The superposition theorem is applied in the resolution of network systems that involve the presence and interconnection of two or more sources. The principle of superposition in electrical engineering asserts that in a linear and bilateral network with multiple sources, the output across any element in the circuit is equal to the summation of the outputs obtained from each source when considered independently.

## What is Superposition Theorem?

The 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 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 does not apply to circuits containing 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.

**References**

- https://onlinelibrary.wiley.com/doi/abs/10.1002/9781119580164.ch23#:~:text=The%20superposition%20theorem%20states%20that,just%20one%20of%20the%20sources.
- https://byjus.com/physics/superposition-theorem/
- https://www.allaboutcircuits.com/textbook/direct-current/chpt-10/superposition-theorem/
- https://circuitglobe.com/what-is-superposition-theorem.html