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Texas A&M University *
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Course
210
Subject
Electrical Engineering
Date
Dec 6, 2023
Type
Pages
14
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EXPERIMENT
dc
Series-Parallel
dc
Circuits
'
'
OBJECTIVES
1.
Test
the
theoretical
analysis
of
series-parallel
networks
through
direct
measurements.
2.
Improve
skills
of
identifying
series
or
parallel
elements.
3.
Measure
properly
the
voltages
and
currents
of
a
series-parallel
network.
4.
Practice
applying
Kirchhoff’s
voltage
and
current
laws,
the
current
divider
rule,
and
the
voltage
divider
rule.
EQUIPMENT
REQUIRED
Resistors
1—1-kQ,
2.2-kQ),
3.3-kQ),
4.7-kQ
(1/4-W)
Instruments
|1—DMM
1—dc
power
supply
108
EQUIPMENT
ISSUED
EXPERIMENT
dc
9
TABLE
9.0
Item
Manufacturer
and
Model
No.
Laboratory
Serial
No.
DMM
Power
supply
RESUME
OF
THEORY
PROCEDURE
Part
1
The
analysis
of
series-parallel
dc
networks
requires
a
firm
understanding
of
the
basics
of
both
series
and
parallel
networks.
In
the
series-parallel
configuration,
you
will
have
to
isolate
series
and
parallel
configurations
and
make
the
necessary
combinations
for
reduction
as
you
work
toward
the
desired
unknown
quantity.
As
arule,
it
is
best
to
make
a
mental
sketch
of
the
path
you
plan
to
take
toward
the
com-
plete
solution
before
introducing
the
numerical
values.
This
may
result
in
savings
in
both
time
and
energy.
Always
work
with
the
isolated
series
or
parallel
combinations
in
a
branch
before
tying
the
branches
together.
For
complex
networks,
a
carefully
redrawn
set
of
reduced
networks
may
be
re-
quired
to
ensure
that
the
unknowns
are
conserved
and
that
every
element
has
been
properly
included.
(a)
Construct
the
series-parallel
network
of
Fig.
9.1.
Insert
the
measured
value
of
each
resistor
in
the
space
provided.
R,
—AM,
22k
R,
,
=
g
Ry
Ry
Ry
1
kO
3.3k
R)
measured
=
R]mcu\'umd
~
FIG.
9.1
o
(b)
Calculate
the
total
resistance
R,
using
the
measured
resistance
values
and
record
in
Table
9.1.
Calculation:
\>SERIES-PARALLEL
dc
CIRCUITS
109
(¢)
Use
the
ohmmeter
section
of
the
multimeter
to
measure
Ry
and
record
in
Table
9.1.
(d)
Determine
the
magnitude
of
the
percent
difference
between
the
calculated
and
measured
values
of
parts
1(b)
and
1(c)
using
the
following
equation
and
record
in
Table
9.1.
%
Difference
=
Calculated
—
Measured
X
100%
Calculated
9.1)
Use
Eq.
(9.1)
for
all
percent
difference
calculations
in
this
laboratory
experiment.
Calculation:
TABLE
9.1
Ry
(calculated)
R
(meas
ured)
%
Difference
()
If
12'V
were
applied,
as
shown
in
Fig.
9.2,
calculate
the
currents
I,
I,
I,
and
I
using
the
measured
resistor
values
and
record
in
Table
9.2.
FIG.
9.2
_]T:'
Calculation:
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110
(f)
Apply
12V,
measure
the
currents
Iy,
I,
I,
and
I
using
the
milliammeter
section
of
your
multimeter,
and
record
in
Table
9.2.
Be
sure
the
meter
is
in
series
with
the
resistor
through
which
the
current
is
to
be
measured.
Calculate
the
magnitude
of
the
percent
difference
between
calculated
and
measured
values
using
Eq.
(9.1)
and
enter
in
Table
9.2.
Calculation:
How
are the
currents
/;
and
/;
related?
Why?
