direction asthe reference polarity, we use a positive sign

for the value of that quantity. If the actual polarity is the opposite direction

from the reference polarity, we use anegative sign for the value of that quantity.

R l i hi b

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Relationship between

Reference Polarity and Actual Polarity

The actual polarity is the direction something isactually going. The reference polarity is adirection chosen for the purposes of keeping

track. We have only two possible directionsfor current and voltage.

Thus, if we have a reference polarity defined,and we know the sign of the value of thatquantity, we can get the actual polarity.

Example: Suppose we pick our referencedirection as up. The distance we go up is

5[feet]. We know then, that we have movedan actual distance of +5[feet] down.

The referencepolarity is up.

The actualpolarity is

down.

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Reference Polarities

Reference polarities do not indicate actualpolarities. They cannot be assigned

incorrectly. You cant make a mistakeassigning a reference polarity to a variable.

Always assign reference polarities for thevoltages and currents that you name.Without this step, these variables remainundefined. All variables must be defined ifthey are used in an expression.

Polarities for Currents

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Polarities for Currents

For current, the reference polarity is given by an arrow.

The actual polarity is indicated by a value that is associatedwith that arrow.

In the diagram below, the currents i1 and i2are not defineduntil the arrows are shown.

Use lowercase variables for current. Uppercase subscriptsare preferred. i2 i1 -3[A] 3[A]

i1 = 3[A]

i2 = -3[A]These are all different ways to show the same thing, a

current of 3 [Coulombs] per [second] of positive charges

moving from left to right through this wire.

The arrow shows a reference polarity, and the sign of the

number that goes with that arrow shows the actual

polarity.

a wire

Polarities for Voltages

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Polarities for Voltages

For voltage, the reference polarity is given by a + symbol

and a symbol, at or near the two points involved. The actual polarity is indicated by a value that is placed

between the + and - symbols.

In the diagram below, the voltages v1

and v2

are not defined

until the + and symbols are shown. Use lowercase variables for voltage. Uppercase subscripts

are preferred.

+

-

v1(t)Device

+

-

v2(t)

+

-

5[V]

+

-

-5[V]

Defining Voltages

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Defining Voltages

For voltage, the reference polarity is given by a +symbol and a symbol, at or near the two pointsinvolved.

The actual polarity is indicated by the sign of thevalue that is placed between the + and - symbols.

In the diagram below, the voltagesv1 and

v2 arenot defined until the + and symbols are shown.

In this case,

v1 = 5[V]and

v2

= -5[V].

These four labels

all mean the same

thing.

+

-

v1(t)Device

+

-

v2(t)

+

-

5[V]

+

-

-5[V]

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Why bother with reference polarities?

Students who are new to circuits oftenquestion whether this is intended just tomake something easy seem complicated.

It is not so; using reference polaritieshelps.

The key is that often the actual polarity ofa voltage or current is not known until

later. We want to be able to writeexpressions that will be valid no matterwhat the actual polarities turn out to be.

To do this, we use reference polarities,

and the actual polarities come out later.

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Overview

In this part, we will cover:

Definitions of current and voltage

Hydraulic analogies to current and voltage

Reference polarities and actual polarities

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PART 2

ENERGY, POWER, AND WHICHWAY THEY GO (INPUT OROUTPUT)

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Overview of this Part

In this part of the module, we will cover thefollowing topics:

Definitions of energy and power

Sign Conventions for power direction

Which way do the energy and power go?

Hydraulic analogy to energy and power, and

yet another hydraulic analogy

This is the definition found in most

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Energy

Energy is the ability or the capacity to do

work. It is a quantity that can take on many forms,

among them heat, light, sound, motion ofobjects with mass.

This is the definition found in mostdictionaries, although it is dangerous touse nontechnical dictionaries to definetechnical terms. For example, some

dictionaries list force and power assynonyms for energy, and we will neverdo that for this course!

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Joule Definition

The unit for energy that we use isthe [Joule] [J].

A [Joule] is a [Newton-meter].

