LAB 3

Answering questions

1

ENGR2105 Lab3 Superposition Theorem

Student Name __________________________________

Objectives:

To solve a network containing resistors and multiple power sources. To learn the use of a

computer to solve electrical circuits and compare calculated results with simulated results.

Materials:

Computer to access Multisim Live. Calculator.

Background Information:

The Superposition Theorem can be used to solve circuits including resistors and multiple

sources. It can be applied only when all the components are linear and passive. The main idea is

that the effect of all power sources can be found by summing the effects of each power source

individually.

You are expected to show all the formulas and calculations needed to find the answers. These

can be handwritten in the worksheets. Take screenshots of each of the Multisim measurements

that you take.

2

ENGR2105 Lab3 Superposition Theorem Worksheet

Apply Superposition Theorem to Circuit 1 to find the current through Resistor 2:

Fig 1. Circuit1

Procedure:

• Build the circuit in Fig1 in MultiSim.

• Measure the voltage potential at point Pcurrent through each resistor (Screen Shot):

Measured I_2 = ________________

• Apply Superposition Theorem to the circuit in Fig 1.

Step1: Short power supply V2

Step2: Calculate the current through R2 for this circuit. This is the contribution to the

current from power supply V1.

Step3: Build this circuit in MultiSim and verify the current through R2. (Screen

Shot)

Calculated I_2 = ________ Measured I_2 =________ Direction = ____________

Step4: Reconnect the Power Supply V2 and short power supply V1.

Step 5: Calculate the current through R2 for this circuit. This is the contribution to the

current from power supply V2. Build this circuit in Multisim and measure the

current. (Screen Shot)

Calculated I_2 = ________ Measured I_2 =________ Direction = ____________

Step6: Combine the effects of the two power supplies by adding or subtracting the two

currents (Hint: Are the power supplies pushing positive charge in the same

direction?.

Calculated I_2 = ________________ Direction of I_2 = ________________

Does it match what you found in the first measurement? If not, something is wrong.

3

Apply Superposition Theorem to Circuit 2 to find the current through R3.

Fig 2. Circuit2

Procedure:

• Build the circuit in Fig. 2 in MultiSim. Pay attention to the polarity (orientation) of V2

throughout this problem.

• Use Multisim to measure the current through R3 (Screen Shot):

Measured I_3 = ________________

• Apply Superposition Theorem to the circuit in Fig 2.

Step1: Short power supply V2

Step2: Calculate the current through R3. This is the contribution from power supply V1.

Step3: Build this circuit in Multisim and measure R3 to verify your result. (Screen

Shot)

Calculated I_3 = ________ Measured I_3 =________ Direction = ____________

Step4: Restore V2 and short V1. Pay attention to the polarity (orientation) of V2!

Compute the current through R3. This is the contribution from power supply V2.

Step5: Build the circuit in Fig 2 in MultiSim and measure the current through R3

(Screen Shot).

Calculated I_3 = ________ Measured I_3 =________ Direction = ____________

Step6: Add the effects of the two power supplies by adding OR subtracting the two

currents

Calculated I_3 = ________________ Direction = ____________

Does it match what you found in the first measurement? If not, something went wrong.

Upload your Lab 3 Deliverables here.  A formal lab report is not required for this lab.

1)  File containing your Multisim screen shots (please paste all of your screen shots into a single file).

2)  The lab document with your answers filled in (handwriting is fine).

3)  A scan of your calculations using the formulas used to obtain your answers.

If you do not have access to a scanner, please use a scanning app, such as Google Drive, Office Lens, or Camscanner.

Lab#3 Worksheet

Watch the Video on eCampus. For each of the Series-Parallel circuits:

1) Build the circuit in Multisim Live and “measure” the Total Current and the current in each of the

parallel branches.

2) Calculate the Total Resistance, RT, of the Circuit.

3) Using RT, use Ohm’s Law to calculate the total current, IT.

4) Use IT current divider formula to determine the current in each of the resistors. Draw the

direction of each current on the diagram.

Scan and upload your work in eCampus. If you do not have a scanner, use a scanning phone app such as

Google Drive, Office Lens, or Camscanner.

Current Divider: 𝑰𝟏 = 𝑰𝑻 (
𝑹𝟐

𝑹𝟏+𝑹𝟐
)

1. Find the current magnitude and direction in each resistor using the current divider formula.

(Remember: The current is the same for resistors that are in series with each other.)

