Duality And What is Duality of circuits

Duality : two networks are said to be dual of each other when the mesh eq’n s of one are the same as node eq’n s for other.

                       the graph g1 & g2 are said to dual of each other if the incidence matrix of any one of them is a circuit matrix of other .thus dual graphs has same no. Of edges

                                          the dual graphs can be drawn  in case of planar graphs . Only planar networks without mutual inductance have duals.

For mutual inductance there is no dual relationship.

Conversion properties:

Original	dual
R	G= 1/R
L	C
Open ckt	Close ckt
V	I
Voltae source	Current source
Kvl	Kcl
Node	Mesh

Advantage: solution of on ckt automatically gives sloution of another ckt.