1. Superposition Theorem. By: Engr.Irshad Raheem Memon

2. OBJECTIVE Objective of this practical is to learn about Superposition Theorem; and how this theorem is used to find out voltage at and/or current through some particular resistor in a complex circuit.

3. What is Super Position Theorem In some circuits there can be more than one energy (current and/or voltage) sources, for such circuits Superposition theorem provides a method for analysis.

4. Continued… This theorem states that “The current in any given branch of a multiple-source circuit can be found by determining the currents in that particular branch produced by each source acting alone, with all other sources replaced by their internal resistances. The total current in the branch is the algebraic sum of the individual currents in that branch”.

5. Continued.. A technique called “Superposition” is used to solve for current flow through, and the voltage drop across any resistor in a multiple source circuit. This strategy is to analyze the circuit using only one of the source at a time. The current are then added and used to describe the original circuit

6. Steps for applying superposition theorem: Step 01: Leave one voltage (or current) source at a time, replace other sources with their internal resistances Step 02: Determine particular current (or voltage) Step 03: Take next source and repeat step 1 & 2 Step 04: Actual current in particular branch is sum of all individual currents. Voltage can be found using Ohm’s law then.

7. Coming Towards Objective Now

8. REQUIRED APPARATUS Multism Software Resistors Bread board Multimeter DC voltage source Connecting wire etc

9. PROCEDURE Realize the circuit on breadboard as shown in figure 01. Now find out current through R2 with the help of multimeter and then solve the circuit step by step with the help of superposition theorem to verify that current found through R2 with both methods is same.

10. Current found through R2 with the help of multimeter is 50mA.

11. Figure 01 Circuit on Multism & Result on Ammeter

12. STEP 01 Leave source 1 and replace source 2 with its internal resistance as shown in figure 02.

13. STEP 01 Circuit on Multism

14. STEP 02 Current found through R2 with help of formulas/multimeter is equal to I(S1)=33.3mA. Result on Ammeter

15. STEP 03 Leave source 2 and replace source 1 with its internal resistance as shown in figure 03.

16. STEP 03 Circuit on Multism

17. STEP 04 Current found through R2 with help of formulas/multimeter is equal to I(S2)=16.7mA. Result on Ammeter

18. STEP 05 Total current through R2 is the sum of I(S1) and I(S2). Which means I(S1+S2)=I(S1)+I(S2)=33.3mA+16.7mA=50mA

19. OBSERVATION Value of current found through R2 with the help of multimeter and Superposition Theorem is same, Hence it proved that Superposition Theorem provides a method for the analysis of a complex circuit containing more than more than one energy sources.

20. Another Cicuit on Multism Proving Superposition Theorem

21. Results of Ammeters of another circuit Total current through R2 is the sum of I(S1) and I(S2). Which means I(S1+S2)=I(S1)+I(S2)=3.33mA+1.667mA=5mA

22. ANY QUERY