Laboratory 5
Superposition
Rohit Vedulla, Rahsaan Young Jones, Quincy Walter-Eze
Objectives
• Study and verify the principle of superposition.
Theoretical Background:
During this lab we had to create a circuit and measure the values of current throughout the circuit.
To do this we used equations such as Kirchhoff’s voltage law in each of the circuits loops to find
the different currents. In addition to this we used the superposition theorem which states that the
total current or voltage in a circuit can be calculated by adding the values obtained by the
contribution made by each source alone. By deactivating each source one at a time and
measuring the values of current and voltage we were able to find the total values for current and
voltage within the circuit.
Experimental Procedures:
In this lab we began the experiment by gathering the necessary resistors, and constructing the
circuit shown below on the breadboards provided in the lab. Next, we connected the power
sources at the appropriate locations in the circuit and began to measure the necessary values. As
the lab manual went, we were able to remove the 10V and the 15V as necessary to measure the
specific values. After we had all the measurements, we did the theoretical calculations and lastly
answered the following questions based off the data we gathered throughout the experiment.
Analysis of Experimental Data:
This lab required us to calculate values such as current and voltage of the circuit using Kirchhoff’s
voltage law as well as the superposition principle. This meant we had to deactivate each voltage
source one at a time and measure the values of voltage and current. We did this in the theoretical
equations as well as in the physical lab and found that our data from the physical lab did not
match our theoretical calculations accurately. We believe this is due to a fault in a piece of our
equipment, as we double-checked the composition of our circuit and the resistance of each resistor
in the circuit.
Equipment and components
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2x Digital multimeter
2x power supply
1x Breadboard
Cables and connecting wires as needed
Resistors: 470 Ω, 1 kΩ, 2.2 kΩ, 3.3 kΩ, 5.6 kΩ
Preliminary Work
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Read section 4.3 of the textbook.
Pre-lab: Calculate and fill up the tables by using superposition for the circuit shown below.
Use a separate sheet to show your work and staple to your handout. Clearly indicate units
for your solutions.
Procedure
1. Construct the circuit shown below using the parts in your kit before turning the power on.
2. Adjust the power supply to the values indicated by the circuit.
3. With the circuit built and the voltages of the power supplies set correctly, turn on the
power supplies and measure the currents and voltages shown in the circuit. Fill in the table
with correct units.
Theoretical
Value
Measured
Value
𝐼1
4.54 mA
𝐼2
𝐼3
𝑉1
𝑉2
3.75 mA
.34 mA
3.2 V
10 V
4. Remove the 10 V source (and replace it with a short circuit). Measure the currents and
voltages shown in the circuit.
Theoretical
Value
Measured
Value
𝐼1
𝐼2
𝐼3
𝑉1
𝑉2
0.7 mA
3.1 mA
2.6 mA
1.8 V
3.2 V
5. Place the 10 V source back in the circuit. Remove the 15 V source (and replace it with a
short circuit). Repeat step 3.
𝐼1
𝐼2
𝐼3
𝑉1
𝑉2
Theoretical
1.98 mA
1.8 V
1.1 mA
3.2 V
4.54 mA
Value
Measured
Value
6. From the measured values filled out in the table above, what would you conclude?
We concluded that most of our measured values were relatively close to the theoretical
values, however some of the values were slightly off which we believe may have been
caused by a faulty resistor or a slight mistake in the calculations.
7. For 𝐼1 and 𝑉1, calculate the percent error using your measured and your calculated
values.
a. When both sources are in place
𝐼1% error: 27.54%
𝑉1% error: 23.08%
b. When only 10 V source is in place
𝐼1% error: 56.01%
𝑉1% error: 44%
c. When only 15 V source is in place
𝐼1% error: 4.63%
𝑉1% error: 2.57%
d. What might account for any differences in measured versus calculated values?
The calculations can differ because of errors in the calculations, as well as using the
wrong formation of circuits or measurement points.
8. If one of the resistors is replaced with an LED, which behaves like a nonlinear resistor,
would the principle of superposition still apply? Explain.
It would not, the principal would not be applicable because the nonlinear resistor in the circuit,
the circuit would need to be linear for it to apply.
9. Clean up and put everything in their original places before leaving labs!
Questions and conclusions
• Summarize your findings and explanations in response to the questions posed in this lab.
For this experiment we were to construct a circuit on a breadboard provided in lab. After
creating the circuit and using appropriate power sources we measured certain values and
made calculations to find the accuracy of those measurements. We were able to conclude that
the principle of superstition wouldn’t apply if an LED were to be introduced.