This document reports on an electrical engineering lab experiment involving the superposition principle and Thevenin's theorem. The experiment used resistors, power supplies, and multimeters to measure voltages and currents in circuits. For the superposition principle part, measurements were taken with individual and combined sources and compared. For Thevenin's theorem, voltage and current across a variable load resistor were measured and recorded in a table to determine the equivalent resistance and voltage of the original circuit.

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Table of Contents
Introduction......................................................................................................................................2
Theory ..............................................................................................................................................2
Figure: 5............................................................................................................................................4
Pre lab ..............................................................................................................................................4
Figure 3 .............................................................................................................................................5
Equipment used ................................................................................................................................6
Proceedures ......................................................................................................................................6
Part: 1 of the report. The superposition principle ...................................................................................6
Part: 2 of the report. Thevenin’s theorem.............................................................................................7
Figure 4 .............................................................................................................................................7
Results ..............................................................................................................................................7
Part 1 of the lab: the superposition principle. ..................................................................................8
Table 1...............................................................................................................................................8
Part 2 of the lab: Thevenin’s theory .....................................................................................................8
Table 2...............................................................................................................................................8
Discussions of results ......................................................................... Error! Bookmark not defined.
Part 1 of the lab ................................................................................... Error! Bookmark not defined.
Part 2 of the lab ................................................................................... Error! Bookmark not defined.
Conclusion ........................................................................................................................................9
BIBLIOGRAPHY..................................................................................................................... 10

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INTRODUCTION
Electricity is an essential part of the modern life experience, and as an engineer it is essential to know
how it behaves and responds to changes in its trajectory. A very important skill that any person analyzing
a circuit must have is the complete understanding of the superposition principle of analyzing circuits.
These law states that the value of any variable may be found by the sum of the values of that variable
produced by each of the values of that variable produced by each of the excitation sources( power
sources) acting separately. Another such important law is the law which lets you reduce a circuit to its
resistance thevenin and voltage thevenin. The thevenin`s theorem may be explained as a virus that
reduces a complex circuit by its simplest equivalent. Therefore the primary goal of this laboratory
experiment is to help students practically prove the concepts of the superposition principle and to prove
that an equivalent thevenin circuit has the same Req and Veq as the original circuit before it was reduced.
Therefore in addition this lab shall consist of the following major parts namely, table of contents,
introduction, theory, pre-lab, equipment used, procedures, results, conclusion, references.
THEORY
 Ohms law states that the resistance across component within a circuit is directly proportional
to that components voltage but inversely proportional to its current.
Resistance=voltage/current (EQUATION 1)
 KVL (Kirchhoff`s voltage law) states that the sum of all the voltages around a
closed loop is equal to zero. This in addition is in accord with the law of
conservation of energy that states that energy cannot be made nor destroyed it can
just be changed from one form to another. For ease of understanding let’s look at
Figure:1
Applying KVL around loop 1
Vs – V2 – V3 – V1 = 0
Loop 1

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Vs = V1+ V2 + V3
Vs = IsR1 + IsR2 + IsR3
Vs = (R1 + R2 + R3) Is
 The equivalent resistance for resistors in series may be replaced with a single resistance. This is a
direct extension of the Kirchhoff’s law therefore Req = R1 + R2 + R3 only for resistors in series.
 A node of a network is defined as a point where two or more branches are joined. If three or more
branches join at a node, then that node is called a principal node or junction.
 KCL (Kirchhoff’s current law) states that the sum of all currents entering a node is equal to the
sum of all currents leaving the node. This however also verifies the law of conservation of energy
at a node, this law is stated above on the second bullet. For simplicity let us consider the single
node circuit illustrated in Figure: 2.
 IS - I1 - I2 - I3 = 0
IS = I1 + I2 + I3
 Equivalent resistance for resistors in parallel is denoted by the following equation REQ = 1 / (1 /
R1 + 1 / R2 + 1 / R3).
Superposition principle states that the value of any variable may be found as the sum of the values of
that variable produced by each of the values of that variable produced by each of the excitation sources
acting separately.
This is done by
 Only using one of the sources separately by setting the voltage source to zero and replacing it by
a short circuit.
 Solve for the currents.
 Insert the voltage source and set the current source to zero by replacing it with an open circuit.
 Solve for currents`
 Add the currents since the total current is the algebraic sum of the independent currents provided
by each source.
 From the currents using ohms law (equation 1) other properties may be found like voltage

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Thevenin`s theorem states that any network consisting of linear resistance and independent sources may
be replaced at a given pair of nodes by an equivalent circuit consisting of a single voltage source and a
series resistor. This is shown below by figure 5
Thevenin equivalent circuit
FIGURE: 5
Figure: 5 shows how the reduction process due to the thevenin principle. From a circuit with 3 resistors
to a circuit with 1 equivalent resistor in series with the power source which is the voltage thevenin...
PRE LAB
For the pre- lab that follows these below are the figures used.
Figure :2 was used for question 1

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FIGURE 3
Figure 3 was used for questions 2, 3, 4 respectivelly.