TABLE
9.2
Calculated
Measured
%
Difference
(g)
Using
the
results
of
part
1(e),
calculate
the
voltages
V,,
V,,
and
V;
using
measured
resistor
values
and
record
in
Table
9.3.
Calculation:
EXPERIMENT
dc
9
)
SERIES-PARALLEL
dc
CIRCUITS
(h)
Measure
the
voltages
V;,
V,
and
V;,
determine
the
magnitude
of
the
percent
difference
between
the
calculated
and
measured
values,
and
record
the
results
in
Table
9.3.
Calculation:
TABLE
9.3
Calculated
Measured
%
Difference
How
are
the
voltages
V,
and
V;
related?
Why?
(i)
Referring
to
Fig.
9.2
and
the
results
in
Table
9.3
does
E
=
V,
+
V,,
as
required
by
Kirchhoff’s
voltage
law?
Part
2
(a)
Construct
the
series-parallel
network
of
Fig.
9.3.
Insert
the
measured
value
of
each
resistor.
O
P
R
3.3
kQ
1
measured
Rr
2.52
kQ)
Ry
R)
measured
=
1
kQ
Ry
measured
=
FIG.
9.3
o
111
112
EXPERIMENT
dc
9
(b)
Calculate
the
total
resistance
Ry
using
measured
resistor
values
and
insert
in
Table
9.4.
Calculation:
(¢)
Use
the
ohmmeter
section
of
your
multimeter
to
measure
the
total
resistance
Ry
and
record
in
Table
9.4.
Calculate
the
magnitude
of
the
percent
difference
between
the
calculated
value
of
part
2(b)
and
the
measured
value
of
part
2(c)
and
insert
in
Table
9.4.
Calculation:
TABLE
9.4
Ry
(calculated)
Ry
(measured)
%
Difference
(d)
If
12V
were
applied
to
the
network,
as
shown
in
Fig.
9.4,
calculate
the
currents
I,
I,
I,
and
I;
using
measured
resistor
values
and
insert
in
Table
9.5,
I
fi"
WI
‘
.
:
$
+
R,
S
33kQV,
R
=
12V
V§
1
!
_]'
1
322k
4
-
RS
1kQ
V;
FIG.
9.4
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'SERIES-PARALLEL
dc
CIRCUITS
113
Calculation:
(e)
Apply
12V
and
measure
the
currents
,,
I},
I,
and
I
and
record
in
Table
9.5.
Calculate
the
magnitude
of
the
percent
difference
between
the
calculated
and
measured
values
for
each
current
and
record
in
Table
9.5.
Calculation:
How
are
the
currents
/,
and
I
related?
Why?
(f)
Referring
to
Fig.
9.4
and
Table
9.5
does
I;
=
I}
+
I,
as
required
by
Kirchhoff’s
current
law?
114
EXPERIMENT
dc
9
TABLE
9.5
Calculated
Measured
%
Difference
(g)
Using
the
results
of
part
2(d)
and
measured
resistor
values,
calculate
the
voltages
Vi,
Vs,
and
V;
and
record
in
Table
9.6.
Calculation:
(h)
Measure
the
voltages
V,,
V,,
and
V;
and
record
in
Table
9.6.
Calculate
the
magnitude
of
the
percent
difference
between
the
calculated
and
measured
values
for
each
voltage
and
insert
in
Table
9.6.
Calculation:
SERIES-PARALLEL
dc
CIRCUITS
TABLE
9.6
Calculated
Measured
%
Difference
115
(i)
How
are
the
voltages
E,
V;,
and
the
sum
of
V,
and
V;
related?
Use
Table
9.6
to
determine
the
sum
of
V,
and
V;.
Part
3
(a)
Construct
the
series-parallel
network
of
Fig.
9.5
and
insert
the
measured
value
of
each
resistor.
[
)
=
47kQ
=
FIG.
9.5
R|
measured
=
RZ
measured
RJ
measured
=
Ry
measured
(b)
How
is
the
total
voltage
across
the
two
series
elements
R,
and
R,
related
to
the
applied
voltage
E?
Why?
