What is the Superposition theorem?

The superposition theorem is applied to linear systems. For such systems, the output from two different inputs equals the sum of the outputs from each input separately. On applying this theorem many times we get the output from any number of inputs equal to the sum of the outputs from the individual inputs separately.

In electrical circuits this theorem is stated as: the total current/voltage in any part of a bilateral/linear circuit is equal to the algebraic sum of the currents/voltages produced by each source separately.

How to apply the Superposition theorem?

The current source value in any part of the line circuit analysis is equal to the algebraic number of currents generated by each power source separately. The precept of superposition states that the voltage drop throughout an item in a line circuit is an algebraic sum of voltage drop because every independent source as each source operates independently. The precept of superposition helps us to investigate the linear circuit in which there may be multiple independent supplies to calculate the contribution of each independent supply one after the other. But, to use the superposition precept, need to hold two matters in mind:

• Consider one unbiased supply at a time while all other independent supplies grow. This means that each power supply is updated through its internal resistance. For the best case, the voltage source is changed with the aid of 0 V and the current source with the aid of 0 A. This manner obtains a simpler and more attainable circuit.
• Established resources are left intact due to the fact they're managed by circuit variables.

Procedure of applying superposition to a given circuit:

Step 1 - Consider any one voltage or current source first. Replace other sources by their internal resistance. In simple words, replace voltage source by short circuit and current source by open circuit.

Step 2 - Find the current or voltage that is asked to find out in question. Kirchhoff's Current Law or Voltage Law is used in this step.

Step 3 - Consider another source now and replace all other voltage sources by short circuit and current sources by open circuit (similar to step 1)

Step 4 - Again calculate the required voltage or current. Do these 4 steps till you finish considering all the sources in the circuit one by one.

Step 5 - Add the voltage or current which you got in step 2 and step 4. That’s a final answer.

How to make a source inoperative?

In order for the power supply to not work, if it is a voltage source, it is shorted for the first time, leaving its internal ohmic resistance or impedance. Applying superposition theory, add each source effect to the value of the variable to be determined. This means that the superposition theorem analyzes each source in a given circuit separately to determine the value of the variable (whether current or voltage) and produces the resulting variable by adding all the variables resulting from the result of each source. Although it is a complex process, it can still be installed in any line circuit. But if it's a current source, then it's open, leaving its internal resistance.

Limitations

• Only valid for direct calculation of voltage or current, invalid for direct calculation of power.
• This theorem is valid only for linear and bilateral networks.
• In this case, the circuit elements may be time-varying or time-invariant.
• It combines properties of homogeneity and superposition.
• Can only be used in a circuit when more than one active source is present.

Formula of the Superposition theorem

The superposition theorem (or principle or property) applies to linear systems. For such a system, the output from two inputs is equal to the sum of the outputs from each input separately. Applying this theorem multiple times yields the output from any number of inputs is equal to the sum of the outputs from the inputs separately.

Below is a circuit diagram for the superposition theorem.

In any linear network containing more than one source means its bilateral network. By considering each source individually and adding their effects, the current source or voltage source on any branch can be found.

$$\begin{gathered} I=I_A+I_B \\ V=V_A+V_B \end{gathered}$$

Common Mistakes

• The dependent sources are left as they are.
• The superposition theorem is not valid in the case of non-linear circuits.
• The theorem does not apply to power measurement.
• It’s also not applicable for a network containing time-varying resistors.

Context and Applications

• This theorem simplifies the investigation of circuits.
• Two sources which are acting on one circuit, the response from that device can be analyzed by supplying an individual source. This means we are capable of analyzing output by breaking it into individual parts .
• It converts a complex circuit into simpler ones like Norton or Thevenin equivalent circuits.

In each of the expert exams for undergraduate and graduate publications, this topic is huge and is mainly used for

• Bachelor of Technology in Electrical and Electronic Engineering
• Bachelor of Science Physics
• Master of Science Physics

And some other applications are,

• Solving real-life practical problems.
• Signal analysis, network theory (KVL,KCL)
• Control theory determining the response of the system
• Reliability analysis of large-capacity power system
• Solving RLC circuits

Related Concepts

• Thevenin’s theorem
• Norton’s theorem
• Sinusoids and phasor

Practice Problems

Q1- The problem superposition theorem is also called:

1. Norton’s theorem
2. Additivity property
3. Kirchhoff's law
4. Thevenin’s theorem

Correct option: (b)

Explanation: The superposition theorem is also called the additivity property.

Q2- The problem superposition theorem only applies to:

1. Linear circuits
2. Network containing
3. Power calculation
4. All of these

Correct option: (a)

Explanation: The superposition theorem applies to any linear circuit with time-varying or time-varying circuits.

Q3- For which one for superposition theorem does not work?

1. Current
2. Voltage
3. Power
4. Works for all: contemporary, voltage, and power

Correct option: c

Explanation: power for the duration of detail isn't always equal to the electricity throughout it because of all of the different resources within the tool.

Q4- The superposition theorem can be very useful when there are more than one ______ sources.

1. Power
2. Voltage
3. Resistance
4. Capacitance

Correct option: b

Explanation: The superposition theorem can be very useful when the circuit has a large number of the value of voltage sources in any branch of the circuit.

Q5- Superposition theorem cannot be applied when the circuit contains non-linear elements like:

1. Diodes
2. Transistors
3. Both a and b
4. None of these

Correct option: c

Explanation: Can’t be applied superposition theorem, when the circuit contains non-linear elements like diodes, transistors, etc.