In everything that we do in circuit

analysis, energy will be conserved. One of the key concerns in circuit

analysis is this: Is a device, object,or element absorbing energy ordelivering energy?

James Prescott Joule(1818 1889)

Isaac Newton (16431727)

http://www.energy.gov/energysources/electricpower.htm

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Electric energy generation

Air molecules

kinetic energy

Blades/turbine

kinetic energy

Electrons energy(electrical energy)

V x I



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Blades/turbine kineticenergy

Electrons energy(electrical energy)

V x I

coal + CO2 moleculeskinetic energy

H2O molecules

kinetic energy(hot steam)

H2O moleculeskinetic energy

(hot steam)

p gy g gy p

El t i tihttp://www.energy.gov/energysources/electricpower.htm

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Power

Power is the rate of change of the energy,with time. It is the rate at which the energy isabsorbed or delivered.

Again, a key concern is this: Is power being

absorbed or delivered? We will show a wayto answer this question.

Mathematically, power is defined as:

Power,typically inWatts [W]

Energy, typically inJoules [J]

Time, typically inseconds [s]

dwp

dt

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Watt Definition

A [Watt] is defined as a [Joule per

second].

We use a capital [W] for this unit.

Light bulbs are rated in [W]. Thus, a100[W] light bulb is one that absorbs100[Joules] every [second] that it is

turned on.

James Watt (1736-1819)

An athlete burning 1300 Wexercising
http://www.youtube.com/watch?v=qdSnx2WHLls

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Power from Voltage and Current

Power can be found from the voltage andcurrent, as shown below. Note that if voltage

is given in [V], and current in [A], power willcome out in [W].

dw dw dq p vidt dq dt

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Capacitor discharge
http://www.youtube.com/watch?v=v_MMxcOpmIg

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Sign Conventions or Polarity Conventions

To determine whether power and energy aredelivered or absorbed, we will introduce signconventions, or polarity conventions.

A sign convention is a relationship betweenreference polarities for voltage and current.

As in all reference polarity issues, you cant

choose reference polarities wrong. You justhave to understand what your choice means.

Passive Sign Convention Definition

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ass e S g Co e t o e t o

The passive sign convention is when the referencepolarity for the current is in the direction of thereference voltage drop.

Another way of saying this is that when thereference polarity for the current enters the positiveterminal for the reference polarity for the voltage,we have used the passive sign convention.

Circuit Circuit

vX

+

-

iX

iYvY

+

-

Passive Sign Convention

Passive Sign Convention Discussion

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g

of the Definition

The two circuits below have reference polaritieswhich are in the passive sign convention.

Notice that although they look different, these twocircuits have the same relationship between thepolarities of the voltage and current.

Circuit Circuit

vX

+

-

iX

iYvY

+

-

Passive Sign Convention

Active Sign Convention Definition

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g

The active sign convention is when the reference polarity forthe current is in the direction of the reference voltage rise.

Another way of saying this is that when the reference polarityfor the current enters the negative terminal for the referencepolarity for the voltage, we have used the active signconvention.

Circuit Circuit

vW

+

-

iW

iZvZ

+

-

Active Sign Convention

Active Sign Convention Discussion of

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g

the Definition

The two circuits below have reference polaritieswhich are in the active sign convention.

Notice that although they look different, these twocircuits have the same relationship between thepolarities of the voltage and current.

Circuit Circuit

vW

+

-

iW

iZvZ

+

-

Active Sign Convention

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Using Sign Conventions for Power

Direction Subscripts We will use the sign conventions that we just

defined in several ways in circuit analysis. Fornow, lets just concentrate on using it to determine

whether power is absorbed, or power isdelivered.

We might want to write an expression for powerabsorbed by a device, circuit element, or other part

of a circuit. It is necessary for you to be clear aboutwhat you are talking about. A good way to do thisis by using appropriate subscripts.

. . ABS BY DEVICEp

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Direction The RulesWe will use the sign conventions to

determine whether power isabsorbed, or power is delivered.

