Cours d'éléctronique pour les débutants 6

8/8/2019 Cours d'lctronique pour les dbutants 6

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SeriesSeries--Parallel CircuitsParallel Circuits

Topics Covered in Chapter 6

6-1: Finding RT for Series-Parallel Resistances

6-2: Resistance Strings in Parallel6-3: Resistance Banks in Series

6-4: Resistance Banks and Strings in Series-Parallel

ChapterChapter66

2007 The McGraw-Hill Companies, Inc. All rights reserved.


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Topics Covered in Chapter 6Topics Covered in Chapter 6

6-5: Analyzing Series-Parallel Circuits with Random

Unknowns

6-6: The Wheatstone Bridge

6-7: Troubleshooting: Opens and Shorts in Series-

Parallel Circuits

McGraw-Hill 2007 The McGraw-Hill Companies, Inc. All rights reserved.


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66--1: Finding1: Finding RRTT

forforSeriesSeries--Parallel ResistancesParallel Resistances

Overview ofSeries-Parallel Circuits

A series-parallel circuit, orcombination circuit,

combines both series and parallel connections.

Most electronic circuits fall into this category.Series-parallel circuits are typically used when different

voltage and current values are required from the same

voltage source.

Series components form a series string.

Parallel components form a parallel bank.


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There are three branches in this

circuit; sections 1 and 2 are series strings.

1

2

3

V


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There are three series sections in this

circuit; sections 1 and 2 are parallel banks.

1

2

3V


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To find RTfor a series-parallel

circuit, add the series

resistances and combine the

parallel resistances.

In this diagram,R1 and R2arein series, and R3 and R4 are in

parallel. However,R2is not in

series with the parallel

resistances: Resistances in

series have the same current,

but the current in R2 is equal

to the sum of the branch

currents I3 and I4.

Fig. 6-1b: Schematic diagram ofa series-

parallel circuit.

Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.


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For Fig. 6-1b,

The series resistances are:

0.5k + 0.5k = 1k

The parallel resistances are:

1k / 2 = 0.5k

The series and parallel values are then added for the

value ofRT:1k + 0.5k = 1.5 k


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66--2: Resistance Strings in Parallel2: Resistance Strings in Parallel

In this figure, branch 1

has two resistances in

series; branch 2 has

only one resistance.

Ohms Law can be

applied to each branch,

using the same rules for

the series and parallel

components that werediscussed in Chapters 4

and 5.

Fig. 6-3a: Series string in parallel with

another branch (schematic diagram).



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Series Circuit

Current is the same in all

components.

Vacross each series RisI R.

VT= V1 + V2+ V3 +...+ etc.

Parallel Circuit

Voltage is the same

across all branches.

Iin each branch Ris V/R.

IT= I1 + I2+ I3 +...+ etc.


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I is the same

in this

section.

V

Vis the same across each parallel branch.


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66--3: Resistance Banks in Series3: Resistance Banks in Series

In this figure,R2and R3are parallel resistances in

a bank. The parallel bank

is in series with R1.

There may be more than

two parallel resistances in

a bank, and any number

ofbanks in series.

Ohms Law is applied tothe series and parallel

components as seen

previously.Fig. 6-4a: Parallel bank ofR2and R3 in

series with R1 (Original circuit).



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66--3: Resistance Banks in Series3: Resistance Banks in Series

To find the total resistance of this type ofcircuit,

combine the parallel resistances in each bank and add

the series resistances.

V

IR =

6 =24V

4A

R=24V

4A

6 =10 (ofR

2+ R

3)

2 branches+ 1 (R

1)

6 = 5 + 1


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66--4: Resistance Banks and Strings in4: Resistance Banks and Strings inSeriesSeries--ParallelParallel

To solve series-parallel (combination) circuits, it is

important to know which components are in series with

one another and which components are in parallel.

Series components must be in one current path withoutany branch points.

To find particular values for this type ofcircuit,

Reduce and combine the components using the rules

for individual series and parallel circuits. Reduce the circuit to its simplest possible form.

Then solve for the needed values using Ohms Law.


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Example:

Find all currents and voltages in Fig. 6-5.

Step 1: Find RT.

