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Network Theorems,Example & Formula

In this article you will see in details about network theorems.We had already described mesh current and nodal voltage analysis of circuit problems.The process involves solving the number of equations based on the complexity of the network. Many networks require only restricted analysis. 
  • E.g., finding current with a particular resistor.
  • Finding the value of the load resistance at which the maximum power will be transferred from the source to the load.

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Network Theorem

Some circuit theorems have been developed to solve such problems. For circuit solutions we will use a special theorem or method based on which less time is required in the calculation.Network theorem is based on circuit theorems discussed in this article are as follows
  • Superposition theorem
  • Thevenin’s theorem
  • Norton’s theorem

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Applications of network theorems

One question that have may comes in your mind that where network theorems are used? or what are the applications of network theorem ?

Network theorem applications are as follows 
  • It is used to states and explain Superposition theorem.
  • It is applied to state and explain Millman’s theorem with example.
  • It is used to set up the condition for max power transfer in a multiplex impedance circuit.
  • To solve superposition theorem examples.
  • To used Norton’s theorem and solve examples.

In addition, the circuit simplification citation using the star – delta transformation method has also been discussed with plenty of examples.

1.Superposition Theorem

To understand network theorem you should have proper idea about superposition theorem.An electrical circuit may have more than one source of supply. The supply source can be a voltage source or a current source. In solving circuit problems from multiple sources of supply, the effect of each source is calculated separately and the combined effect of all sources is taken into account. 
This is the essence of the superposition theorem.

The superposition theorem states that "a linear network has more than one source, the current flowing in any branch is the algebraic sum of the currents generated one by one.The source is taken separately, with all other sources replaced by their respective internal resistances. If the internal resistance of a source is not provided, voltage sources will be less operational and current sources will be open circulated"

Superposition theorem examples

The example of superposition theorem is shown in the diagram given below.We will consider each source separately and calculate the current flowing through the BD branch. The 24 V source is taken by shortening the 12 V source as shown in the given diagram.

Superposition theorem examples

Superposition theorem formula

Given formula is used to calculate question related to superposition are given below :
  • Formula used to calculate current flowing from the battery is current flowing from the battery.
  • The current division rule is also used  usedcurrent division rule

Thevenin’s Theorem

The application of this Thevenin's theorem is often useful when we want to determine the current flowing through any branch or component of a network. 
We can easily determine the current through any component when it is necessary that the component be replaced. It takes time to use kirchchoff 's laws to calculate the branch current for the changed value of a resistor because we have to repeat the calculations.

The steps involved in applying Thevenin's theorem in calculating current in circuit components are as follows:
1. Remove the resistance from the circuit terminals through which the current will be determined.

2.Determine the open-circuit voltage that will appear in the circuit terminals, where the resistance is removed.

3.Calculate the equivalent resistance across the entire circuit across the terminals after the EMF sources have been replaced by their internal resistors (or only by short-circuiting if the internal resistance is not provided or not known) and keeping current sources open ( I,e considering having infinite resistance).

4.Calculate the current through R using the following relation 
                                                                          Thevenin’s Theorem Formula

Norton’s Theorem

We have seen earlier that in applying the Norton's theorem, a network is converted into a voltage source and an equal series resistance connected to the two terminals of any resistance through which the current is to be calculated.
By applying Norton's theorem, a network transforms into a constant current source and a parallel resistance across the terminals of resistance through which the current is to be calculated. Norton's theorem is as follows:

Norton's theorem states that " Any two-terminal network consisting of voltage sources and resistors can be converted to a constant current source and a parallel resistance. The magnitude of the constant current is equal.If the two terminals are less operational and it is a parallel current, the equivalent resistance of the entire network will be seen from the open transmission terminals after all voltage and current sources have been replaced by their internal resistors."

Conclusion

This Information about Network Theorem is provided to you for to guide you and create awareness about use,definition,formula,example and other information information related to this topic.If you have any question you can ask to us by commenting on below section.


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