# Superposition Theorem

Superposition theorem states that” In an active linear network containing several sources(including dependent sources) , the overall response(branch current or voltage) in any branch in the network equals the algebraic sum of the responses of each individual source considered separately with all other sources made** inoperative**, i.e replaced by their internal resistances or impedances.”

For voltage sources to make a source **inoperative** it is short circuited leaving behind its internal resistance or impedance.

For current sources to make a source** inoperative** it is open circuited leaving behind its internal resistance or impedance.

**The principle of superposition is the combined property of additivity and homogeneity.**

## Explanation of Superposition Theorem

Consider voltage sources V1 and V2 respectively. Applying the superposition theorem in the given circuit,

consider voltage source V1 and replace voltage source V2 by a short circuit. I’ is the current in the R3 resistance.

The current from the voltage source V1 is,

Now consider voltage source V2 and replace V1 by a short circuit. I” is the current in R3 resistance.

The current from the voltage source V2 is,

Now when we apply super position theorem, then current through resistance R3 is,

## Applications of Super-position Theorem

- It is applicable for any linear circuit having time-varying or time-invariant elements.
- It is useful in circuit analysis for finding the values of current and voltage in any branch of the circuit, when the circuit has large number of independent sources.

## Limitations of Super-position Theorem

- It is not applicable to the circuits containing of only dependent sources.
- It is not applicable to the circuits consisting of non-linear elements like diode, transistor etc.
- Also not applicable for calculation of power ,as the power is proportional to the square of current or voltage(non-linear).
- It is not applicable to the circuits consisting of less than two independent sources.

## Related Terms:

## For more notes on Electrical Engineering:

- http://notesforengineering.com/
- http://abhinavbhattarai.com.np/2020/09/20/from-maxwells-equations-to-electrical-engineering/

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