# Network Theorems

**Superposition Theorem**

If a number of voltage or current sources are acting simultaneously in a linear network, the resultant current in any branch is the algebraic sum of the currents that would be produced in it, when each source acts alone replacing all other independent sources by their internal resistances.

Theveninâ€™s Theorem

Any two terminal bilateral linear d.c. circuit can be replaced by an equivalent circuit consisting of a voltage source and a series resistor.

Current through the branch is given by

**Fig.**

Nortonsâ€™s Theorem

A linear active network consisting of independent or dependant voltage and current sources and linear bilateral network elements can be replaced by an equivalent circuit consisting of a current source in parallel with a resistance, the current source being the short circuited current across the load terminal and the resistance being the internal resistance of the source network looking through the open circuited load terminals.

This theorem is converse of Theveninâ€™s theorem.

Current through the branch of interest is given by,

# Maximum Power Transfer Theorem

A resistance load, being connected to a dc network, receive maximum power when the load resistance is equal to the internal resistance (Theveninâ€™s equivalent resistance) of the source network as seen from the load terminals.

As per maximum power transfer theorem, this R_{Th} is the load resistance of the network i.e., R_{L} = R_{Th} that allows maximum power transfer.

Maximum power transfer is given by : .

Reciprocity Theorem

In any linear network consisting of linear and bilateral impedances and active sources, the ratio of voltage V introduced in one loop to the current I in other loop is same as the ratio obtained if positions of V and I are interchanged in the network.

Telleganâ€™s Theorem

In an arbitrary lumped network, algebraic sum of the instantaneous powers in all the branches, at any instant is zero.

Millmanâ€™s Theorem

When a number of voltage sources (V_{1}, V_{2},..... V* _{n}*) are in parallel having internal resistances (R

_{1}, R

_{2},..... R

*) respectively, the arrangement can be replaced by a single equivalent voltage source V in series with an equivalent series resistance R as given in fig.*

_{n}

**Fig.** (i) **Fig.** (ii)

# Wye (Or Star) Delta Transformation

**Star or Y connection **

**T connection (similar to Yconnection)**

**Delta (Î”) connection **

**Ï€ connection (similar to Î” connection)**

**Delta-to wye or star transformation equations :**

**Wye or Star-to-delta transformation equations :**

* *

* *

* *