2. Find the current magnitude and direction in each resistor using the current divider formula. Hint:

First find the current through R2. The current will first branch at node A. The first branch has

resistance R2. The 2nd branch resistance will be the combined resistance of resistors 4-9. Trace a

path from point A to point B to determine which of theses resistors are in series and which are in

parallel and calculate accordingly.

ENGR 2105

Dr. Kory Goldammer

Superposition Theorem

Superposition Theorem – Components

The superposition theorem extends the use of Ohm’s Law to circuits with multiple voltage or current sources.

In order to apply the superposition, all the components must be linear, or “Ohmic”, meaning that the component obeys Ohm’s Law

Yes: Resistors, Capacitors, Inductors

No: Transistors, semiconductor diodes, and electron tubes, Operational Amplifiers. Such components are never bilateral and seldom linear.

Superposition Theorem
The Superposition is useful when we have more than one Voltage Source or more than one Current Source
We will only consider Voltage Sources in this course
This analysis is done by calculating the current contributed by each source, and then adding or subtracting (i.e. taking the Superposition) the currents contributed by each source

7-2: Current Dividers with
Two Parallel Resistances
This slide applies to the special case where we have just 2 resistors in parallel
IT is divided into individual branch currents.
Each branch current is inversely proportional to the branch resistance value.
For two (and only 2) resistors, R1 and R2, in parallel:

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7-2: Current Dividers with
Two Parallel Resistances

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

The result validates Kirchoff’s Current Law: The sum of the currents entering a node = the sum of the currents leaving a node:

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Determine The Currents going through each resistors
Last time, we analyzed this circuit and determined the total current was 2 Amps. All of the current flows through R1 and R2, so the current in those resistors must be 2 Amps
2A
2A

Determine The Currents going through each resistors
At Point A, the current splits into two branches. The resistance of Branch 1 is R5 = 10Ω. Last time, we determined the resistance of branch 2 was also 10Ω

2A
2A

Determine The Currents going through each resistors
2 Amps enters node A. We can use the current divider to determine the current leaving node A.
2A

8

Determine The Currents going through each resistors
Since 1 Amp goes into each branch, we know the currents through R5 and R6 are each 1 Amp. Use the current divider to find the current through the 12 Ohm resistors.
2A
2A
1A
1A
0.5A
0.5A

1A

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Superposition Theorem – Step 1
R1
R2

R3
V1
100 W
20 W
10 W
15 V
V2 shorted
Problem: R3 is the load resistor. Find the the current through
R3 and the voltage across R3

Step 1: Short Voltage Source V2. Find I3
R2
R1

R3
V1
V2
100 W
20 W
10 W
15 V
13 V

Step 1 – Find RT and IT
R1
R2

R3
V1
100 W
20 W
10 W
15 V
V2 shorted
Step 1: Short Voltage Source V2. Find I3

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Step 1 – Current Divider
R1
R2

R3
V1
100 W
20 W
10 W
15 V
V2 shorted
Step 1: Short Voltage Source V2. Find I3
Now that we know the total current is 0.141A, we can apply the current divider approach to find the current through Resistors 1 and 2

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Step 1 – Direction of Current through R3
The total current leaves V1 from the positive (top) terminal and passes through R1. It then splits into two branches. The current passing through R3 is going in in the downward direction.
R1
R2

R3
V1
100 W
20 W
10 W
15 V
V2 shorted
Step 1: Short Voltage Source V2. Find I3
 

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Problem: R3 is the load resistor. Find the the current through
R3 and the voltage across R3

Step 2: Short Voltage Source V1. Find I3
R2
R1

R3
V1
V2
100 W
20 W
10 W
15 V
13 V
Superposition Theorem – Step 2

Step 2 – Find RT and IT
Step 2: Short Voltage Source V1. Find I3

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Step 2 – Find R3
Step 2: Short Voltage Source V1. Find I3

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Step 2 – Direction of Current through R3
The total current leaves V2 from the positive (top) terminal and passes through R2. It then splits into two branches. The current passing through R3 is going in in the downward direction.
Step 1: Short Voltage Source V2. Find I3
 

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Case 1: Currents are going in opposite direction. Subtract the smaller from the larger. The direction of the current is the same as the direction of the larger current.
Case 2: Currents are going in the same direction: Add the currents. The resulting current is in the same direction as both currents.

Step 3 Add or Subtract the Currents to Determine R3 for the Original Circuit

18

Verify in Multisim