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Network Theorem In Electrical Engineering | Superposition Theorem | Electrical Diary

In Electrical Engineering Network theorem plays a very important while solving electronics circuits to find out the response in any branch of the circuit. Network theorems are the equation of mathematics that relate various electrical parameters like Voltage, Current,resistance-capacitance, etc. In this article, We will discuss all the theorem like the Superposition theorem, Tellegen's theorem, Maximum Power Transfer Theorem, Thevenin's theorem, Norton's Theorem, Compensation Theorem.

What is the Superposition theorem?

While Solving a problem in electrical engineering related to electronics circuits. we have seen that more than two emf sources are connected in the circuit. In this case, it becomes more complicated to solve the problem. To make calculation easy we use the superposition theorem.
it states that if a linear network consists of two or more than two sources of emf then the resultant current in any branch of the circuit is the algebraic sum of the current, that would have been produced by each source of emf taken separately with all the other sources of emf being replaced by its internal resistance. if Current Source is Connected in the Circuit Then it is replaced by a Open circuit during calculation.

let's take an example

Find the current flowing in the 9Ω resistor by the superposition theorem of the given circuit.

In the given circuit, two Source is connected one Voltage Source and another Current source.

step -1

While Considering Voltage Source, the branch of the Current source will replace by an open circuit and it will be like this.

Superposition theorem
Then Current Flowing through 9Ω Resistor is 

I1 = 28/(9+5)
I1 = 28/14
I1 = 2 A

Step -2

Now Consider the Current Source by replacing the Voltage Source with its Internal Resistance

By Using Current Division Rule
I2 = 14 {(5/ (5+9)}
I2  = 5A

Then Current Flowing Through 9Ω Resistor is 

I = I1 +I2
I = 2 + 5
I = 7A

What is Tellegen's theorem?

According to Tellegen's theorem, the algebraic sum of instantaneous power across each element in the circuit is zero.

this theorem was proposed by B.D.H Tellegen in 1952. this theorem gives the concept of conservation of energy. In any network, the energy provided by all connected independent power sources is will be consumed by all connected passive elements in the network. i.e

∑(Power Delivered By Active element = ∑(Power Consumed By Passive element

The merit of Tellegen's theorem

  • it is applicable for both linear and non-linear Networks.
  • it is applicable for both time-variant and invariant circuits.
  • it is easy to apply in any circuit.
  • it is similar to Kirchoff's voltage law.

What is the Maximum Power Theorem?

As the name suggests that it is related to maximum power. According to this theorem if the total circuit internal resistance is equal to the resistance of the load then the power source connected in the circuit will provide the maximum power to the load.

The merit of the Maximum Power theorem

  • this theorem is applicable for all types of circuits either it is AC or DC.
  • This theorem is applicable for all types of load whether it is Resistive. inductive or Capacitive load.
  • this theorem is used in a communication network where maximum power is required instead of efficiency

What is Compensation Theorem?

According to the Compensation theorem if there is a voltage drop IZ across an Impedance Z in a Circuit then this impedance may be replaced by a dependent source of equivalent value of EMF of IZ. Similar to it if the Voltage across an element or branch of a network containing an impedance Z is V then this branch or Element may be replaced by an equivalent dependent Current Source of Value I = V/Z

The merit of the Maximum Power theorem

  • During analyzing complex circuits, complex elements or branches can be replaced by Voltage or Current Sources.
  • it is useful to determine the current-voltage change in the circuit when the value of its impedance change.

 What is Thevenin's theorem?

According to this theorem, any linear active bilateral complex network across it load terminal can be replaced by a single voltage source along with a series Connected load.
this theorem was purposed in 1883 by french engineer Leon Thevenin to solve complicated network

Procedure for Applying Thevenin's Theorem

  • First of all, remove the circuit element (load )across which response is desired.
  • By using the maxwell loop or node, the method finds open circuit Voltage Across load and called it Thevenin equivalent Voltage VTH
  • Replace all the independent voltage sources by their internal impedance and open the Circuit across the Current Source. Then find driving point impedance across the is called Thevenin's equivalent Impedance.
  • Now draw a circuit that consists of Thevenin's equivalent Voltage in series with Thevenin's equivalent impedance ZTH
  • Now connect the load in series with Thevenin's equivalent impedance.
Thevenin's theorem

I L = VTH /(ZTH + ZL)

I L = load current flowing through the load

ZL = Load Impedance

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