Electrical Principles - Chapter 6: Superposition
Publish Date: Mar 27, 2013
Overview
The Electrical Principles/Fundamentals series present the basic theories and concepts taught at entry level electronics courses
both 2 year and 4 year institutions. This series of content provides examples to professors to enable them to easily teach conce
to students, who can develop a solid underlying knowledge of electronics using the NI solution. This series focuses on some of
basic theory as well as providing the NI Multisim circuits to enable practical implementation end experimentation as homework
students.
Table of Contents
1.
2.
3.
4.
5.
6.
In this Chapter
Example Courses
Superposition Theorem
Example Problem
Suggested NI Solution
References
1. In this Chapter
We begin this chapter by exploring the superposition theorem and then we will apply it to a simple circuit to calculate the individ
currents passing through the different resistors. We will use the NI Multisim circuit teaching environment to verify our results wit
example circuits that can be used by any educator or student.
If you do not have NI Multisim installed on your computer, you can download a free 30 day evaluation at
http://www.ni.com/multisim/try/ (http://www.ni.com/multisim/try/)
2. Example Courses
Listed below are example courses that teach this concept at their schools.
Course Name
School
Learn More
Electrical
Principles
Conestoga College
http://www.conestogac.on.ca/fulltime/0071.jsp
Electronic
Technology 1
Macomb
Community College
http://www.macomb.edu/noncms/Search/Courses/coursekey.asp?coursekey=ELEC-11
3. Superposition Theorem
This theorem is applied when solving a circuit with more than one source to determine voltage/current for a specific element.
To apply the theorem, we will look at each individual source alone and study its effects on the circuit. To remove the remaining
sources from the circuit simply replace the voltage source with a short circuit, and the current source with an open circuit. Once
have studied the effects of the first source, we will go back and repeat the same steps for all the other sources in the circuit. Th
final step would be going back to the original circuit and add the individual values across each resistor to find the final value, i.e
the combined contributions from all the existing sources in the circuit [1].
4. Example Problem
Let us now examine the following circuit find the individual currents going through each resistor.
STEP 1: Open circuit file “superposition_example.ms12” using NI Multisim. You will find the circuit below [2].
Answer Sub-Step 1: Find the voltage drops across each resistor by considering the voltage source effect on the circuit.
Begin by replacing the current source with an open circuit. The resulting circuit will look as follows:
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Req = 2 + 2 + 6 = 10 Ω
Ieq = Veq/Req = 12/10 = 1.2A
Therefore:
VR1 = 1.2 x 2 = 2.4V
VR2 = 1.2 x 2 = 2.4V
VR3 = 1.2 x 6 = 7.2V
STEP 2: Open circuit file “superposition_voltage.ms12”. Then by double-clicking on the multimeters, open their screens and
choose “V” to measure the voltage. Then run the simulation by choosing “Simulation>>Run Simulation”.
You will notice that the voltmeters’ readings confirmed our calculations.
Answer Sub-Step 2: Find the currents through each resistor by considering the current source effect on the circuit.
Begin by replacing the voltage source with a short circuit. The resulting circuit looks as follows (Circuit file
‘superposition_current.ms12’):
Rseries = 2 + 6 = 8Ω
Req = 1/ ((1/8) + (1/2)) = 1.6Ω
The resulting circuit is then:
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Using the current divider rule:
IR2 = (Req/R2) x I = (1.6/2) x 3 = 2.4 A , then the current going through Rseries = 3 – 2.4 = 0.6A
Answer Sub-Step 3: Combine the effects of both sources to determine the resulting currents and voltages in the original circuit.
Applying Kirchhoff’s Current Law based on the results we calculated earlier, we find:
Note: Make sure when adding the current values to pay attention to the direction of each current since that may result in
subtracting the values not adding them.
STEP 3: Re-open circuit file “superposition_example.ms12” and run the simulation. You will notice the results below.
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Comparing the calculated values versus the measured values in NI Multisim confirms our calculations and the application of the
superposition theorem.
5. Suggested NI Solution
National Instruments offers a number of products that combine to provide a scalable and powerful teaching platform for educato
The solution includes:
NI Multisim circuit teaching environment: Combining an intuitive circuit definition environment, with powerful SPICE simulation
technology, educators can use NI Multisim to easily teach the ins-and-outs of circuits in a safe environment.
NI ELVIS teaching and measurement platform allows educators to provide students with a compact, all-in-one unit for their
measurement and analysis needs. Combining an oscilloscope, function generator, DMM, bode analyzer and 8 other instrument
into a small platform; it simplifies the laboratory experience for students and lab instructors.
6. References
[1] University of Texas at Austin. “Electronic Circuit Theory”. Lesson 8 - Superposition.
[http://utwired.engr.utexas.edu/rgd1/lesson08.cfm]. (05/02/2013)
[2] Sinclair Community College. “DC Circuits”. Unit 6: Circuit Theorems.
[http://people.sinclair.edu/nickreeder/eet150/mod06.htm]. (05/02/2013)
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