Step 2: Calculate main line current as IT= VT/RT

Fig. 6-5: Reducing a series-parallel circuit to an equivalent series circuit to find the RT. (a)

Actual circuit. (b) R3 and R4 in parallel combined for the equivalent RT.Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.


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Fig. 6-5, cont. (c) RTand R6 in series added forR13. (d) R13 and R5 in parallel combined forR18.



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Fig. 6-5e: The R18,R1, and R2 in series are added for the total resistance of50 forRT.



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66--5: Analyzing Series5: Analyzing Series--Parallel CircuitsParallel Circuitswith Random Unknownswith Random Unknowns

In solving such circuits, apply the same principles as

before:

Reduce the circuit to its simplest possible form.

Apply Ohms Law.


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Example:

In Fig. 6-6, we can

find branch

currents I1 and I2-3,and IT, and

voltage drops V1,

V2, and V3,

without knowing

the value ofRT.

Fig. 6-6: Finding all the currents and voltages by calculating the branch currents first.



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Find I1,I2-3, and IT.

V

R

I1 =

I1=3A

I1=

90V

30

(parallel branches have the same voltage)


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6-5: Analyzing Series-Parallel Circuitswith Random Unknowns

I2-3

=V

R

I2-3=2A

I2-3=

90V

20 + 25

I2-3=

90V

45

IT= I

1+ I

2-3

IT= 3A + 2A

IT

= 5A


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Find voltage drops V1, V2,

and V3:



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V1

= VA

(parallel branches have the same voltage)

V1

= 90V

or

V1= I

1R

1V

2= I

2-3R

2V

3= I

2-3R

3

V1

= 3A 30 V2

= 2A(20 ) V3

= 2A(25 )

V1

= 90V V2

= 40V V3

= 50V

Note: V2

+ V3= V

A

40V + 50V = 90V


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=RT

IT

VA

=RT5A

90A

18=RT


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66--6: The Wheatstone Bridge6: The Wheatstone Bridge

A Wheatstone bridge is a circuit that is used to

determine the value ofan unknown resistance.

The unknown resistor (RX) is in the same branch as the

standard resistor (RS).

Fig. 6-10: Wheatstone bridge.Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.


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Resistors R1 and R2 form the ratio arm; they have very

tight resistance tolerances.

The galvanometer (M1), a sensitive current meter, is

connected between the output terminals C and D. When R1/R2=R3/R4, the bridge is balanced.

When the bridge is balanced, the current in M1 is zero.


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Using a Wheatstone Bridge to Measure an Unknown

Resistance

RS is adjusted for zero current in M1..

When the current in M1 = 0A, the voltage divisionbetween RXand RS is equal to that between R1 and R2.



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Note: When the Wheatstone bridge is balanced, it can be

analyzed as two series strings in parallel. Note the

following relationship:

=

RS

RX

R1

R2

=RX RSR

1

R2


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66--7: Troubleshooting: Opens and7: Troubleshooting: Opens andShorts in SeriesShorts in Series--Parallel CircuitsParallel Circuits

In series-parallel circuits, an open or short in one part of

the circuit changes the values in the entire circuit.

When troubleshooting series-parallel circuits, combinethe techniques used when troubleshooting individual

series and parallel circuits.


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Effect ofa Short in a Series-Parallel Circuit

The total current and total power increase.

Fig. 6-13: Effect ofa short circuit with series-parallel connections. (a) Normal circuit with S1open. (b) Circuit with short between points A and B when S1 is closed; now R2and R3 are short-

circuited.

.



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Effect ofa Short in a Series-Parallel Circuit


The total current increases from 2Awith S

1open to 10A with S

1closed.

With S1 closed,R2 and R3are shorted out.


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Effect ofan Open in a Series-Parallel Circuit

Fig. 6-14: Effect ofan open path in a series-

parallel circuit. (a) Normal circuit with S2closed. (b) Series circuit with R1 and R2when

S2is open. Now R3 in the open path has nocurrent and zero IRvoltage drop.


With S2 open,R3 is effectively removed from

the circuit.


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Effect ofan Open in a Series-Parallel Circuit


With S2

open the voltage across points C and D equals the

voltage across R2,which is 89V. The voltage across R

3is

zero.

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Cours d'éléctronique pour les débutants 6