Superposition Theorem with Solved Examples

Hi friends, here are going to learn a superposition theorem. We will also solve on simple example using superposition theorem.

Statement of Superposition Theorem

Superposition theorem states that, the responce 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 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 figure below.

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Solution

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

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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 voltage across resistor.

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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 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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