THE UNIVERSITY OF ZAMBIA
SCHOOL OF ENGINEERING
DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING
EEE 2019 LABORATORY REPORT
NAME
COMPUTER #
GROUP
COURSE CODE
LAB #
TITLE
DATE OF LAB
DUE DATE
LAB PARTNERS
PHIRI BEATRICE
SINKAMBA BERNARD
FOR THE ATTENTION OF:
: MWAPE CABINET
: 2020003082
: C2
: EEE 2019
: 04
: NETWORK THEOREMS (PART B)
: 25TH AUGUST, 2022
: 1ST JUNE, 2022
2020050072
2020046873
Dr. L. NGOYI
1.0 TITLE: NETWORK THEOREMS II.
Part B: Norton’s Theorem
2.0 OBJECTIVES:


To get impacted with knowledge about and get introduced to the Norton's equivalence
theorem.
To be able to analyze complex circuit, electric networks and simplify them using the
principles of the aforementioned theorem and appreciate it.
3.0 EQUIPMENT USED
i.
A Multimeter
ii.
0-20V voltmeter
iii.
0-20mA ammeter
iv.
Calculator
v.
Conducting wires
vi.
Desktop computer
vii.
Resistors
Three (3) resistors rated 2.1KΩ
One (1) resistor rated 1KΩ
viii. NI Elvis board
4.0 INTRODUCTION
This part of the lab under the network theorems shifts the attention on the Norton’s theorem, a
quantum basis which was made 43 years later after the French Engineer M.L Thevenin
invented his theorem (the Thevenin’s theorem) by Engineer Norton, hence the name of the
theorem.
2-terminal Linear, active circuits and complex networks are often reduced and replaced with
their Norton equivalent circuits to simplify analysis. That is to say; Any linear electric network
or complex circuit having a voltage and current sources can be replaced by an equivalent circuit
containing an independent current (IN) source and a resistor (RN) connected in parallel to it.
The understanding of the basic laws governing the simplification and analysis of complex
circuit networks is essential in electrical engineering as it helps us realize that a linear circuit
is equivalent to a real independent current source in specific terminals.
The basic instance/ illustration of this theorem is in the analysis of a household electric power
systems, the Norton equivalency is applied in finding out how much quantity is delivered at
the end terminals (in households normally 220-250V outlets) when appliances of different
ratings are connected for daily home use.
5.0 THEORY
Electric current through all elements connected in series in a circuit is constant while voltage
across them differs and vice versa depending on how they are connected. However, not all
electric circuits can be analyzed using the above-mentioned statement because some circuits
may be built in a complicated way such that the simple statement (above) may not be enough
to satisfy the analysis need of such a circuit. Therefore, there comes the need to use the
Norton’s Theorem because it is useful to quickly and easily deal with such problems. This
theorem is not itself an analysis tool but the basis for a very useful method of simplifying active
circuits and complex networks. Especially electric circuits and electronic networks.
Like the Thevenin’s theorem which reduces linear active circuits and complex networks to an
equivalent simple circuit, the Norton’s theorem is another useful technique to analyze electric
circuits. The major difference between the two theorems is that Thevenin’s theorem provides
an equivalent voltage source and equivalent series resistance while Norton’s theorem provides
an equivalent current source and equivalent parallel resistance. This current source is the
Norton current (IN) and the equivalent parallel resistance is the Norton’s resistance (RN)
The magnitude of the current produced by the independent current source is equal to the short
circuit current through the output terminals with the load resistance shorted. The Norton’s
equivalent resistance is equal to the effective resistance measured between the output terminals
with the load resistance removed and the voltage source short circuited.
Therefore, based on the theory the theorem is summarized as follows:
‘Any linear electric network or a complex circuit with current and voltage sources can be
replaced with an equivalent circuit containing a single independent current source and a
parallel resistance.’
6.0 PROCEDOURE:
(1). The DC power was adjusted so as to maintain the supply at 10V which was verified
with the digital Multimeter. The circuit was set as shown in circuit-1 below.
The short circuit current, Norton’s equivalent resistance and the current through the load
resistor were calculated using the Norton’s theorem and measured using the Multimeter on
the NI Elvis board for confirmation. (i.e. connect the ammeter between nodes A and B,
isolating the load resistor 1k Ω).
(2). the value of the Norton’s resistance was found by shorting the voltage source and
measuring the equivalent resistance across open circuited R L (1KΩ) terminals using a
Multimeter. This measured resistance was then compared to the value calculated.
