```FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL
EXPERIMENT 2
RESISTORS IN SERIES AND PARALLEL
1.0 INTRODUCTION
An electric circuit is a complete path from the positive terminal to the negative
terminal of a power source. If the elements of the circuit are arranged in such a way
that only one path exists for current flow (i.e. the current is identical for all elements),
then the circuit is a series one. If an identical voltage exists across a number of
alternative current paths then the circuit is a parallel one. Most practical circuits
involve various combinations of series and parallel components. Of course
components can be connected so that they are neither in series or parallel. Answer the
following questions in your lab books:
1. If voltages are identical, then how are the components connected?
2. If currents are identical, then how are the components connected?
2.0 SERIES CIRCUITS
2.1 SERIES CIRCUIT THEORY
A typical series circuit is shown in Figure 2.1, this circuit having four resistors
and a power source
R1
Vs
R2
It
R4
R3
Figure 2.1
The total resistance Rt in the circuit may be calculated by a simple summation
of the individual resistors:
Rt = R1 + R2 + R3 + R4
This may be extended for n number of resistors. From Ohm’s Law, the total
current in the circuit may be calculated.
Vs = ItRt or It = Vs/Rt
An important requirement of a series circuit is that the current is identical
throughout the circuit. This feature will be observed in this experiment.
Dr. Daniel Nankoo
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FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL
2.2 REQUIREMENTS FOR SERIES CONNECTION TEST
Select the resistors 1k, 820 and 680, and use the DMM to measure their
values. Record your results in Table 2.1, which is to be drawn in your lab
book.
Nominal Resistance 
R1 =
R2 =
R3 =
Rtot =
Measured Resistance 
% Difference
Table 2.1
Connect the resistors in series on your breadboard, and measure the total
resistance, Rtot (do not connect the DC power supply yet, and do the %
calculations outside lab time).
2.3 VOLTAGE TESTS
Draw Table 2.2 in your lab book.
Quantity
Measured value from
DMM
Theoretical predictions using
DMM values for Vs and R
% Difference
Vs
Rtot
VR1
VR2
VR3
IA
IB
IC
ID
Table 2.2
DMM
V/
COM
red
black
A
B
R1 = 680
R2 = 820
Vs ≈ 15V
C
D
R3 = 1k
Figure 2.2
Connect the variable DC power supply and, using the DMM in voltmeter
mode, adjust the output to about 15V. Measure and record the actual value
Dr. Daniel Nankoo
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FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL
from the DMM into Table 2.2. It is essential that this voltage remains
unchanged at the recorded value for the entire series test. Figure 2.2 shows the
meter connections for measuring the voltage across R1. You will need to
reconnect the red and black wires to measure the voltages across the other
resistors.
2.4 CURRENT TESTS
The next part of the experiment is to measure the current at various points in
the circuit. Use the DMM set up in ammeter mode to measure milliamps at the
four points A, B, C and D. Note that it will be necessary to break your circuit
and remake it in order to insert the ammeter. Record your results in the
appropriate fields in Table 2.2 in your lab book.
Discuss the reasons for any differences in Table 2.1. Use Ohm’s Law to
calculate the current flowing in the circuit It and hence calculate the voltage
drop expected across each resistor (e.g. voltage drop across R1 is calculated as
VR1 = ItR1, etc). Use the values as indicated in the third column of Table 2.2.
Compare these theoretical values with the measured values and express them
as percentage differences using the following formula:
(Measured value – Theoretical value)/Theoretical value  100
List the possible reasons for any differences. If any difference is greater than
5%, there could be a serious problem with either your calculations or tests, and
checks will be needed. Comment on the sum of the three measured resistor
voltages. Is this result consistent with expectations? Also comment on your
current measurements.
3.0 PARALLEL CIRCUITS
3.1 THEORY FOR PARALLEL CIRCUITS
It
DMM
AMMETER
Ia
Vs
+
RA
Ib
mA
COM
RB
-
red
black
Figure 3.1
Dr. Daniel Nankoo
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FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL
A typical parallel circuit is shown in Figure 3.1. Parallel circuits have more
than one path for current flow and there must be the identical voltage across
all parallel paths. Two such paths exist in the example circuit as shown. The
identical voltage appears across all the resistors in the circuit and the current
through each arm is inversely proportional to the circuit resistance (from
Ohm’s Law). The total current in the circuit is given by It = Ia + Ib (from
Kirchoff’s current law). Note the ‘break-then-remake’ method in order to
measure the current using an ammeter.
By Ohm’s Law:
Ia = Vs / RA
Ib = Vs / RB
These can be substituted into Kirchoff’s Current Law equation to give:
It = Vs(1/RA + 1/RB)
= Vs((RA)-1 + (RB)-1)
= Vs(RARB)/[RA + RB])
The term RARB / (RA + RB) expresses the total value of resistance (Rt = Vs / It)
in the circuit. In practice the inverse form, (Rt)-1 = (RA)-1 + (RB)-1, is often
simpler to work with as a calculator’s inverse button (x-1) can be used thus
reducing the amount of resistance data inputting. In addition this inverse form
is directly extendable to any number of resistors.
3.2 REQUIREMENTS FOR PARALLEL TESTS
The following tables are to be drawn into your lab books.
