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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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66--1: Finding1: Finding RRTT
forforSeriesSeries--Parallel ResistancesParallel Resistances
Overview ofSeries-Parallel Circuits
There are three branches in this
circuit; sections 1 and 2 are series strings.
1
2
3
V
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66--1: Finding1: Finding RRTT
forforSeriesSeries--Parallel ResistancesParallel Resistances
Overview ofSeries-Parallel Circuits
There are three series sections in this
circuit; sections 1 and 2 are parallel banks.
1
2
3V
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66--1: Finding1: Finding RRTT
forforSeriesSeries--Parallel ResistancesParallel Resistances
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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66--1: Finding1: Finding RRTT
forforSeriesSeries--Parallel ResistancesParallel Resistances
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).
Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.
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66--2: Resistance Strings in Parallel2: Resistance Strings in Parallel
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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66--2: Resistance Strings in Parallel2: Resistance Strings in Parallel
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).
Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.
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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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66--4: Resistance Banks and Strings in4: Resistance Banks and Strings inSeriesSeries--ParallelParallel
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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66--4: Resistance Banks and Strings in4: Resistance Banks and Strings inSeriesSeries--ParallelParallel
Fig. 6-5, cont. (c) RTand R6 in series added forR13. (d) R13 and R5 in parallel combined forR18.
Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.
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66--4: Resistance Banks and Strings in4: Resistance Banks and Strings inSeriesSeries--ParallelParallel
Fig. 6-5e: The R18,R1, and R2 in series are added for the total resistance of50 forRT.
Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.
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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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66--5: Analyzing Series5: Analyzing Series--Parallel CircuitsParallel Circuitswith Random Unknownswith Random Unknowns
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.
Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.
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66--5: Analyzing Series5: Analyzing Series--Parallel CircuitsParallel Circuitswith Random Unknownswith Random Unknowns
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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6-5: Analyzing Series-Parallel Circuitswith Random Unknowns
Find voltage drops V1, V2,
and V3:
Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.
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6-5: Analyzing Series-Parallel Circuitswith Random Unknowns
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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6-5: Analyzing Series-Parallel Circuitswith Random Unknowns
=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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66--6: The Wheatstone Bridge6: The Wheatstone Bridge
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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66--6: The Wheatstone Bridge6: The Wheatstone Bridge
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.
Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.
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66--6: The Wheatstone Bridge6: The Wheatstone Bridge
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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66--7: Troubleshooting: Opens and7: Troubleshooting: Opens andShorts in SeriesShorts in Series--Parallel CircuitsParallel Circuits
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.
.
Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.
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66--7: Troubleshooting: Opens and7: Troubleshooting: Opens andShorts in SeriesShorts in Series--Parallel CircuitsParallel Circuits
Effect ofa Short in a Series-Parallel Circuit
Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.
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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66--7: Troubleshooting: Opens and7: Troubleshooting: Opens andShorts in SeriesShorts in Series--Parallel CircuitsParallel Circuits
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.
Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.
With S2 open,R3 is effectively removed from
the circuit.
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66--7: Troubleshooting: Opens and7: Troubleshooting: Opens andShorts in SeriesShorts in Series--Parallel CircuitsParallel Circuits
Effect ofan Open in a Series-Parallel Circuit
Copyright The McGraw-Hill Companies,Inc. Permission required for reproduction or display.
With S2
open the voltage across points C and D equals the
voltage across R2,which is 89V. The voltage across R
3is
zero.