Study of Superposition Theorem

Introduction: 
The purpose of this experiment is:
 • To find the voltage across of any element of the fixed circuit.
 • To find the current through of any element of the fixed circuit.

Theory and Methodology: 

The superposition theorem states that " The current through or voltage across an element in a linear bilateral network is equal to the algebraic sum of the currents or voltages produced independently by each source" . 

To remove a voltage source when applying this theorem, the difference in potential between the terminals of the voltage source must be set to zero (short circuit) and removing a current source requires that its terminals be opened (open circuit). Any internal resistance or conductance associated with the displaced sources is not eliminated but must still be considered .

 The total current through any portion of the network is equal to the algebraic sum of the currents produced independently by each source. That is for a two-source network if the current produced by one source is in one direction while that produced by the other is in the opposite direction through the same resistor, the resulting current is the difference of the two and has the direction of the larger. If the individual currents are in the same direction, the resulting current is the sum of two in the direction of either current. This rule holds true for the voltage across a portion of a network as determined by polarities, and it can be extended to networks with any number of sources.

The total power delivered to a resistive element must be determined using the total current through or the total voltage across the element and cannot be determined by a simple sum of the power levels established by each source.

 Pre-Lab Homework: 

 Read about the basic steps of performing the superposition theorem in a circuit from "Introductory Circuit Analysis" by Robert L. Boylestad and use NI Multisim to measure the voltages across each resistance and currents through each branch of the circuits provided in the lab sheet. Compare the theoretical results with simulation results. Save the simulation result and bring it to lab. ( Note : Do not write Pre Lab Homework in practical notebook )

Apparatus: 

1. Trainer Board 

2. Digital Multimeter 

3. DC source 

4. Resistors 

5. Connecting Wires 

Precautions: 

1. Check whether all the apparatus are working fine or not. 

2. Implement the circuit carefully where necessary. 

3. While connecting DC source make sure it is not shorted while placing in the trainer board.

4. Do not switch on the DC source while implementing the circuit in the trainer board.

5. While measuring voltage. Digital multimeter should be placed in parallel across the elements of the circuit where the voltage is to be measured, multimeter should be in voltmeter mode. 

6. While measuring current, Digital multimeter should be placed in series with the branch of the circuit where the current is to be measured, multimeter should be in ammeter mode. 

Circuit Diagram: 

Experimental Procedure: 

1. Connect the circuit as shown in the figure 1. Measure the voltage across node A of the circuit. Set the voltage source E1 to zero leaving the other and calculate the voltage across node A. Replace the voltage source E1 to the original position and set E2 to zero and calculate the voltage across node A. Fill the following table with necessary calculations. 

2. Connect the circuit as shown in the figure 2. Measure the current through resistor R4 of the circuit. Set the voltage source E1 to zero leaving the other and calculate the current through resistor R4. Replace the voltage source E1 to the original position and set E2 to zero and calculate the current through resistor R4. Fill the following table with necessary calculations.

Simulation and Measurement: 

Compare the simulation results with experimental data and comment on the differences (if any). 

Data Table: 

Table-1 (For Figure-1)

Table-2 (For Figure-2) 

Report: 

1. Verify the superposition theorem by analyzing practical data and support them by comparing the results with the theoretical values by proper circuit solution. 

2. Verify the measured value with calculated value of total circuit. Show necessary calculation. 

3. Comment on the result as a whole. 

Discussion: 

Determine whether or not the theorem was verified. Discuss about the reasons behind the achieved results and practical applications of the theorem based on the experiment. 

Conclusion: 

Summarize the experiment here and discuss whether the objectives were fulfilled or not within short paragraph.

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