1. Topics in
Covered Chapter 6
6-1 Finding
: Rrfor Series-Parallel
Resistances
6-2:Resistance
Strings Parallel
in
6-3:Resistance
Banks Series
in
6-4:Resistance
Banks Strings Series-Parallel
and in
@2ffi7 The McGrc*Hilt Cwanies Inc. All iskts rcm eil.
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Tcpfc-s
Covered In Chapf,er
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6
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i i t t Cirnp d ni es, In c. Al I i gkts resn ed:

2. 6-.[:FfndiftS for
Ru
Reslstan
Serfes-Pcrsilie[ ces
. Overviewof Series-Parallel Circuits
. A series-parallel
circuit,or combination circuit,
combines series parallel
both and connections.
r Mostelectroniccircuits intothiscategory.
fall
circuits typically
Series-parallel are usedwhendifferent
voltage curent values required
and are fromthe same
voltagesource.
. Series
components a seriesstring.
form
r Parallel
components a parallel
form bank.
. Overview Series-Parallel
of Circuits
There arethreebranches this
in
circuit sections

3. To findRrfor a series-parallel ff'l'= &H
s.$ kf} .
n.S!rt}
circuit, theseries
add
resistances combine
and the
.fa=.1;*,1;9 &t+ I*
=
parallel resistances.
fn thisdiagram, and Rrare
R,
in series,and R, andRoare in
parallel. However, is not in
R,
serieswiththe parallel
resistances: Resistancesin
serieshavethe samecurrent,
butthe current R, is equal
in
to the sumof the branch
currentsI, andln. {#i
Fig. &1b. Schematicdiagram of a series-
parallel circuit.
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4. Ff*ding ftuf*n
6--T:
Series-Pcra[fe]
Reslsta rlces
. F or F i g .6 - 1 b ,
. Theseries resistances
are:
0.5ko+0.5ko: lkft
. Theparallel resistances
are:
lka I 2: 0. 5kQ
. Theseries parallel
and values thenadded the
are for
valueof Rr:
lka + 0.5kfi: 1"5 kQ

5. . :,1 .j : r' - : .;:i- ii ,_ ::
-. -. : - -
: i: : ' . : r : i: : . ! : : . i' - r l: i I
+
6*2: Resfs,fftce Strf gs fft Parat$el
ff n
SeriesGircuit Parallel Gircuit
. Current thesamein all
is . Voltage thesame
is
bir
across branches.
all
#
i:,-t:
at:
components.
. V across
eachseries is
R . I in eachbranch is V/R.
R
iti . lr ' lr + lz + ls + . . . + c .
lii / xR. et
iti
iii . Vr= Vr* Vza Vs+...+
etc.
i:t
,ii
;ii
Z is the sameacrosseachparallelbranch.

6. &*2:Resfsfafice
Strfngs Para[fel
En
i
. Thecurrent eachbranch
in equals voltage
the applied
across branch
the divided the branch
by Rr.
. Thetotallinecurrent equals sumof the branch
the
currents all parallel
for strings.
. The Rl-for the entirecircuitequals applied
the voltage
divided thetotallinecurrent.
by
r Foranyresistance a series
in string, /R voltage
the drop
acrossthatresistance equals string's
the current
multiplied the resistance.
by
. The sumof the valtage dropsin the series stringequals
thevoltage across entire
the string.
i:
;' ll1 '* 4V
Inthisfigure, andR.
R, i F r '=1 t l
areparallel resistancesin
a bank. Theparallel bank
is in series Rr.
with
There maybemore than
twoparallel resistances in
a bank, anynumber
and
in
of banks series.
Ohm's Lawis applied to
theseries parallel
and
components seen
as
previously. Fig. &4a: Parallelbank of R, and R. in
serles with R, {Originalcircuit).
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7. 6:3: Res$sfaftce
Banksfn Sertes
+;ii;?ii:rrl
il
' To findthetotalresistance thistypeof circuit,
of
combine parallel
the resistances eachbankandadd
in
theseries resistances.
I rr 10 A (ofR, + Rr)
6o:ffi +lo(Rr)
rr z4v
n:
4A
24v 6o:5cl + 1fl
6fl :
4A
:;t.-::- ',',
,S*fSjl$i, i i,:: .:.::!i.,:::,':','';,-'.::.'-':
-
To solve (combination)
series-parallel circuits, is
it
important knowwhichcomponents in series
to are with
oneanother which
and components in parallel.
are
Series components be in onecurrent
must pathwithout
anybranch points.
To findparticular for
values thistypeof circuit,
r Reduce combine components
and the using rules
the
series paralfel
for individual and circuits.
r Reduce circuit itssimplest
the to possibleform.
' Thensolve the needed
for valuesusingOhm's Law.

