Current Interruption Transients Calculation, 2nd Edition

Appendix BPrinciple of Duality

In electrical engineering, a dual of a relationship is formed by interchanging voltage and current in an expression. The notion is more complex than that since reciprocal circuit elements also need to be considered. Basic electrical dualities are shown in Table B.1.

A simple example is Ohm's Law where we can write v = Ri and apply the principle of duality to derive i = Gv.

Duality means that the current or voltage in one circuit behaves in a similar manner as the voltage or current respectively, in another circuit. For example, if we apply a DC voltage V to a series RL circuit, then the equation to derive the current i is:

and the solution is

Now take a parallel RC circuit and inject a current I for which the corresponding equation and solution for the common voltage v are:

and

Clearly, by making the duality conversions given in Table B.1, either set of equations can be derived from the other and duality exists between the two cases.

Duality also exists between series and parallel RLC circuits but care needs to be exercised in applying it. Duality ...