PRACTICAL 09 Superposition Theorem By Engr Irshad Raheem

PRACTICAL # 09 Superposition Theorem. By: Engr. Irshad Raheem Memon

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.

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.

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”.

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

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.

Coming Towards Objective Now

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

PROCEDURE � Realize the circuit on breadboard as shown in figure 01. Now find out current through R 2 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 R 2 with both methods is same.

�Current found through R 2 with the help of multimeter is 50 m. A.

Figure 01 Circuit on Multism & Result on Ammeter

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

STEP 01 Circuit on Multism

STEP 02 �Current found through R 2 with help of formulas/multimeter is equal to I(S 1)=33. 3 m. A. �Result on Ammeter

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

STEP 03 Circuit on Multism

STEP 04 �Current found through R 2 with help of formulas/multimeter is equal to I(S 2)=16. 7 m. A. �Result on Ammeter

STEP 05 �Total current through R 2 is the sum of I(S 1) and I(S 2). Which means I(S 1+S 2)=I(S 1)+I(S 2)=33. 3 m. A+16. 7 m. A=50 m. A

OBSERVATION �Value of current found through R 2 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 one energy sources.

Another Cicuit on Multism Proving Superposition Theorem

Results of Ammeters of another circuit �Total current through R 2 is the sum of I(S 1) and I(S 2). Which means I(S 1+S 2)=I(S 1)+I(S 2)=3. 33 m. A+1. 667 m. A=5 m. A

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