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116
EXPERIMENT
dc
¢
How
is
the
total
voltage
across
the
two
series
elements
Ry
and
R,
related
to
the
applied
voltage
E?
Why?
(¢)
Using
the
conclusions
of
part
3(b),
calculate
the
voltages
V,
and
V,
using
the
vo-
age
divider
rule
and
measured
resistor
values.
Insert
the
results
in
Table
9.7.
Calculation:
(d)
Measure
the
voltages
V,
and
V,
and
record
in
Table
9.7.
Calculate
the
magnitude
of
the
percent
difference
between
calculated
and
measured
values
and
insert
in
Table
9.7.
Calculation:
TABLE
9.7
Calculated
Measured
%
Difference
(¢)
Using
the
results
of
part
3(c),
calculate
the
voltage
V,,
using
Kirchhoff’s
voltage
law
and
record
in
Table
9.7.
Calculation:
SERIES-PARALLEL
dc
CIRCUITS
117
(f)
Measure
the
voltage
V,,
and
determine
the
magnitude
of
the
percent
difference
between
the
calculated
and
measured
values
and
record
each
in
Table
9.7.
Calculation:
()
Is
the
voltage
V,,
also
equal
to
V;
—
V,?
Why?
(h)
Calculate
the
current
/,
using
any
method
you
prefer.
Use
measured
resistor
values
and
record
in
Table
9.7.
Calculation:
(i)
Measure
the
current
/,
and
calculate
the
magnitude
of
the
percent
difference
between
calculated
and
measured
values
and
record
both
in
Table
9.7.
Calculation:
118
EXPERIMENT
dc
¢
Part
4
(a)
Construct
the
network
of
Fig.
9.6.
Insert
the
measured
value
of
each
resistor,
l‘.(—’
MWy
"
MWN——
Ry
=
22kQ
Ry
=
47kQ
fi
RT
+
"'I
measured
E
2=2ULY
Ry
="1k0)
Ry=33
RQ§
v,
R,
measured
)
-
R‘mvgmm-d
=
R~!
measured
=
LB
:
FIG.
9.6
-
(b)
Calculate
the
voltage
V,
using
the
measured
resistor
values
and
insert
the
results
in
Table
9.8.
Calculation:
(c)
Measure
the
voltage
V,
and
calculate
the
magnitude
of
the
percent
difference
between
calculated
and
measured
values
and
record
in
Table
9.8.
Calculation:
(d)
Measure
the
current
/,
and
calculate
the
total
input
resistance
from
R,
=
E/I,
and
record
both
in
Table
9.8.
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\\'SERIES-PARALLEL
dc
CIRCUITS
TABLE
9.8
Calculated
Measured
%
Difference
119
(e)
Disconnect
the
power
supply
and
measure
Ry
using
the
ohmmeter
section
of
the
DMM.
Then
calculate
the
magnitude
of
the
percent
difference
between
the
calculated
and
measured
values.
Record
both
results
in
Table
9.8.
Calculation:
EXERCISES
1.
For
the
series-parallel
network
of
Fig.
9.7,
determine
Vi,
Ry,
and
R,
using
the
information
provided.
Show
all
work!
Assume
Riyema
=
0
{2
for
all
meters.
FIG.
9.7
R,
120
EXPERIMENT
dc
9!
determine
V,,
R,,
and
R;
using
the
information
0
()
for
all
meters.
2.
For
the
series-parallel
network
of
Fig.
9.8,
provided.
Show
all
work!
Assume
Ripemal
=
FIG.9.8
V|:
.R2=
,R3=
3.
For
the
series-parallel
network
of
Fig.
9.5
record
the
measured
values
of
V,,
V,,
and
V,,
in
Table
9.9
(from
Table
9.7).
Then,
using
PSpice
or
Multisim,
determine
the
same
voltages
and
enter
the
results
in
Table
9.9.
Use
measured
values
for
the
resistors.
TABLE
9.9
Table
9.7
PSpice
or
Multisim
How
do
the
results
compare?
Try
to
explain
any
differences.
Attach
all
appropriate
printouts.
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