Nominal Resistance

R4 = 1.5k
R5 = 1.5k
R6 = 2.7k
Rtoti
Rtotii
Rtotiii
Measured Resistance 
Calculated Resistance from
measured V/I ratio 
Table 3.1: Parallel Circuit Components
Quantity
Vs
VR4
Ia
Ib
Measured Value from DMM
Calculated Values
Table 3.2: Parallel Circuit – 1 Resistor
Dr. Daniel Nankoo
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FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL
Quantity
Vs
VR4
VR5
Ia
Ib
Ic
Measured Value from DMM
Calculated Values
Table 3.3: Parallel Circuit -2 Resistors
Quantity
Vs
VR4
VR5
VR6
Ia
Ib
Ic
Id
Measured Value from DMM
Calculated Values
Table 3.4: Parallel Circuit – 3 Resistors
Select the resistors R4, R5 and R6 as listed in Table 3.1. Use the DMM to
measure their values and record your results in Table 3.1.
3.3 ONE RESISTOR IN PARALLEL WITH VOLTAGE SOURCE
b
Vs ≈ 10V
+
R4
a
Figure 3.2i
Connect the circuit as shown in Figure 3.2i with only R4 in the circuit. Use the
DMM’s voltmeter in order to ensure that the DC power supply is set to about
10V. It is essential that this voltage remains unchanged at the recorded value
for the entire parallel test.
Disconnect the DMM and reset it as an ammeter. Use the ‘break-then-make’
method (Figure 3.1) to measure and record the currents flowing at points a and
b. Then use the DMM to measure and record the voltage across R4. Enter your
results in your lab book in Table 3.2.
Dr. Daniel Nankoo
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FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL
3.4 TWO RESISTORS IN PARALLEL
Add resistor R5 to your circuit, so that it is in parallel with R4, as shown in
Figure 3.2ii. Measure the resistance of the (R4R5) combination, remembering
that when the DMM measures resistances, power to your circuit must be off.
Measure the currents through points a, b and c, and the voltages across R4 and
R5. Record all your results in Table 3.3.
b
+
Vs ≈ 10V
c
R4
R5
a
Figure 3.2ii
3.5 TESTS ON THREE RESISTORS IN PARALLEL
b
Vs ≈ 10V
+
R4
d
c
R5
R6
a
Figure 3.2iii
Add R6 to the circuit as shown in Figure 3.2iii. Use the DMM to measure the
total resistance, Rtotiii and record it in Table 3.1. Then, using the DMM
connected in the correct configuration, measure and record all the currents and
voltages associated with this circuit, recording your results in your lab books
in Table 3.4.
This is to be done outside lab time. Carry out the calculations to complete
Tables 3.1 to 3.4. Check your results in the event of any serious discrepancy
between theory and practice. Comment on the relation between your measured
V and I results and the voltage and current principles of the parallel
connection.
Dr. Daniel Nankoo
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FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL
4.0 SERIES – PARALLEL CIRCUITS
4.1 THEORY FOR SERIES-PARALLEL CIRCUITS
Many circuits consist of resistor networks, in which series and parallel
connections appear. Such a circuit is shown in Figure 4.1. The theory required
derives directly from that for the series and parallel tests.
R8
I8
I7
R7
I9
Vs ≈ 10V
R9
+
IA
A
Figure 4.1
The total resistance in this case is a combination of series and parallel
principles.
4.2 REQUIREMENTS FOR TESTS
Draw the following tables into your lab books.
Nominal Resistance

R7 = 820
R8 = 680
R9 = 680
Rtot
Resistance
DMM 
Measured
by
Resistance calculated from V/I
ratio 
Table 4.1
Quantity
Vs
V7
V8
V9
IA
I7
I8
I9
DMM Measurement
Calculated Values
% Difference
Table 4.2
Select the resistors R7, R8 and R9 listed in Table 4.1 and use the DMM to
measure their values, recording your results. Now connect the three resistors
Measure their total value Rtot, and record this result (do not connect the DC
power supply yet).
Dr. Daniel Nankoo
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FOUNDATION EXP 2 – RESISTORS IN SERIES AND PARALLEL
4.3 TESTS FOR SERIES-PARALLEL CIRCUIT
Connect the power supply and using the DMM in voltmeter mode, adjust the
output so that Vs is about 10V. Record the DMM reading. As before, it is
essential that this voltage remains unchanged at the recorded value for the
entire test.
Change the DMM connections and thus measure and record the voltage drops
across each of the three resistors.
Reconfigure the DMM in order to measure current and reconnect it as an
ammeter at point A, noting the ammeter wiring principle indicated in Figure
3.1. Then, still using the ‘break-then-make’ principle, reconnect it to measure
the currents through the three resistors. Record all your results in Table 4.2.
Based on your observations, why do you think that an ammeter must always
be connected in series with a resistor and never in parallel? You should
consider that the DMM has an internal resistance when thinking of an answer
to this question.
This is to be done outside of the lab time. Carry out the necessary calculations
to complete Tables 4.1 and 4.2. Check your results in the event of any serious
discrepancy between theory and practice. Comment on the relation between
your measured results and the voltage and current principles of the series and
parallel connections.
5.0 GENERAL POINTS
Before leaving the lab, ensure that your work has been signed by a member of
staff. When handing in your work, this signature must be present in order to
get a mark.
Your write up should contain three aspects:
i) An outline of what you did in the lab (its aim, theory, method, equipment
and results using data tables and graphs)
ii) Theoretical calculations. Make sure your methods are clear by providing a
single, typical example worked out with detailed steps for each method. Just
give the end results of other calculations that use the same method.
iii) Conclusions, comments, calculations on what principles are demonstrated
by the data obtained and any comparisons between theory and practice.
The first part is relatively straight forward, but it is the second and third parts
that are important as they help to develop your engineering competence. Some
suggestions have been made above, but you should extend these making
reference to series, parallel, Ohm’s Law and Kirchhoff’s Laws where
appropriate.
Dr. Daniel Nankoo
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