Tellegen’s theorem

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Tellegen’s theorem statement

The Tellenen’s theorem states that the algebraic sum of powers in a network is zero. Where the powers delivered by the active elements are taken as negative and the power consumed at the passive elements is taken as positive or vice versa. Alternatively it can be explained as
the sum of power delivered in all branches of a lumped network is equal to the power absorbed in the network.

i.e Σ V_KI_K=0

where k is the number of elements in the network

Explanation of Tellegen’s theorem

Consider the following circuit having two sources and two resistors.

Circuit for Tellegen's theorem 

Let I₁, I₂, I₃ be the branch currents. Then,
The power delivered by the voltage source is P_V=VI₁
The power delivered by the current source is P_I=V₂I
The power absorbed by the resistor R₁ is P_R1=V₁I₁
The power absorbed by the resistor R₂ is P_R2=V₂I₂

By applying the tellegen’s theorem,
Power delivered= Power absorbed

⇒ P_V+P_I = P_R1+ P_R2

(or)

P_V+P_I-P_R1-P_R2=0

⇒ VI₁+ V₂I -V₁I₁- V₂I₂=0

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Also Read:
Thevenin's theorem
Reciprocity theorem