Ddj2003 Notes Chap1 (Dc Circuits)

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1

CHAPTER 1

DIRECT CURRENT (DC)

CIRCUITS



2

Current

The movement of free electrons from negative to

positive is electrical current (I).

By definition: electrical current is the rate of flow of charge,

where ; I = current (A) , Q = electric charge (C) &

t = time (s)

t

Q I !



3

There must be a driving influence to cause the

continuous current flow. This influence is provided by the

source which causes the current to leave at a high

potential and to move round the circuit until it returns to

the source at a low potential. The term voltage meant a

difference of potential and is expressed in volts. One volt is the potential difference between two points when one

joule of energy is used to move one coulomb from one

point to the other.

where ; V = voltage (V) , W = energy (J) & Q =

charge (C)

Q

W V !

Voltage



4

Energy is the ability to do work; and

Power is the rate at which energy is used.

Power = energy/time;

Therefore: W = Pt (J)where ; W = energy (J) , P = power (W) & t = time (s)

and,

WattsVIt

VQ

t

W P !!!

Energy and Power



5

The driving influence that causes a current to flow is termed the

electromotive force, hereafter called the e.m.f and is alwaysconnected with energy conversion

An electromotive force, e.m.f. is that which tends to produce an

electric current in a circuit. The unit of e.m.f. is volt (V), symbolized

by e. The principal sources of e.m.f. are as follows:

1. The electrodes of dissimilar materials immersed in an

electrolyte, as in primary and secondary cells, i.e. batteries.

(Sources from batteries is in dc current or constant current)

2. The relative movement of a conductor and a magnetic flux, in

an electric generator. This source can be expressed as thevariation of magnetic flux linked with a coil. (Basic principle of

generators)

3. The difference of temperature between junctions of dissimilar

metals, as in thermo-junction.

EMF



6

Resistance

The resistance of any material is due

primarily to four factors:

± Material resistivity ( V) ± Length (l)

± Cross-sectional area (A)

± Temperature of the material



7

Temperature Effects

Temperature Coefficient of Resistance

± the higher the temperature coefficient of

resistance for a material, the more sensitive

the resistance level to changes in temperature



8

Types of Resistors

Today, the most

common fixed type

resistors are metal

film resistors ± resistance is achieved

by depositing a thin

metal film on a ceramic

rod, then trimming the

metal film in a helicalmanner to establish

resistance



9

Types of Resistors

For a particular

manufacturer, and

style, the size of aresistor will increase

with the power or

wattage rating

The size of a resistor does not define its

resistance level



10

Types of Resistors

Variable resistors are referred to as rheostats (if

used as a variable resistor) or potentiometers (if

used for controlling potential levels)

± a contact is moved along a resistive element



11

Resistor Color Coding

First two bands represent the first and second

digits, respectively

Third band determines the power-of-tenmultiplier for the first two digits

Fourth band is the manufacturer¶s tolerance



12

Resistor Color Coding



13

Ohm¶s Law

Ohm¶s Law: Basic equations used in the analysis of electrical circuits.

Describe linear relationships

or



14

Ohm¶s Law

The symbol E is

applied to all sources

of voltage

The symbol V isapplied to all voltage

drops across

components of the

network



15

Ohm¶s Law

For any resistor, in any network, the direction of

current through a resistor will define the polarity

of the voltage drop across the resistor



16

SERIES CIRCUITS



17

Resistors in Series

A series circuit provides only one path for current between two points so that the current isthe same through each series resistor.



18

Series Resistors

The total resistance of

a series configuration

is the sum of the

resistance levels



19

Current in a Series Circuit

The current is the same through all points

in a series circuit. The current through

each resistor in a series circuit is the same

as the current through all the other

resistors that are in series with it.



20

Total Series Resistance

The total resistance of a series circuit is equal tothe sum of the resistances of each individualseries resistor.



21

Series Resistance Formula

For any number of individual resistors

connected in series, the total resistance is

the sum of each of the individual values.

RT = R1 + R2 + R3 + . . . + Rn



22

Ohm¶s Law in Series Circuits

Current through one of the series resistor is the

same as the current through each of the other

resistors and is the total current.

