Electrical Engineering ⇒ Topic : Tellegens Theorem with d.c

Tellegen's Theorem

Tellegen's theorem is valid for any lumped network which may be linear or non linear, passive or active, time-varying or time-invarient. This theorem states that in an arbitrary lumped network, the algebraic sum of the powers in all branches at any instant is zero. All branch currents and voltages in that network must satisfy Kirchhoff's laws. Otherwise, in a given network, the algebraic sum of the powers delivered by all sources is equal to the algebraic sum of the powers absorbed by all elements. This theorem is based on Kirchhoff's two laws, but not on the type of circuit elements.

Consider two networks N₁ and N₂, having the same graph with different types of elements between the corresponding nodes.

To verify Tellegen's theorem, consider two circuits having same graphs as shown in Fig. (1).

In Fig. 1 (a)

In Fig. 1 (b)

                                                                                          figure (1)

This verifies Tellegen's theorem.