When we use the passive signconvention to assign referencepolarities, vigives the powerabsorbed, and vigives the powerdelivered.

When we use the active signconvention to assign referencepolarities, vigives the powerdelivered, and vigives the power

absorbed.


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g g

Direction The Rules

We will use the sign conventions to determine whether poweris absorbed, or power is delivered.

When we use the passive sign convention to assignreference polarities, vigives the power absorbed, and vigives the power delivered.

When we use the active sign convention to assignreference polarities, vigives the power delivered, and vigives thepowerabsorbed.

PassiveConvention

ActiveConvention

Powerabsorbed

pABS= vi p ABS= -vi

Power

delivered

pDEL

= -vi p DEL

= vi

Example of Using the Power Direction

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p g

Table Step 1

We want an expression for the power absorbed by thisSample Circuit.

1. Determine which sign convention has beenused to assign reference polarities for thisSample Circuit.

Sample

Circuit

iS

vS

+

-

PassiveConvention

ActiveConvention

Powerabsorbed

pABS= vi p ABS= -vi

Powerdelivered

pDEL = -vi p DEL = vi


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p g

Table Step 2


1. Determine which sign convention has been used.

2. Next, we find the cell that is of interest to ushere in the table. It is highlighted in red below.

Sample

Circuit

iS

vS

+

-

This is the active sign convention.

Passive

Convention

Active

Convention

Power

absorbedpABS= vi pABS= -vi

Power

deliveredp

DEL

= -vi p DEL

= vi


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p g

Table Step 3



2. Find the cell that is of interest to us here in thetable. This cell is highlighted in red.

3. Thus, we write pABS,CIR= -vSiS.

Sample

Circuit

iS

vS

+

-

Go back toOverview

slide.

This is the active signconvention.

Passive

Convention

Active

Convention

Power

absorbedpABS= vi pABS= -vi

Power

delivered

pDEL

= -vi p DEL

= vi


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p g

Table Note on Notation



2. Find the cell that is of interest to us here in thetable. This cell is highlighted in red.

3. Thus, we write pABS.BY.CIR= -vSiS.

Sample

Circuit

iS

vS

+

-

In your power expressions, always

use lowercase variables for power.Uppercase subscripts are preferred.Always use a two-part subscript for allpower and energy variables. Indicate

whether abs or del, and by what.

Hydraulic Analogy

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Hydraulic Analogy

The hydraulic analogy here can be used to test our rule

for finding the direction that power goes. Imagine awaterfall. A real waterfall, and a schematic waterfallare shown here.

Hydraulic Analogy

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Hydraulic Analogy

for Power Directions Test

The hydraulic analogy here can be used to test our rule for findingthe direction that power goes. Imagine a waterfall.

The waterflow is in the direction of the drop in height. Thus, this isanalogous to the passive sign convention. Thus, if we wrote anexpression for power absorbed, we would write:

pabs= vi

Since the values are positive, the power absorbed will be positive.

Does this make sense?

Height

Flow direction

Hydraulic Analogy

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Hydraulic Analogy

for Power Directions Answer

The power absorbed will be positive. Does this make sense? Yes, but only if we understand a key assumption. In circuits, when

we say energy absorbed, we mean the energy absorbed from theelectrical system, and delivered somewhere else.

In this hydraulic analogy, energy is being lost from the water as it

falls. This energy is being delivered somewhere else, as sound,heat, or in other forms. We call this energy absorbed. Thus, thepower absorbed is positive.

Height

Flow direction

Power Directions Assumption #1

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Electrical System

made up of various parts

and componentsComponent

in circuit

which

delivers

positive

power

Electrical power

that is delivered

to the system

Nonelectrical power

that will be converted

to electrical power

p

So, a key assumption is that when we say power delivered, wemean that there is power taken from someplace else, converted

and delivered to the electrical system. This is the how thisapproach gives us direction.

For example, in a battery, this power comes from chemical powerin the battery, and is converted to electrical power.

Remember that energy is conserved, and therefore power will be

conserved as well.

