Superposition Theorem – Steps and Circuit Analysis with Solved Example

By Basar

Posted on May 31, 2022

The superposition position theorem is based on the linearity. It state that any linear network whose contain more than one source present, the response across any element in the circuit is the algebraic sum of the individual response of source. In this tutorial we are going to discuss the superposition position theorem, solved examples and limitations.

What is Superposition Theorem?

The superposition theorem is use for solve the network where more than one source are present.

Superposition theorem states the following:

“If more than one independent source is present in an electrical circuit, then the current through any one branch of the circuit is the algebraic sum of the individual effect of source at one time.”

In this method, we will consider only independent source at a time. So we have to element the other source from the circuit. We can element the voltage source by short circuiting of two terminals and the current source are eliminated by opening their two terminals.

Important points keep in mind while applying superposition theorems

When you sum the individual contribution of each source, you should be careful while assigning signs to the quantities. The reference direction is use for assign positive and negative sign to each unknown quantity. If contribution source is in same direction as the reference direction, take positive sign. And if it is opposite direction, than take negative sign.
It is only applicable for liner network.
The superposition theorem is not applied for power because the power is not a liner quantity.

How to Apply Superposition Theorem?

Select the one source from the multiple sources present in the bilateral network. And eliminate the remaining independent source present in network.
Except the selected source, all source must be replace by their internal impedance.
Evaluate the current or voltage drop across a particular element in a network.
Upon obtaining the respective response for individual source, and perform the algebraic sum of all individual drop or current in particular branch.

Superposition Theorem Solved Example

Let us understand the superposition theorem with solve example.

Example: Using the superposition theorem find the current flowing through 20 Ω.

superposition-theorem-1

Solution:

Step 1: firstly we consider the 20V and find out the current in circuit. The current source can be open-circuited. The modified circuit is given below.

superposition-theorem-2

Step 2: Using node analysis at V₁.

The nodal equation is:

node-analysis
The current in 20 Ω resistor is:
I₁ = V₁ /10+20
Put V₁ = 12 v in the above equation, we get
I₁ = 0.4 A
Therefore, the currant in 20 ohm resistor is 0.4A.

Step 3: now considering the 4 ampere current in a circuit and eliminate the 20 volt by short circuiting of two terminals. The new circuit is shown below.

superposition-theorem-3

The above circuit diagram, the resistors 5 Ω and 10 Ω are parallel to each other, and this parallel combination are series with 10 Ω resistances. Then the equivalent resistance will be R_AB =40/3

Now, the new circuit is shown as follows:

circuit-analysis

The current in 20 Ω resistor can be determined by current division rule.

I₂ = I_s (R₁ /R₁+R₂)
I₂ = 1.6 A
Therefore the current following through 4A current source is 1.6 A.

Step 4: The algebraic sum of currents I₁ and I₂ will give us the current flowing through the 20 Ω resistor.
Mathematically, this is represented as follows:
I = I₁ + I₂
Put I₁ and I₂ value in the above equation, we get
I = 0.4+1.6 = 2 A
The current flowing through the resistor 20 Ω is 2 A.

Limitations of Superposition Theorem

It is not applicable for non-liner network circuit.
It is not suitable for find out power.
It is only applicable of more than one source.

People also ask

What is the superposition theorem’s formula?

The current in a liner network is equal to the algebraic sum of the current produce by individual source. To evaluate the superposition theorem consider only one source and other source replace all other voltage sources by short circuits and all other current sources by open circuits.

What are the steps of superposition theorems?

The step for solve circuit using superposition theorem;-

Only consider one EMF or current source at a time.
The voltage source, replace it with a short circuit.
The current source, replace it with an open circuit.

Why is superposition theorem used?

The superposition theorem is simple and it is use when two or more the two voltage or current source. It is mainly used to shorten the calculations of the circuit.