To construct the dual of a four-mesh network how many nodes are required?

Concept:

Duality:

• Two electrical networks are said to be dual networks if the mesh equations of one network are equal to the node equation of others.
• Identical behavior patterns observed between voltages and currents in two circuits illustrate the principle of duality.
• The dual networks are based on Kirchhoff Current Law and Kirchhoff Voltage Law.

Nodal Analysis:

Nodal analysis is a method of analyzing networks with the help of KCL equations.

For a network of N nodes, the number of simultaneous equations to be solved to get the unknowns

= Number of KCL equations

= N - 1

Mesh Analysis:

Mesh analysis is a method of analyzing networks with the help of KVL equations.

For a network having N nodes and B branches, the number of simultaneous equations to be solved to get the unknowns

= Number of KVL equations

= number of independent loop equations

= B - N + 1

Application:

Given: KVL equations = 4, 

Therefore, B - N + 1 = 4

B = 3 + N ........(1)

For duality of two networks,

Mesh equations of one network = nodal equations of other

Hence,

B - N + 1 = N - 1

\(N =\frac{B \ + \ 2}{2}\ .....(2)\)

substitute (1) in (2)

\(N =\frac{N\ + \ 5}{2}\)

N = 5