Superposition Theorem is one of the electrical network analysis theorem, which helps to solve linear circuit with more than one current or voltage source easily.

In a linear circuit with several sources the voltage and current responses in any branch is the algebraic sum of the voltage and current responses due to each source acting independently with all other sources replaced by their internal impedance.

Suppose an electrical circuit having several branches and or loads and also several source some being current source and some being voltage source. Then Superposition theorem suggests that:

If we find the branch responses (Voltage drop and Current through it) on a branch due to only of those source by ignoring effect of all other sources or replacing all other sources by their corresponding internal impedance , and repeat the process for every source on the circuit. Then the Combined responses (Voltage drop and Current through it) on a branch due to all the sources combined is the algebraic sum of responses on the branches due to each individual sources.

### The process of using Superposition Theorem on a circuit:

To solve a circuit with the help of Superposition theorem follow the following steps:

- First of all make sure the circuit is a linear circuit; or a circuit where Ohm’s law implies, because Superposition theorem is applicable only to linear circuits and responses.
- Replace all the voltage and current sources on the circuit except for one of them.While replacing a Voltage source or Current Source replace it with their internal resistance or impedance. If the Source is an Ideal source or internal impedance is not given then replace a Voltage source with a short ; so as to maintain a 0 V potential difference between two terminals of the voltage source. And replace a Current source with an Open ; so as to maintain a 0 Amps Current between two terminals of the current source.
- Determine the branch responses or voltage drop and current on every branches simply by using KCL , KVL or Ohm’s Law.
- Repeat step 2 and 3 for every source the circuit have.
- Now algebraically add the responses due to each source on a branch to find the response on the branch due to the combined effect of all the sources.

## Superposition Theorem in Action:

In the following circuit:

We can use Superposition Theorem to solves the circuit as following:

Let us first Find Responses on the branches due to the Voltage source:

To Remove the Current source it is opened , which converts the circuit into a simple voltage divider circuit and the responses can be calculated simply by using ohm’s law as following:

Thus The responses due to The voltage source are:

On R1 ; Voltage Drop = 6V , Current = 0.5 Amps

On R2 ; Voltage Drop = 0V , Current = 0 Amps

On R3 ; Voltage Drop = 6V , Current = 0.5 Amps

Now let us find the responses on various branches due to the current source:

To remove the Voltage source it is shorted which converts the circuit into a simple network of parallel and series connection of resistors ; and the responses can be easily calculated using ohm’s law as following:

Thus The responses due to the current source are:

On R1 ; Voltage Drop = 3V , Current = 0.25 Amps

On R2 ; Voltage Drop = 3V , Current = 0.5 Amps

On R3 ; Voltage Drop = 3V , Current = 0.25 Amps

Now finally to find the responses on each branch due to the combined effect of both current source and voltage source we add the individual responses.

So,

On R1 ; Voltage Drop = (6+3)V = 9V , Current = (0.5+0.25) Amps = 0.75 Amps

On R2 ; Voltage Drop = (0+3)V = 3V , Current = (0+0.5) Amps = 0.5 Amps

On R3 ; Voltage Drop = (6+3)V = 9V , Current = (0.5+0.25) Amps = 0.75 Amps