If you know the total voltage and the totalresistance, you can determine the total current

by using: IT = VT /RT

If you know the voltage drop across one of the

series resistors, you can determine the current

by using: I = VR /R



23


If you know the total current, you can find

the voltage drop across any of the series

resistors by using: VR

= ITR

The polarity of a voltage drop across a

resistor is positive at the end of the

resistor that is closest to the positive

terminal of the voltage source.



24


An open in a series circuit prevents

current; and, there is zero voltage drop

across each series resistor. The total

voltage appears across the points

between which there is an open.



25

Power in a Series Circuit

The total amount of power in a series

resistive circuit is equal to the sum of the

powers in each resistor in series.

PT = P1 + P2 + P3 + . . . + Pn



26

Power Distribution in a Series

Circuit The power applied by the dc supply must

equal that dissipated by the resistive

elements

In a series configuration, maximum power

is delivered to the largest resistor



27

Power in a Resistor

The amount of power in a resistor is

important because the power rating of the

resistor must be high enough to handle the

expected power in the circuit.



28

Voltage Sources in Series

A voltage source is an energy source that

provides a constant voltage to a load.

Batteries and electronic power supplied

are practical examples of dc voltage

sources.



29

Voltage Sources in Series

When two or more voltage sources are in series,

the total voltage is equal to the the algebraic

sum (including polarities of the sources) of the

individual source voltages.



30

Kirchhoff¶s Voltage Law

The algebraic sum of

the potential rises and

drops around a

closed path (or loop)is zero



31


This law requires that we define a

closed path of investigation permitting

us to start at one point in the network,travel through the network, and find our

way back to the original starting point



32


The applied voltage of a series dc circuit

will equal the sum of the voltage drops of

the circuit

The sum of the voltage rises around a

closed path will always equal the sum of

the voltage drops



33


When applying Kirchhoff¶s voltage law, be sure

to concentrate on the polarities of the voltage

rises or drops rather than the type of elements

± do not treat a voltage drop across a resistive elementdifferently from a voltage rise (or drop) across a

source

± polarity indicates that a drop (or rise) has occurred,

not whether it is a resistive element or source



34


The sum of all the

voltage drops around

a single closed loop in

a circuit is equal tothe total source

voltage in that loop.

VS = V1 + V2 + V3 + « +

Vn



35

Another Way to state


The algebraic sum of all voltages (both

sources and drops) around a closed path

is zero.

VS

- V1

- V2

- V3

= 0



36

Voltage Dividers

Since each resistor

has the same current,

the voltage drops are

proportional to theresistance values.



37

Voltage-Divider Formula

The voltage drop across any resistor or

combination of resistors in a series circuit

is equal to the ratio of that resistance

value to the total resistance, multiplied by

the source voltage.

Vx = (Rx/RT)VS



38

Voltage-Divider Rule

Where: VX is the voltageacross the resistor RX, Eis the impressed voltageacross the serieselements, and RT is the

total resistance of theseries circuit



39

PARALLEL CIRCUITS



40

Identifying Parallel Circuits

If there is more than one current path

(branch) between two separate points

(nodes), then there is a parallel circuit

between those two points.



41

Voltage in Parallel Circuits

The voltage across any given branch of a

parallel circuit is equal to the voltage

across each of the other branches in

parallel.



42

Parallel Resistors

Two elements, branches or circuits are in

parallel if they have two, and only two points in

common

For resistors in parallel, the total resistance is



43

Parallel Resistors

The total resistance of parallel resistors

is less than the smallest parallel resistor

± If the smallest resistor of a parallel

combination is much smaller than the other

parallel resistors, the total resistance will

be very close to the smallest resistor value

The total resistance of parallel resistors

will always drop as new resistors are

added in parallel, irrespective of their

value



44

Parallel Resistors

For resistors in parallel

± The total resistance of N parallel resistors

of equal value is the resistance of oneresistor divided by the number (N) of

parallel resistors

± The total resistance of two parallel

resistors is the product of their values

divided by their sum



45

Parallel Resistors

The voltage is the

same across parallel

elements The source does not

³see´ the parallel

combination, it only

reacts to the totalresistance

The source current is:



46

Parallel Resistors

Since the voltage is the same across

parallel elements, the current through

each resistor can be determined using

Ohm¶s law

For single-source parallel networks, thesource current (IS) is equal to the sum of

the individual branch currents



47

Parallel Resistors

For parallel resistors, the greatest current

will exist in the branch with the least

resistance

± current always seeks the path of least

resistance

To measure current through a resistor in a

parallel circuit, break the connection at thepoint of interest and insert the ammeter

with the current entering the positive (red)

lead



48

Power Distribution in a Parallel

Circuit For any network composed of resistive

elements, the power applied by the battery

will equal that dissipated by the resistive

elements

In a parallel resistive network, the larger the resistor the less the power absorbed



49

Kirchhoff¶s Current Law

The algebraic sum of the currents entering

and leaving a junction (also termed

³node´) of a network is zero

± the sum of the currents entering a node of a

network must equal the sum of the currents

leaving the same node



50




51

Kirchhoff¶s Current Law (KCL)

The sum of the currents into a junction

(total current in) is equal to the sum of

the currents out of that junction (total

current out).

IIN(1) + IIN(2) + . . . + IIN(n) = IOUT(1) + IOUT(2) +

. . . +IOUT(m)



52

Generalized circuit junction

illustrating KCL



53


Kirchhoff¶s current Law (KCL) can be

stated another way:

The algebraic sum of all the currents

entering and leaving a junction is equal

to zero.



54


If the direction of the current is not known:

± make an assumption about the direction and

then check out the result

± if the result is negative, the wrong direction

was assumed

± if positive, the correct direction was assumed

± in either case, the magnitude of the currentwill be correct



55

Current Divider Rule

The current entering parallel resistive

elements will split as the inverse of their

resistive values

± the current through equal parallel resistorswill be the same

The Current Divider Rule:



56


In words:

± The current through any branch of a parallel

resistive network is equal to the total resistance of

the parallel network divided by the resistor of

interest and multiplied by the total current enteringthe parallel configuration



57


The current through the smallest resistor

will be very close to the total current for a

parallel network if the other parallel

elements of the configuration are much

larger in magnitude



58


For two parallel resistors, the current

through one is equal to the other resistor

times the total entering current divided by

the sum of the two resistors



59

Current Sources in Parallel

A current source is a type of energy

source that provides a constant current to

a load even if the resistance of that load

changes.



60

Sum of Current Sources

The total current produced by all current sourcesis equal to the algebraic sum of the individualcurrent sources.



61

Voltage Sources in Parallel

Voltage sources can only be placed in

parallel if they have the same voltage

± the primary reason for placing two or more

batteries or supplies in parallel would be to

increase the current rating above that of a

single supply

± the total source current using Kirchhoff¶scurrent law is the sum of the rated currents of

each supply



62

SERIES-PARALLEL CIRCUITS



63

Series-Parallel Network

A series-parallel configuration is one that is

formed by a combination of series and parallel

elements

Analysis

± study the problem to determine an overall approach

± examine each region of the network independently

before tying them together in series-parallelcombinations

± redraw the network with reduced branches

± check that the solution is reasonable



64

Reduce and Return Approach

Reduction phase

± combine series

resistors to form an

equivalent resistor ± combine parallel

resistors to establish

the total resistance

Return phase ± work back to the

desired voltage



65

Reduce and Return Approach

The network is reduced to its simplest

form across the source, and the source

current is determined

The return phase is where the resulting

source current is used to work back to the

desired unknown



66

Open Circuit

The most common failure in a series

circuit is an open.

When an open occurs in a series circuit,

all of the source voltage appears across

the open.



67

Open Circuit

An open circuit is

simply two isolated

terminals notconnected by an

element of any kind

± an open circuit can

have a potentialdifference (voltage)

across its terminals,

but the current is

always zero amperes



68

Short Circuit

When there is a short, a portion of the

series resistance is bypassed, thus

reducing the total resistance.

A short in a series circuit results in more

current than normal.



69

Short Circuit

A short circuit is a very low resistance, direct

connection between two terminals of a network

± a short circuit can carry a current of a level

determined by the external circuit, but the potentialdifference (voltage) across its terminals is always

zero volts

Ddj2003 Notes Chap1 (Dc Circuits)

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