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EQUIPMENT USED
 2 power supplies
 3 digital Multimeters (D.M.M) will serve as both the voltmeter and the ammeter) for the
laboratory experiment
 2 decade resistor box(s).
 1 decade resistor box with a variable resistor to be used as the load during part 2 of the lab.
 Different conductor cables
PROCEEDURES
Part: 1 of the report. The superposition principle
 Construct the circuit illustrated in figure 2.
 Remember to set the power supplies to the required values of 10V and 5V.
 Supply voltages should be set prior to connection to the circuit.
 Measure the value of resistors. R1, ( nominally 1.8 K ), R2 (1.2K) and R3 (1.2K)
 Note that quantities V1, V2 and VR1, VR2 and VR3 are measured using the Multimeter.
 Currents IR1, IR2 and IR3 are to be calculated using Ohms Law (equation 1) above..
 Repeat this for each of the following conditions:
 Both sources on.
 With the 10 V (VS1) source replaced with a short circuit and 5 V on.
 With the 10 V source on and the 5 V (VS2) source replaced with a short circuit.
 Measure and record the data as required in Table 1 below
 Using the values measured for R1, R2, R3, V1, and V2 calculate the theoretical values of VR1,
VR2, VR3, IR1, IR2 and IR3.
 The theoretical values are part of the pre-lab exercise calculated outside the lab. These are
provided above.
 Briefly illustrate that the principle of superposition appears to be valid by comparison.

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Part: 2 of the report. Thevenin’s theorem
 Set up the circuit illustrated in Figure 3.
 Note that the load resistor is variable; use a decade boxes
 Set the power supply to 10V
 Vary the value of the load resistor (Rload) from 0 in intervals of 20  to any large value e.g.
infinity.
 Record the voltage and current readings as indicated in Table 2 below.
 Note that one can easily take voltage and current measurements with a single Multimeter.
 Figure 4 shows the same circuit except that the physical location of the ammeter has been
relocated.
 Note that voltage is measured between the top and middle terminals, and current flowing in the
bottom and out the middle.
 Determine the Thevenin equivalent of the circuit illustrated in Figure 3 below..
 First disconnect the load resistor and measure the open circuit voltage across load terminals
(record the values measured, VOC).
 Then introduce a short circuit across load terminals (load removed) and measure the short circuit
current, ISC.
 Record all the values in table 2 below in the results section of the report.
FIGURE 4
RESULTS

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Part 1 of the lab: the superposition principle.
Actual Measured Values: R1 = 1.84K ; R2 = 1.99K ; and R3 = 1.2K
TABLE 1
Part I Part II Part III
Theoretical Experimental Theoretical Experimental Theoretical Experimental
VS1 10V 10V 0 V 0V 10 V 10V
VS2 0 0V 5 V 5V 5 V 5V
VR1 7.5V 7.4V 1.875V 1.85V 5.625V 5.56V
VR2 2.5V 2.5V 1.875V 1.85V 4.375V 4.38V
VR3 2.5V 2.5V 3.125V 3.10V 0.625V 0.57V
IR1 4.2mA 4.02mA 1.04mA 1mA 3.125mA 3.02mA
IR2 2.08mA 2.01mA 1.56mA 1.55mA 3.65mA 3.68mA
IR1 2.08mA 2.08mA 2.6mA 2.6mA 0.52mA 0.47mA
The values acquired in the theoretical columns were acquired during the pre-lab by using the various
appropriate laws and theories discussed above in the theory section.
Part 2 of the lab: Thevenin’s theory
TABLE 2
Original Circuit Thevenin Equivalent Circuit
RLOAD ILOAD (mA) VLOAD(mV) ILOAD (mA) VLOAD(mV)
0 4.15 0.1 4.09 0.1
20 4.07 81.7 4.09 80
40 4.00 160.5 3.98 159.1
60 3.95 238 3.86 224
80 3.87 306 3.86 295
99.4 3.79 380 3.79 360

9. 180.00
160.00
140.00
120.00
100.00
80.00
60.00
40.00
20.00
0.00
-20.00
-40.00
nd
Vol tage (mV)
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Voltage Vs Current graph original
0.00 0.10
81.70
circuit
160.50
0.00 0.00 0.00
0 1 2 3 4 5 6 7 8
Currents (mA)
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Compare your results with the theoretically calculated values. Explain the why the values are not the
same!
CONCLUSION
In conclusion with all of the above information and all of the theoretical similarities in the results
obtained experimentally it is safe to assume that ohms law explains how any circuit operates in terms of
voltage, current and resistance. In addition the only thing that changes the results is the problem of
internal resistance, this change is so small that it can be considered negligible. Furthermore this
knowledge will aid me in my engineering career both theoretically and practically.

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BIBLIOGRAPHY
bird, j. (2003). electrical circuit theory. sidney: newnes.
chand, S. (2000). a textbook of electrical technology. singapore: newnes.