### 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 individual currents passing through the different resistors. We will use the NI Multisim circuit teaching environment to verify our results with 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/

### 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-1161) |

### 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 we 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. The 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:

R_{eq} = 2 + 2 + 6 = 10 Ω

**I _{eq} = V_{eq}/R_{eq}** = 12/10 =

**1.2A**

Therefore:

**V _{R1}** = 1.2 x 2 = 2.4V

**V _{R2}** = 1.2 x 2 = 2.4V

**V _{R3} **= 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’):

**R _{series}** = 2 + 6 =

**8Ω**

**R _{eq}** = 1/ ((1/8) + (1/2)) =

**1.6Ω**

The resulting circuit is then:

Using the current divider rule:

**I _{R2} = (R_{eq}/R_{2}) x I **= (1.6/2) x 3 =

**2.4 A**, then the current going through

**R**= 3 – 2.4 =

_{series}**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.

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 educators. 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 instruments 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)