Superposition Theorem with Solved Examples

by - Mayuresh Joshi on - March 13, 2017
Hello friends, in this article, we are going to learn a superposition theorem. We will also solve some simple examples using superposition theorem.

Statement of Superposition Theorem


Superposition theorem states that the response in any element of LTI linear bilateral network containing more than one sources is the sum of the responses produced by the sources each acting independently.

The superposition theorem is not applicable for the power, as power is directly proportional to the square of the current which is not a linear function.

Steps



  1. Select any one source and short all other voltage sources and open all current sources if the internal impedance is not known. If known replace them by their impedance.

  2. Find out the current or voltage across the required element, due to the source under consideration.

  3. Repeat the above steps for all other sources.

  4. Add all the individual effects produced by individual sources to obtain the total current in or across the voltage element.


Example


Using the superposition theorem, determine the voltage drop and current across the resistor 3.3K as shown in the figure below.

superposition theorem 1

Solution


Step 1: Remove the 8V power supply from the original circuit, such that the new circuit becomes as the following and then measure the voltage across a resistor.

superposition theorem 2

Here 3.3K and 2K are in parallel, therefore resultant resistance will be 1.245K.

Using voltage divider rule voltage across 1.245K will be

V1= [1.245/(1.245+4.7)]*5 = 1.047V

Step 2: Remove the 5V power supply from the original circuit such that the new circuit becomes as the following and then measure the voltage across a resistor.

superposition theorem 3

Here 3.3K and 4.7K are in parallel, therefore resultant resistance will be 1.938K.

Using voltage divider rule voltage across 1.938K will be

V2= [1.938/(1.938+2)]*8 = 3.9377V

Therefore voltage drop across a 3.3K resistor is V1+V2 = 1.047+3.9377=4.9847

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Tags: superposition theorem solved problems, superposition theorem examples, superposition principle.
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