Superposition Theorem | Applications & Limitations

Superposition Theorem Definition

In any linear bi-directional circuit having more number of sources, the response in anyone of the elements is equal to an algebraic sum of the responses caused by individual sources while the rest of the sources are replaced by its internal resistance.

OR

In a network of linear impedances containing more than one source, the current which flows at any point is algebraic/phasor sum of all currents which would flow at that point if each source was considered separately and all other sources are replaced by their internal impedances.

Note: Superposition theorem is also called as additivity property.

How to solve a problem using superposition theorem?

1. In a circuit, take any one source.
2. Set all other independent sources equal to zero. It means that replace independent voltage sources with short circuit and independent current sources with the open circuit.
3. Keep the dependent sources as it is.
4. Calculate the magnitude and direction of current through the desired branch as a result of the single source selected in step-1.
5. Repeat steps from 1 to 4 for each source in turn until the desired branch current has been calculated due to each & every source acting alone.
6. Add all the component current of the desired branch with directions. In case of AC circuit, phasor sum is to be done.
7. Similar steps can be followed to calculate the voltage across any element of the circuit.

Note:

1. Superposition theorem is not applicable for power calculations.
2. Superposition theorem is applicable for Linear circuits only.
3. Superposition theorem is not applicable to a network containing time varying resistors.

Exercise

Q. Can we apply superposition theorem to an electric circuit with a nonlinear resistance?

Ans. No. Superposition theorem can’t be applied to an electric circuit with a nonlinear resistance.

Q. What is the utility or application of superposition theorem?

Ans. Superposition theorem is applied when we are to determine the current in one particular branch of a network containing several voltage sources and/or current sources.

Q. What are the limitations of Superposition Theorem?

Ans. Limitations are as follows

1. Not applicable to the branches which are coupled to the branch of the circuit.

2. Not applicable to the branches of the circuit when the voltages and current of these branches are known.

3. Not applicable to the network containing two or more sources that are not in series or in parallel.

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