8. tsanks Strfngs
6-4:Resfstance and
Serfes-.Fg,rctIe"I
Example.
r Findall currents
and voltages Fig.6-5.
in
. Step1. FindRr.
mainline currentas /, = Vr/ R,
' Step2: Calculate
{d} tb}
Fig.6-5: Reducing series-parallel
a to seriescircuitto findthe RL (a)
circuit an equivalent
Actualcircuit.(b) Rs and R, in parallel for
cornbined the equivalentRt
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9. f t r*
5il JI
Fig.6-5e:The Rrr, Rr, and R, in seriesare addedfor the totalresistance 50Qfor R,
of
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Jl f
e
6'-5tAnafyzlng Sen[es--PcFs Cfr"cu[ts
wlth Randonn Unknowns
. In solving apply sameprinciples
suchcircuits, the as
before:
. Reduce circuitto itssimplest
the possible
form.
' ApplyOhm'sLaw.
t.'
.-. :""'

10. 6*5:Anatyzing Cfrcuffs
SerFes-Pcrqffef
wlth Rsind:onn
Unknowns
, , t. .. :
.
. '. :
t' - - : i :
.
1 - 'r , 1
:,... -
:
I : '
,t.,t. ,,, '
Example:
. In Fig.6-6,we can
find branch
currentsl, andlr_u,
and /r, and
voltage drops Vr,
Vr, and l/r, without
knowing value
the
of Rr.
Fig.6-6: Finding the cunentsand voltages calculating branch
all by the cunentsflrst.
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Ana JynngSeries--Paratfef
6,-5: Cfrcuft-s
wfth RandomUnknowns
r Find 11, and lr.
124,
T
gAY {parallelbranches
havethe sanne
voltage)
t1
30s
I1

11. i : i : : , i : a i : j i . , : t , ri : : r: : : . r. : ; t ::::.:: :::
6-5:Analyzing
Series-Porollel
Circuits
with Rondom Unknowns
. FindvoltagedropsV1,V2,
and vs:
$, ,*;
t* $t
,.1-.
. . f f r=
* Jti lJ
.j;t, ff." t-
: zsir
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12. 6-5:Anolyzing Circuits
Series-Parollel
with RondomUnknowns
Vr : Vo(parallelbranches havethe samevoltage)
Vr:90V
or
Vt : IrR, Vz: Ir 8, Vs: I, It
Vt : 34 x 30f} Vz: LA|ZA A) Vs:2A{25 O)
Vr:90V Vz:40V Ys :5 0 V
Note: V, * Vs: Ve
40V + 50V:90V
Rr
904
Rr
ftr 18f}

13. &*&:TheWhecfsfofte firfdge
';.j.'1f..r;t,'',
A Wheatstone bridge a circuit is usedto
is that
determine valueof an unknown
the resistance.
The unknown resistor(R*)is in the samebranch the
as
resistor
standard {Rr).
*tandardrcslsicr,
il-*$gg llivsnlable
ln t-{t *lepc}
bridge.
Fig.6-10:Wheatstone
Copyright The Mc€raw-l-lill
@ reguired reproduction dsCay.
companies,lnc. Permission for or
:-:-.1'.-.:
:- '.,r .: .:,- ,:,- .:i .l
Resistors andR, formthe ratio
Rr theyhavevery
tight resistance
tolerances.
Thegalvanometer a sensitive
(Mr), currentmeter,
is
connected between output
the terminals andD.
C
WhenR',/Rz=Rt/ Rn,thebridge balanced.
is
is in
Whenthe bridge balanced, current M, is zero.
the

