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The superposition theorem states that there is a response across any element in the circuit where one or more sources are present in any bilateral or linear network. The response is equal to the sum of all the responses that have been recorded from each source. The superposition theorem is beneficial in solving the network where two or more networks are connected. The superposition principle and Coulomb's law are responsible for electrostatics.
- It is used to convert any circuit into its Norton or Thevenin equivalent.
- The superposition theorem can be applied to linear networks.
- It is also used when the circuit includes two or more sources.
- To shorten the calculations of the circuit, this theorem is used.
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Key terms: superposition theorem, circuit, voltage, current, bilateral network, sources, application
Read More: Unit of Voltage
What is Superposition Theorem?
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The solution of a network that consists of two or more connected sources is done by the superposition theorem. This is also known as the circuit analysis theorem. In order to calculate each contribution of every source in the circuit, the final result should not be disturbed while removing or replacing the other sources.
- The final result will remain intact by using a short circuit in place of the voltage source.
- The value of the voltage source is set to zero while removing it.
- The value of the current source is set to infinite while removing it which is done by using an open circuit in the place of the current source.
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Application of Superposition Theorem
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The applications of the superposition theorem are as follows:
- From the bilateral network, choose the appropriate source from the many sources available. One can pick any one source first from the various options.
- The rest of the sources other than the ones which have been chosen should be modified by their internal blockage.
- The flow of the current or the reduction in the voltage across a particular element in the network should be calculated by the network simplification approach.
- The same process is applied to all the other sources in the network
- When all the individual responses are recorded from each source, all the responses should be added to get the value of the total reduction of current or voltage through the circuit element.
Limitations of Superposition Theorem
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The superposition theorem also has certain limitations -
- The circuits which are not linear are not taken into consideration by this theorem. The necessity of linearity presents that the superposition theorem is used to calculate only current or voltage. Loss of power is a nonlinear function that is not calculated by the theorem.
- Two or more sources in the circuit are required to calculate the superposition theorem.
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| Capacitive Reactance Formula | Transformer Formula | Power in AC Circuit |
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Things to Remember
- Superposition theorem is an essential concept in electrical engineering, which states that in a linear circuit with multiple sources, the total response is the sum of the responses due to each individual source acting alone.
- This theorem is particularly useful in circuit analysis, as it allows us to calculate the behavior of a complex circuit by analyzing the effects of each source separately and then combining them.
- To apply the superposition theorem, all sources except one are turned off, and the resulting circuit is analyzed to determine the response due to that source. This process is repeated for each source.
- It is important to note that the superposition theorem only applies to linear circuits. In non-linear circuits, the response due to each source cannot be simply added together.
- The superposition theorem can also be used to analyze circuits with dependent sources, such as transistors or operational amplifiers.
- Overall, the superposition theorem is a powerful tool for simplifying complex circuits and for understanding the behavior of linear circuits with multiple sources.
Sample Questions
Ques. Can we apply the superposition theorem on an AC circuit? (3 marks)
Ans: The superposition theorem states that the total response that we get from each source individually is equivalent to the response of any element in a linear network or a network of more than one direction with multiple sources.
While applying the superposition theorem to the AC circuit, the highest value of each source's contribution or the complex affective is to be calculated individually first .this should be followed by summing up the results. Thus, the superposition theorem can be applied to AC circuits as any linear circuit can be used to demonstrate the theorem.
Ques. What are the advantages of the superposition theorem? (3 marks)
Ans: the advantages of the superposition theorem are:
- It calculates the aggregate current in the circuit
- This theorem can convert any circuit into Thevenin equivalent
- It assists in the application of network sources elements
Ques. What are the steps to be followed while calculating circuits using the superposition theorem? (3 marks)
Ans: The steps that should be followed are:
- Select the load resistor in the given problem
- Assuming that a single source is effective in the circuit, open the current sources if there are any.
- The single source initiates the flow of current through the load resistor which needs to be calculated
- Repeat the previous two steps for the rest of the sources in the circuit
- By summing up the flow of current in each source, the total current flow through the load resistor is to be calculated.
Ques. Using the superposition theorem, calculate the voltage across through a 15Ω resistor. (5 marks)
Ans: Let the voltage across 15Ω resistor = V1, V2, V3, V4.
The different sources = 20v, 10v, 10A, 5A
Resultant voltage V4 = V1 + V2+ V3+ V4
- V1 =
By considering the 20v source separately, the voltage source is short-circuited and the other two sources are open-circuited.
By applying Kirchhoff's voltage law (KVL), the current flowing through a 15Ω resistor is :
I1 = 2015+40 = 0.363A
The voltage through the 15Ω resistor is :
V1 = I1 x R
= 0.363 x 15 = 5.445 V
- V2 =
By applying KVL, the current flow is,
I2 = 1015+40 = 0.182A
Voltage,
V2 = I2 x R = 0.363 x 15 = 2.73V
- V3 =
Here, we will use the current division rule as 40Ω and 15Ω resistors are parallel to each other. The current flow is,
I3 = 10 x 4015+40 = 7.27A
Voltage (V3) = I3 x R
= 7.27 x 15
= 109. 05V
- V4 =
Very less amount of current flow is detected through a 15Ω resistor because the circuit has a low resistance path. Hence, the current flow is,
I4 = 0
Voltage (V4) = 0
Thus, by applying the superposition theorem,
The total voltage (VT) = V1 + V2 + V3 + V4
= 5.445 +2.73 -109.05+ 0
= -100.875V
Ques. What is the superposition principle? (2 marks)
Ans: In space, when two or more waves of similar features collide at a point, the resulting displacement at the point is equal to the vector sum of the displacements that each of the two waves would produce at that point.
Ques. What are the suitable conditions for the application of the superposition theorem? (4 marks)
Ans: The conditions for the application of the superposition theorem are:
- Non-linear active components such as semiconductor diodes and transistors cannot be used
- Components such as capacitors, resistors, and inductors must be used because they do not rectify or amplify the circuits
- All bilateral components are used in the circuits
- Only linear components should be used where the current flow must be directly proportional to the voltage
- The theorem initiated the use of Ohm's law in complex circuits.
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