Capacitor-inductor duality

This is actually quite encouraging, as it seems we have, after all, heard of the duality principle. In simple terms this principle says that a capacitor can be considered as an inverse (or mirror ) of an inductor, because the voltage-current equations of the two devices can be transformed into one another by exchanging the voltage and current terms. So, in essence, capacitors are analogous to inductors, and voltage to current. 

With the duality principle in mind, let us attempt to open the switch in the inductor circuit and try to predict the outcome. What happens No Unfortunately, things don t remain almost unchanged as they did for a capacitor. In fact, the behavior of the inductor during the off-phase is really no replica of the off-phase of the capacitor circuit. 

The principle of duality concerns the transformation between two apparently different circuits, which have similar properties when current and voltage are interchanged. Duality transformations are applicable to planar circuits only, and involve a topological conversion capacitor and inductor interchange, resistance and conductance interchange, and voltage source and current source interchange. 

To analyze what happens in Figure 1-6 we must first learn the capacitor equation — analogous to the inductor equation derived previously. If the duality principle is correct,... 

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