The dual network are based on Kirchhoff Current Law and Kirchhoff Voltage Law.
Applying Kirchhoff Voltage Law in the network A, above we get,
Applying Kirchhoff Current Law in the network B, above we get,
Here we have found that equation (i) and (ii) are similar in their mathematical form. Equation (i) is in mesh form and equation (ii) is in nodal form. Here, left side variable of equation (i) is voltage and left side variable of equation (ii) is current. Similarly, right side of equation (i) is product of current and total impedance of the circuit. Similarly, right side of equation (ii) is the product of voltage and admittance of the circuit. So, it is needless to say these two networks are dual network. From, the examples it is also clear that dual network may not be equivalent network. The circuit equation of two dual network are similar in form but the variable are interchanged.
Construction of Dual Network
Let us replace all the variables and constants by their dual in the equation.By doing that, we get,
The electrical network drawn by the circuit equation (iv), would be
It is needless to say
This is nothing but Kirchhoff Current Law. As per definition of dual network, the network C and network D are dual to each other.
Table of Dual Elements
|Service Branch||Parallel Branch|
|Switch Closed||Switch Open|