Thursday, 9 July 2026

Capacitor - Inductor duality

We must look for a new effect in which, the energy of a capacitor/inductor, instead of 

$$E=\frac{1}{2}CV^2,$$ $$E=\frac{1}{2}LI^2,$$ 

is given by 

$$E \propto \dot{I},$$ $$E \propto \dot{V}.$$

This can only happen with AC currents. 

Associate electric charge to an inductor!

$$\boxed{Q=\frac{\hbar}{LI}}$$ 

Similarly associate magnetic flux to a capacitor

$$\boxed{\Phi=\frac{\hbar}{CV}}$$

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