Positive power delivered bysomething means that powerfrom somewhere else enters

the electrical system aselectrical power, through thatsomething. In this diagram,the red power (nonelectrical)is being changed to the bluepower (electrical).

Power Directions Assumption #2

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Electrical System


and components

Component

in circuit

which

absorbs

positive

power

Electrical power

that is absorbed

out of the system

Nonelectrical power

that was converted

from electrical power

p

So, a key assumption is that when we say power absorbed, we

mean that there is power from the electrical system that isconverted to nonelectrical power. This is the how this approachgives us direction.

For example, in a lightbulb, the electrical power is converted tolight and heat (nonelectrical power).

Remember that energy is conserved, and therefore power will beconserved as well.

Positive power absorbed bysomething means that powerfrom the electrical system

leaves as nonelectrical power,through that something. Inthis diagram, the blue power(electrical) is being changedto the red power(nonelectrical).

Power Directions Terminology

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Power Directions Terminology

Synonyms

There are a number of terms that are synonyms for powerabsorbed. We may use:

Power absorbed by Power consumed by Power delivered to Power provided to Power supplied to Power dissipated byThere are a number of terms that are synonyms for power

delivered. We may use: Power delivered by Power provided by Power supplied by

Electrical System


and components

Component

in circuitwhich

absorbs

positive

power

Electrical power

that is absorbed

out of the system

Nonelectrical power

that was converted

from electrical power

Electrical System


and components

Component

in circuit

which

delivers

positive

power

Electrical power

that is delivered

to the system

Nonelectrical power

that will be converted

to electrical power

Another Hydraulic Analogy

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ot e yd au c a ogy

Another useful hydraulic analogy that can be used to help

us understand this is presented by A. Bruce Carlson in histextbook, Circuits, published by Brooks/Cole. Thediagram, Figure 1.9, from page 11 of that textbook, isduplicated here.

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Another Hydraulic Analogy Details In this analogy, the electrical circuit is shown at the

left, and the hydraulic analog on the right. As Carlson puts it, The pump (source) forces water

flow (current) through pipes (wires) to drive theturbine (load). The water pressure (potential) ishigher at the inlet port of the turbine than at theoutlet.

Note that the Source isgiven with referencepolarities in the activeconvention, and the Load

with reference polarities inthe passive convention. Asa result, in this case, sinceall quantities are positive,the Source delivers power,and the Load absorbs

power.

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Another Point on Terminology

We always need to be careful of our context.When we say things like the Source deliverspower, we implicitly mean the Source

delivers positive power.Note that the Source isgiven with referencepolarities in the activeconvention, and the Loadwith reference polarities inthe passive convention. Asa result, in this case, sinceall quantities are positive,the Source delivers power,and the Load absorbspower.

Another Point on Terminology

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At the same time, it is also acceptable to write

expressions such as pABS.BY.SOURCE=-5000[W]. This isthe same thing as saying that the power delivered is5000[W].

However, unless the context is clear, it is ambiguous tojust write p =5000[W]. Your answer must be clear,because the direction is important!

Note that the Source isgiven with referencepolarities in the activeconvention, and the Load

with reference polarities inthe passive convention. Asa result, in this case, sinceall quantities are positive,the Source delivers power,and the Load absorbs

power.

Why bother with Sign Conventions?

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Why bother with Sign Conventions?

Students who are new to circuits often questionwhether sign conventions are intended just to makesomething easy seem complicated. It is not so;using sign conventions helps.

The key is that often the direction that power ismoving is not known until later. We want to be ableto write expressions now that will be valid no matterwhat the actual polarities turn out to be.

To do this, we use sign conventions, and the actualdirections come out later whenwe plug values in.

O i f hi P

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Overview of this Part

In this part of the module, we will cover thefollowing topics:

Definitions of energy and power

Sign Conventions for power direction

Which way do the energy and power go?

Hydraulic analogy to energy and power, and

yet another hydraulic analogy

Documents

3336 Lect 1-Intro