(3). the load resistor was then removed so as to achieve the circuit like the one shown in
the figure below
From which the ammeter reading was taken and was read as 2.66mA
(4). after having noted down the Norton’s current from the above illustration, the circuit
was then set to its equivalent as in the figure hereunder.
Where it was further analyzed and the turnouts were as recorded in the data collection table
of observations.
PRE-CALCULATIONS
From the above diagram, the total resistance was found as follows:
Adding 1.2KΩ to 1.2KΩ in parallel, then add the 1.2KΩ in series
R=
1.2x1.2
1⋅2+1⋅2
v=
+ 1.2 =
1.44
2.4
+ 1.2 = 1.8KΩ
Now to find the circuits total current;
IT = V/R
= 10V/1800Ω = 0.005555555556A = 5.56mA
Now to find Norton’s current using the current divider rule
1.2
IN= 5.56mA(
) = 5.56 X 0.5 = 0.002777777778A = 2.778mA
1⋅2+1⋅2
And the Norton’s resistance is equal to the total resistance
RN =
1.2x1.2
1⋅2+1⋅2
+ 1.2 =
R=
1.44
2.4
+ 1.2 = 1.8KΩ
Lastly the current through the load resistor is calculated as follows;
IL= IN(
𝑅𝑁
𝑅𝐿+𝑅𝑁
)
I L=
2.78𝑚𝐴 𝑋 1800Ω
1000Ω +1800Ω
=
5.00
2800Ω
= 0.001785714286A = 1.786mA
7.0 DATA COLLECTION AND ANALYSIS
Theoretical / Measured quantities
QUANTITY
CALCULATED/
THORETICAL
RECORDED/ ACTUAL
Short circuit current IN
2.778mA
Norton’s equivalent
resistance RN
Current through the load
resistor IL
1.8KΩ
1.786mA
8.0 DUSCUSSION
Short circuit current through the load resistor while maintaining the equivalency of the built
electric circuit/network was well determined.
Confirmation of the voltage input was made simple by the use of the Multimeter on the NI
Elvis board as this facilitated the yield of precise recordings using the prescribed energy
input.
Short circuit current which in this case is the Norton’s current of interest was measured in
mili-Amps, equivalent resistance (Norton’s) was measured in Kilo Ohms. Hence, by
comparing the calculated values of the currents (short circuit and IL) and resistance yielded
by the equivalent resistor to the values read using the built-in Multimeter of the NI Elvis
board using proper units’ conversions, it was observed that the values gotten were all within
the expected range dependence upon the correctness of the procedure followed.
The tolerance of the resistors used in this experiment (3 x 1.2KΩ and a 1KΩ) and also the
resistance in the connecting wires used to build the circuits could have contributed to the
minimal deviations observed between the theoretical and the actual reading of the quantities
(current, voltage and power). Such that the two values (theoretical and actual) deviated from
each other by 0.01 of each quantity. This analysis came about because the tolerance in
theoretical calculations is not considered and we learnt that resistance of a conducting
material depends on the type of the material as well as its dimensional area.
Prioritized factor during this experiment was safety, in that before switching on the
workstation comprising of the built circuit, present instructors inspected all the built circuits
for confirmation of the correctness in their (circuits) establishment. This was to ensure that
elements were safely connected in the circuit before allowing current to pass through so as
to reduce the damaging risk of the elements and equipment at large as well as precise results
yielding facilitation.
9.0 QUESTION
1. Does the current through the load resistance using Norton’s theorem match with the
measured value of the current from circuit-1?
Answer: Yes, the by Norton’s theorem calculated current through the load resistor
was the same as the measured one, any minimal deviation was as the result of the
resistance in the used connecting wires. Therefore, this proves the truthfulness of
the Norton’s theorem.
10. CONCLUSION
This lab experiment was a success as the objective of the lab/experiment was achieved. The
use of the Norton’s theorem to analyze complex networks and come up with the simpler
equivalent circuit was the major thing done in appreciating the work done by engineer Norton.
The theorem was proved through comparison of the theoretical (calculated) and actual
(recorded) values that were recorded during this experiment.
11. DECLARATION
I MWAPE CABINET of Computer Number 2020003082 do declare that I conducted this
laboratory experiment on the 25th day of August in 2022 and that this report is accurate to
the best of my knowledge and is a true representation of my laboratory works and results.
Signature:
.
12. REFERENCES
1. Electrical and Electronic Department (2022) EEE2019 Laboratory Manual; University
of Zambia printing press, Lusaka.
2. https://www.electricaltechnology.org/2014/01/norton-theorem.html
3. Lecture notes by Dr. Ngoyi .L