14. 6-d:The Whee*fs,fofte
Srtdge
Bridge Measure Unknown
Using Wheatstone
a to an
Resistance
' Rs is adjusted zerocurrent Mt..
for in
. Whenthecurrent M1=04, thevoltage
in division
Rr
between andR* is equalto thatbetween andR .
Rx
Stii.ndard
r€sisBa,
{Fg3$S $*,?dable 1 ..
l* !-f:SeFl
Copyright@ Mccraw]-lillCompanies, Permission
The Inc- ordsday.
requiredforreproducEon
WhentheWheatstone
Note: bridge balanced,
is
strings parallel.
analyzed twoseries
as in Notethe
followingrelationship:
Rx RI
Rs R2
R,
RX - R OdR2
*

15. T,rcubtesha,effng: and
&-7: Opens
Shorts Ser[es-Pen'aftef
En C[rcults
. Whentroubleshooting
series-parallel
circuits,
combine
thetechniques whentroubleshooting
used individual
series parallel
and circuits.
6,-7Troub,[eshooffng:
: Opensanid,
[n
Shorfs Serfes-Pcrqt[e[
Clrculf,s
Effect a Shortin a Series-Parallel
of Circuit
Thetotalcurrent totalpowerincrease.
and
ffr = fS{i fle*SF91 Fi * 1${}
,t
ii. i
- !,i
lf,r'r: ig6 U
{5}
Fig.6-13:Effect a shortcircuit
of withseries-parallel
connections. Normal
(a) circuit
with S,
open.(b) Circuitwith shortbetweenpointsA and B when S, is closed;nowR, and R, are
circuited.
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16. Treub[esh*otfng:
&*7: *pens cnd
Cfrcui,ts
Shart,s Serfes*Pera[te[
[n
in a Series-Parallel
Circuit
Vr = "!*6-
V
?r-=:,;+
"1;".4+
t#:
Thetotalcurrentincreases 2A
from With S?closed,R, and R,
withS, opento l0Awith S, closed. are shortedout.
rsquiredfor reproduction dspfay.
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@ Inc- or
Opensand
&*7Troubfeshaat[nE:
:
[n Cfrcufts
Sharts Serfes-F€Nra[tet
Effect an Openin a Series-Parallel
of Circuit
.F. * 1Sll t?* = 80 f! Fig.6-14:Effectof an openpathin a series-
paralleleircuit. Normalcircuit Sz
(a) with
closed.(E)Seriescircuitwith R, and R, when
S, is open.NowR, in the openpathhas no
currentand zero /R voltagedrop.
!.: : tf 1,I
9. *, 1$ !L &=8+fl
= 8$ {i
With 52 open,R, is effectively
removedfrom
1fi* V .";=" l$ t' i
;-.,:-.r
the circuit.
tftj
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I or
requit€dfor reproduction dsplay.

17. &*7: Cper]scnd
Tr*ubfesho,cffng:
Shorts Ser[es*Pera$tet s
Cfrculf,
Short a Series-Parallel
in Circuit
ff* * 1${l
Thetotalcurrentincreases 2A
from With S, closed,R, and R,
withS, opento l0Awith S, closed. are shortedout.
Copynght @ The Mccraw.Hill Companies, Inc. Permission tequircd for reproduclion or dsplay-
Qpensqnd
&-7 Traubfeshcot[nE:
:
f
Shortsn SerEes*Fcrat[ef
Cfr-cufts
Effect an Openin a Series-Parallel
of Circuit
-Hr* 1S$1 fT* = $S fI Fig.6-14:Effectof an openpathin a series-
,#,t parallelcireuit.(a) Normalcircuitwith Sz
"'r ,'-:i; Y
closed.(b) Seriescircuitwith R, and R, when
it', .;,.** lf S, is open.NowR, in the open path has no
cunentand zero lR voltagedrop.
!.;.-: 1i lr I,r -:
-
t
f r , + lgf i €= * * lJ { :
."
With S?open,R, is efiectivelyremovedfrom
tOS'V ',1 ltitl ffz ,= SS fI ,;3r:l::
the circuit.
tft]
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18. :
&*7 Tr:cu#esh*affngQpefts and
:
C[rcu[ts
Shart's SenEes-Fers[te[
[n
Circuit
Effectof an Openin a Series-Parallel
1'':i 'r; !d
"itf
f/s $FgS i,i
Wth Szopenthe voltageacrosspointsC and D equals the
voltageacrossRowhichis 89V.The voltageacrossRr is
zero.
Copyright @ The McGraw-Hill Cmpanies, tnc Perm'rssion requited for reproductiot or dispay-